When a thin layer of oil lies on top of water or wet

(I) Monochromatic light falling on two slits 0.018 mm apart produces the fifth-order bright fringe at an 8.6° angle. What is the wavelength of the light used?

(I) The third-order bright fringe of 610-nm light is observed at an angle of 31° when the light falls on two narrow slits. How far apart are the slits?

Monochromatic light falls on two very narrow slits 0.048 mm apart. Successive fringes on a screen 6.50 m away are 8.5 cm apart near the center of the pattern. Determine the wavelength and frequency of the light.

If 720-nm and 660-nm light passes through two slits 0.62 mm apart, how far apart are the second- order fringes for these two wavelengths on a screen 1.0 m away?

Water waves having parallel crests 4.5 cm apart pass through two openings 7.5 cm apart in a board. At a point 3.0 m beyond the board, at what angle relative to the straight-through direction would there be little or no wave action?

A red laser from the physics lab is marked as producing 632.8-nm light. When light from this laser falls on two closely spaced slits, an interference pattern formed on a wall several meters away has bright red fringes spaced 5.00 mm apart near the center of the pattern. When the laser is replaced by a small laser pointer, the fringes are 5.14 mm apart. What is the wavelength of light produced by the laser pointer?

Light of wavelength 680 nm falls on two slits and produces an interference pattern in which the third- order bright red fringe is 38 mm from the central fringe on a screen 2.8 m away. What is the separation of the two slits?

(II) Light of wavelength \(\lambda\) passes through a pair of slits separated by 0.17 mm, forming a double-slit interference pattern on a screen located a distance 37 cm away. Suppose that the image in Fig. 24-9a is an actual-size reproduction of this interference pattern. Use a ruler to measure a pertinent distance on this image; then utilize this measured value to determine \(\lambda(\mathrm{nm})\). Equation Transcription: Text Transcription: lambda lambda (nm)

A parallel beam of light from a HeNe laser, with a wavelength 633 nm, falls on two very narrow slits 0.068 mm apart. How far apart are the fringes in the center of the pattern on a screen 3.3 m away?

(II) A physics professor wants to perform a lecture demonstration of Young's double-slit experiment for her class using the 633-nm light from a He-Ne laser. Because the lecture hall is very large, the interference pattern will be projected on a wall that is 5.0 m from the slits. For easy viewing by all students in the class, the professor wants the distance between the \(m=0\) and \(m=1\) maxima to be 35 cm. What slit separation is required in order to produce the desired interference pattern? Equation Transcription: Text Transcription: m=0 m=1

(II) Suppose a thin piece of glass is placed in front of the lower slit in Fig. 24–7 so that the two waves enter the slits \(180^{\circ}\) out of phase (Fig.24–58). Draw in detail the interference pattern seen on the screen.

In a double-slit experiment it is found that blue light of wavelength 480 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a minimum at the same location?

(II) Two narrow slits separated by 1.0 mm are illuminated by 544-nm light. Find the distance between adjacent bright fringes on a screen 4.0 m from the slits.

(II) Assume that light of a single color, rather than white light, passes through the two-slit setup described in Example 24–3. If the distance from the central fringe to a first-order fringe is measured to be 2.9 mm on the screen, determine the light’s wavelength (in nm) and color (see Fig. 24–12).

In a double-slit experiment, the third-order maximum for light of wavelength 480 nm is located 16 mm from the central bright spot on a screen 1.6 m from the slits. Light of wavelength 650 nm is then projected through the same slits. How far from the central bright spot will the secondorder maximum of this light be located?

(II) Light of wavelength 470 nm in air shines on two slits \(6.00 \times 10^{-2} \mathrm{~mm}\) apart. The slits are immersed in water, as is a viewing screen 40.0 cm away. How far apart are the fringes on the screen? Equation Transcription: Text Transcription: 6.00 times 10^-2 mm

(III) A very thin sheet of plastic \((n=1.60)\) covers one slit of a double-slit apparatus illuminated by 680-nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic? Equation Transcription: Text Transcription: (n=1.60)

(I) By what percent is the speed of blue light (450 nm) less than the speed of red light (680 nm), in silicate flint glass (see Fig. 24-14)?

(II) A light beam strikes a piece of glass at a 65.00° incident angle. The beam contains two wavelengths, 450.0 nm and 700.0 nm, for which the index of refraction of the glass is 1.4831 and 1.4754, respectively. What is the angle between the two refracted beams?

(III) A parallel beam of light containing two wavelengths, \(\lambda_{1}=455 \mathrm{~nm}\) and \(\lambda_{2}=642 \mathrm{~nm}\), enters the silicate flint glass of an equilateral prism as shown in Fig. 24-59. At what angles, \(\theta_{1}\) and \(\theta_{2}\), does each beam leave the prism (give angle with normal to the face)? See Fig. 24-14. Equation Transcription: Text Transcription: lambda_1=455 nm lambda_2=642 nm theta_1 theta_2

If 680-nm light falls on a slit 0.0425 mm wide, what is the angular width of the central diffraction peak?

(I) Monochromatic light falls on a slit that is \(2.60 \times 10^{-3} \mathrm{~mm}\) wide. If the angle between the first dark fringes on either side of the central maximum is \(28.0^{\circ}\) (dark fringe to dark fringe), what is the wavelength of the light used? Equation Transcription: Text Transcription: 2.60 times 10^-3 mm 28^circ

(II) When blue light of wavelength 440 nm falls on a single slit, the first dark bands on either side of center are separated by \(51.0^{\circ} .\) Determine the width of the slit. Equation Transcription: Text Transcription: 51.0^circ

A single slit 1.0 mm wide is illuminated by 450-nm light. What is the width of the central maximum (in cm) in the diffraction pattern on a screen 6.0 m away?

(II) How wide is the central diffraction peak on a screen 2.30m behind a 0.0348-mm-wide slit illuminated by 558-nm light?

Consider microwaves which are incident perpendicular to a metal plate which has a 1.6-cm slit in it. Discuss the angles at which there are diffraction minima for wavelengths of (a) 0.50 cm, (b) 1.0 cm, and (c) 3.0 cm.

(II) (a) For a given wavelength \(\lambda\), what is the minimum slit width for which there will be no diffraction minima? (b) What is the minimum slit width so that no visible light exhibits a diffraction minimum? Equation Transcription: Text Transcription: lambda

(II) Light of wavelength 620 nm falls on a slit that is \(3.80 \times 10^{-3} \mathrm{~mm}\) wide. Estimate how far the first bright diffraction fringe is from the strong central maximum if the screen is 10.0 m away. Equation Transcription: Text Transcription: 3.80 times 10^-3 mm

(II) Monochromatic light of wavelength 633 nm falls on a slit. If the angle between the first two bright fringes on either side of the central maximum is \(32^{\circ}\), estimate the slit width. Equation Transcription: Text Transcription: 32^circ

(II) Coherent light from a laser diode is emitted through a rectangular area \(3.0 \mu \mathrm{m} \times 1.5 \mu \mathrm{m}\) (horizontal-by vertical). If the laser light has a wavelength of 780 nm, determine the angle between the first diffraction minima (a) above and below the central maximum, (b) to the left and right of the central maximum. Equation Transcription: Text Transcription: 3.0 mu m times 1.5 mu m

(III) If parallel light falls on a single slit of width \(D\) at a \(28.0^{\circ}\) angle to the normal, describe the diffraction pattern. Equation Transcription: Text Transcription: D 28.0^circ

(I) At what angle will 510-nm light produce a second-order maximum when falling on a grating whose slits are \(1.35 \times 10^{-3} \mathrm{~cm}\) apart? Equation Transcription: Text Transcription: 1.35 times 10^-3 cm

(I) A grating that has 3800 slits per cm produces a third-order fringe at a \(22.0^{\circ}\) angle. What wavelength of light is being used? Equation Transcription: Text Transcription: 22.0^circ

(I) A grating has 7400 slits/cm. How many spectral orders can be seen ( 400 to 700 nm ) when it is illuminated by white light?

(II) Red laser light from a He-Ne laser \((\lambda=632.8 \mathrm{~nm})\) creates a second-order fringe at \(53.2^{\circ}\) after passing through the grating. What is the wavelength \(\lambda\) of light that creates a first-order fringe at \(20.6^{\circ}\) ? Equation Transcription: Text Transcription: (lambda=632.8 nm) 53.2^circ lambda 20.6^circ

(II) How many slits per centimeter does a grating have if the third order occurs at a \(15.0^{\circ}\) angle for 620-nm light? Equation Transcription: Text Transcription: 15.0^circ

(II) A source produces first-order lines when incident normally on a 9800-slit/cm diffraction grating at angles \(28.8^{\circ}, 36.7^{\circ}, 38.6^{\circ}\), and \(41.2^{\circ} .\) What are the wavelengths? Equation Transcription: Text Transcription: 28.8^circ,36.7^circ,38.6^circ, 41.2^circ

(II) White light containing wavelengths from 410 nm to 750 nm falls on a grating with 7800 slits/cm. How wide is the first-order spectrum on a screen 3.40 m way?

(II) A diffraction grating has \(6.5 \times 10^5 \ \mathrm {slits/m}\) Find the angular spread in the second-order spectrum between red light of wavelength \(7.0 \times 10^{-7} \ \mathrm m\) and blue light of wavelength \(4.5 \times 10^{-7} \ \mathrm m\).

(II) Two first-order spectrum lines are measured by a \(9650-\mathrm{slit} / \mathrm{cm}\) spectroscope at angles, on each side of center, of \(+26^{\circ} 38^{\prime},+41^{\circ} 02^{\prime}\) and \(-26^{\circ} 18^{\prime},-40^{\circ} 27^{\prime} .\) Calculate the wavelengths based on these data. Equation Transcription: Text Transcription: 9650-slit/cm 26^circ 38',+41^circ 02' -26 ^circ 18',-40^circ 27'

What is the highest spectral order that can be seen if a grating with 6500 slits per cm is illuminated with 633-nm laser light? Assume normal incidence.

(II) The first-order line of 589-nm light falling on a diffraction grating is observed at a \(14.5^{\circ}\) angle. How far apart are the slits? At what angle will the third order be observed? Equation Transcription: Text Transcription: 14.5^circ

Two (and only two) full spectral orders can be seen on either side of the central maximum when white light is sent through a diffraction grating. What is the maximum number of slits per cm for the grating?

(I) If a soap bubble is 120 nm thick, what wavelength is most strongly reflected at the center of the outer surface when illuminated normally by white light? Assume that n = 1.32.

How far apart are the dark bands in Example 2410 if the glass plates are each 21.5 cm long?

(II) (a) What is the smallest thickness of a soap film \((n=1.33)\) that would appear black if illuminated with 480-nm light? Assume there is air on both sides of the soap film. (b) What are two other possible thicknesses for the film to appear black? (c) If the thickness \(t\) was much less than \(\lambda\), why would the film also appear black? Equation Transcription: Text Transcription: (n=1.33) t lambda

(II) A lens appears greenish yellow \((\lambda=570 \mathrm{~nm}\) is strongest) when white light reflects from it. What minimum thickness of coating ( \(n=1.25\) ) do you think is used on such a glass lens \((n=1.52)\), and why? Equation Transcription: Text Transcription: lambda=570 nm (n=1.25) (n=1.52)

(II) A thin film of oil \(\left(n_{\mathrm{o}}=1.50\right)\) with varying thickness floats on water \(\left(n_{\mathrm{w}}=1.33\right)\). When it is illuminated from above by white light, the reflected colors are as shown in Fig. 24-60. In air, the wavelength of yellow light is 580 nm. (a) Why are there no reflected colors at point A? (b) What is the oil's thickness \(t\) at point B? Equation Transcription: Text Transcription: (n_o=1.50) (n_W=1.33) t

How many uncoated thin lenses in an optical instrument would reduce the amount of light passing through the instrument to 50% or less? (Assume the same transmission percent at each of the two surfacessee page 697.)

A total of 35 bright and 35 dark Newtons rings (not counting the dark spot at the center) are observed when 560-nm light falls normally on a planoconvex lens resting on a flat glass surface (Fig. 2431). How much thicker is the lens at the center than the edges?

(II) If the wedge between the glass plates of Example 24-10 is filled with some transparent substance other than airsay, water-the pattern shifts because the wavelength of the light changes. In a material where the index of refraction is \(n\), the wavelength is \(\lambda_{n}=\lambda / n\), where \(\lambda\) is the wavelength in vacuum (Eq. 24-1). How many dark bands would there be if the wedge of Example 24-10 were filled with water? Equation Transcription: Text Transcription: n lambda_n=lambda_/n lambda

(II) A fine metal foil separates one end of two pieces of optically flat glass, as in Fig. 24-33. When light of wavelength 670 nm is incident normally, 24 dark bands are observed (with one at each end). How thick is the foil?

How thick (minimum) should the air layer be between two flat glass surfaces if the glass is to appear bright when 450-nm light is incident normally? What if the glass is to appear dark?

(III) A thin oil slick \(\left(n_{\mathrm{o}}=1.50\right)\) floats on water \(\left(n_{\mathrm{w}}=1.33\right)\). When a beam of white light strikes this film at normal incidence from air, the only enhanced reflected colors are red (650 nm) and violet (390 nm). From this information, deduce the (minimum) thickness \(t\) of the oil slick. Equation Transcription: Text Transcription: (n_o=1.50) (n_w=1.33) t

(III) A uniform thin film of alcohol ( \(n=1.36\) ) lies on a flat glass plate \((n=1.56)\). When monochromatic light, whose wavelength can be changed, is incident normally, the reflected light is a minimum for \(\lambda=525 \mathrm{~nm}\) and a maximum for \(\lambda=655 \mathrm{~nm}\). What is the minimum thickness of the film? Equation Transcription: Text Transcription: n=1.36 (n=1.56) lambda=525 nm lambda=655 nm

(II) How far must the mirror \(\mathrm{M}_{1}\) in a Michelson interferometer be moved if 680 fringes of 589-nm light are to pass by a reference line? Equation Transcription: Text Transcription: M_1

What is the wavelength of the light entering an interferometer if 362 bright fringes are counted when the movable mirror moves 0.125 mm?

A micrometer is connected to the movable mirror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net number of bright fringes that move, compared to closing the empty micrometer, is 296. What is the thickness of the foil? The wavelength of light used is 589 nm

(III) One of the beams of an interferometer (Fig. 24-61) passes through a small evacuated glass container 1.155 cm deep. When a gas is allowed to slowly fill the container, a total of 158 dark fringes are counted to move past a reference line. The light used has a wavelength of 632.8 nm. Calculate the index of refraction of the gas at its final density, assuming that the interferometer is in vacuum.

(I) Two polarizers are oriented at \(72^{\circ}\) to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted? Equation Transcription: Text Transcription: 72^circ

(I) What is Brewster's angle for an air-glass \((n=1.56)\) surface? Equation Transcription: Text Transcription: (n=1.56)

(II) At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light to \((a) \frac{1}{3},(b) \frac{1}{10}\) ? Equation Transcription: Text Transcription: (a)1/3,(b)1/10

(II) Two polarizers are oriented at \(42.0^{\circ}\) to one another. Light polarized at a \(21.0^{\circ}\) angle to each polarizer passes through both. What is the transmitted intensity (%)? Equation Transcription: Text Transcription: 42.0^circ 21.0^circ

(II) Three perfectly polarizing sheets are spaced 2 cm apart and in parallel planes. The transmission axis of the second sheet is \(30^{\circ}\) relative to the first one. The transmission axis of the third sheet is \(90^{\circ}\) relative to the first one. Unpolarized light impinges on the first polarizing sheet. What percent of this light is transmitted out through the third polarizer? Equation Transcription: Text Transcription: 30^circ 90^circ

(II) A piece of material, suspected of being a stolen diamond \((n=2.42)\), is submerged in oil of refractive index 1.43 and illuminated by unpolarized light. It is found that the reflected light is completely polarized at an angle of \(62^{\circ}\). Is it diamond? Explain. Equation Transcription: Text Transcription: (n=2.42) 62^circ

Two Polaroids are aligned so that the initially unpolarized light passing through them is a maximum. At what angle should one of them be placed so the transmitted intensity is subsequently reduced by half?

(II) What is Brewster’s angle for a diamond submerged in water?

(II) The critical angle for total internal reflection at a boundary between two materials is \(58^{\circ}\). What is Brewster's angle at this boundary? Give two answers, one for each material. Equation Transcription: Text Transcription: 58^circ

What would Brewsters angle be for reflections off the surface of water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewsters angle from above the surface.

(II) Unpolarized light of intensity \(I_{0}\) passes through six successive Polaroid sheets each of whose axis makes a \(35^{\circ}\) angle with the previous one. What is the intensity of the transmitted beam? Equation Transcription: Text Transcription: I_0 35^circ

(III) Two polarizers are oriented at \(48^{\circ}\) to each other and plane-polarized light is incident on them. If only 35% of the light gets through both of them, what was the initial polarization direction of the incident light? Equation Transcription: Text Transcription: 48^circ

(III) Four polarizers are placed in succession with their axes vertical, at \(30.0^{\circ}\) to the vertical, at \(60.0^{\circ}\) to the vertical, and at \(90.0^{\circ}\) to the vertical. (a) Calculate what fraction of the incident unpolarized light is transmitted by the four polarizers. (b) Can the transmitted light be decreased by removing one of the polarizers? If so, which one? (c) Can the transmitted light intensity be extinguished by removing polarizers? If so, which one(s)? Equation Transcription: Text Transcription: 30.0^circ 60.0^circ 90.0^circ

Light of wavelength \(5.0 \times 10^{-7} \mathrm{~m}\) passes through two parallel slits and falls on a screen 5.0 m away. Adjacent bright bands of the interference pattern are 2.0 cm apart. (a) Find the distance between the slits. (b) The same two slits are next illuminated by light of a different wavelength, and the fifth-order minimum for this light occurs at the same point on the screen as the fourth-order minimum for the previous light. What is the wavelength of the second source of light? Equation Transcription: Text Transcription: 5.0 times 10^-7 m

Television and radio waves reflecting from mountains or airplanes can interfere with the direct signal from the station. (a) What kind of interference will occur when 75-MHz television signals arrive at a receiver directly from a distant station, and are reflected from a nearby airplane 122 m directly above the receiver? Assume \(\frac{1}{2} \lambda\) change in phase of the signal upon reflection. (b) What kind of interference will occur if the plane is 22 m closer to the receiver? Equation Transcription: Text Transcription: 1/2lambda

Red light from three separate sources passes through a diffraction grating with \(3.60 \times 10^{5}\) slits/m. The wavelengths of the three lines are \(6.56 \times 10^{-7} \mathrm{~m}\) (hydrogen), \(6.50 \times 10^{-7} \mathrm{~m}\) (neon), and \(6.97 \times 10^{-7} \mathrm{~m}\) (argon). Calculate the angles for the first-order diffraction line of each source. Equation Transcription: Text Transcription: 3.60 times 10^5 6.56 times 10^-7 m 6.50 times 10^-7 m 6.97 times 10^-7 m

What is the index of refraction of a clear material if a minimum thickness of 125 nm, when laid on glass, is needed to reduce reflection to nearly zero when light of 675 nm is incident normally upon it? Do you have a choice for an answer?

Light of wavelength 650 nm passes through two narrow slits 0.66 mm apart. The screen is 2.40 m away. A second source of unknown wavelength produces its second-order fringe 1.23 mm closer to the central maximum than the 650-nm light. What is the wavelength of the unknown light?

Monochromatic light of variable wavelength is incident normally on a thin sheet of plastic film in air. The reflected light is a maximum only for \(\lambda=491.4 \mathrm{~nm}\) and \(\lambda=688.0 \mathrm{~nm}\) in the visible spectrum. What is the thickness of the film \((n=1.58) ?\) [Hint: Assume successive values of \(m\) .] Equation Transcription: Text Transcription: lambda=491.4 nm lambda=688.0 nm (n=1.58) m

Show that the second- and third-order spectra of white light produced by a diffraction grating always overlap. What wavelengths overlap?

A radio station operating at 90.3 MHz broadcasts from two identical antennas at the same elevation but separated by a 9.0-m horizontal distance \(d\), Fig. 24-62. A maximum signal is found along the midline, perpendicular to \(d\) at its midpoint and extending horizontally in both directions. If the midline is taken as \(0^{\circ}\), at what other angle(s) \(\theta\) is a maximum signal detected? A minimum signal? Assume all measurements are made much farther than 9.0 m from the antenna towers. Equation Transcription: Text Transcription: d d 0^circ theta

Calculate the minimum thickness needed for an antireflective coating \((n=1.38)\) applied to a glass lens in order to eliminate (a) blue (450 nm), or (b) red (720nm) reflections for light at normal incidence. Equation Transcription: Text Transcription: (n=1.38)

Stealth aircraft are designed to not reflect radar, whose wavelength is typically 2 cm, by using an antireflecting coating. Ignoring any change in wavelength in the coating, estimate its thickness

A laser beam passes through a slit of width 1.0 cm and is pointed at the Moon, which is approximately 380,000 km from the Earth. Assume the laser emits waves of wavelength 633 nm (the red light of a HeNe laser). Estimate the width of the beam when it reaches the Moon due to diffraction.

A thin film of soap coats a piece of flat glass How thick is the film if it reflects 643-nm red light most strongly when illuminated normally by white light

When violet light of wavelength 415 nm falls on a single slit, it creates a central diffraction peak that is 8.20 cm wide on a screen that is 3.15 m away. How wide is the slit?

A series of polarizers are each rotated \(10^{\circ}\) from the previous polarizer. Unpolarized light is incident on this series of polarizers. How many polarizers does the light have to go through before it is \(\frac{1}{5}\) of its original intensity? Equation Transcription: Text Transcription: 10^circ 1/5

The wings of a certain beetle have a series of parallel lines across them. When normally incident 480-nm light is reflected from the wing, the wing appears bright when viewed at an angle of \(56^{\circ}\). How far apart are the lines? Equation Transcription: Text Transcription: 56^circ

A teacher stands well back from an outside doorway 0.88 m wide, and blows a whistle of frequency 950 Hz. Ignoring reflections, estimate at what angle(s) it is not possible to hear the whistle clearly on the playground outside the doorway. Assume 340 m/s for the speed of sound.

Light is incident on a diffraction grating with 7200 slits/cm and the pattern is viewed on a screen located 2.5 m from the grating. The incident light beam consists of two wavelengths, \(\lambda_{1}=4.4 \times 10^{-7} \mathrm{~m}\) and \(\lambda_{2}=6.8 \times 10^{-7} \mathrm{~m}\). Calculate the linear distance between the first-order bright fringes of these two wavelengths on the screen. Equation Transcription: Text Transcription: lambda_1=4.4 times 10^-7 m lambda_2=6.8 times 10^-7 m

How many slits per centimeter must a grating have if there is to be no second-order spectrum for any visible wavelength?

When yellow sodium light, \(\lambda=589 \mathrm{~nm}\), falls on a diffraction grating, its first-order peak on a screen 72.0 cm away falls 3.32 cm from the central peak. Another source produces a line 3.71 cm from the central peak. What is its wavelength? How many slits/cm are on the grating? Equation Transcription: Text Transcription: lambda=589 nm

Two of the lines of the atomic hydrogen spectrum have wavelengths of 656 nm and 410 nm. If these fall at normal incidence on a grating with 7700 slits/cm what will be the angular separation of the two wavelengths in the first-order spectrum?

A tungsten-halogen bulb emits a continuous spectrum of ultraviolet, visible, and infrared light in the wavelength range 360 nm to 2000 nm. Assume that the light from a tungsten-halogen bulb is incident on a diffraction grating with slit spacing \(d\) and that the first-order brightness maximum for the wavelength of 1200 nm occurs at angle \(\theta\). What other wavelengths within the spectrum of incident light will produce a brightness maximum at this same angle \(\theta\)? [Optical filters are used to deal with this bothersome effect when a continuous spectrum of light is measured by a spectrometer.] Equation Transcription: Text Transcription: d theta theta

At what angle above the horizon is the Sun when light reflecting off a smooth lake is polarized most strongly?

Unpolarized light falls on two polarizer sheets whose axes are at right angles. (a) What fraction of the incident light intensity is transmitted? (b) What fraction is transmitted if a third polarizer is placed between the first two so that its axis makes a \(56^{\circ}\) angle with the axis of the first polarizer? (c) What if the third polarizer is in front of the other two? Equation Transcription: Text Transcription: 56^circ

At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the first Polaroid cuts it in half) of (a) 4, (b) 10, (c) 100?

Problem 1COQ When a thin layer of oil lies on top of water or wet pavement, you can often see swirls of color. We also see swirls of color on the soap bubble shown above. What causes these colors? (a) Additives in the oil or soap reflect various colors. (b) Chemicals in the oil or soap absorb various colors. (c) Dispersion due to differences in index of refraction in the oil or soap. (d) The interactions of the light with a thin boundary layer where the oil (or soap) and the water have mixed irregularly. (e) Light waves reflected from the top and bottom surfaces of the thin oil or soap film can add up constructively for particular wavelengths.

Problem 1MCQ Light passing through a double-slit arrangement is viewed on a distant screen. The interference pattern observed on the screen would have the widest spaced fringes for the case of (a) red light and a small slit spacing. (b) blue light and a small slit spacing. (c) red light and a large slit spacing. (d) blue light and a large slit spacing.

Problem 1P (I) Monochromatic light falling on two slits 0.018 mm apart produces the fifth-order bright fringe at an 8.6° angle. What is the wavelength of the light used?

Problem 1Q Does Huygens’ principle apply to sound waves? To water waves? Explain how Huygens’ principle makes sense for water waves, where each point vibrates up and down.

Problem 1SL Compare Figs. 24–5, 24–6, and 24–7, which are different representations of the double-slit experiment. For each figure state the direction the light is traveling. Where are the wave crests in terms of this direction? How are they represented in each figure? Give one advantage of each figure in helping you understand the double-slit experiment and interference.

Light from a green laser of wavelength \(530 \mathrm{~nm}\) passes through two slits that are \(400 \mathrm{~nm}\) apart. The resulting pattern formed on a screen in front of the slits is shown in Fig. 24–55. If point A is the same distance from both slits, how much closer is point B to one slit than to the other? (a) \(530 \mathrm{~nm}\) (b) \(265 \mathrm{~nm}\) (c) \(400 \mathrm{~nm}\) (d) \(0 \mathrm{~nm}\) (e) It depends on the distance to the screen. FIGURE 24–55 MisConceptual Question 2. Equation Transcription: Text Transcription: 530 nm 400 nm 530 nm 265 nm 400 nm 0 nm

Problem 2P (I) The third-order bright fringe of 610-nm light is observed at an angle of 31° when the light falls on two narrow slits. How far apart are the slits?

Problem 2Q Why is light sometimes described as rays and sometimes as waves?

Problem 2SL Discuss the similarities, and differences, of double-slit interference and single-slit diffraction.

Problem 3MCQ The colors in a rainbow are caused by (a) the interaction of the light reflected from different raindrops. (b) different amounts of absorption for light of different colors by the water in the raindrops. (c) different amounts of refraction for light of different colors by the water in the raindrops. (d) the downward motion of the raindrops.

Problem 3P (II) Monochromatic light falls on two very narrow slits 0.048 mm apart. Successive fringes on a screen 6.50 m away are 8.5 cm apart near the center of the pattern. Determine the wavelength and frequency of the light.

Problem 3Q We can hear sounds around corners but we cannot see around corners; yet both sound and light are waves. Explain the difference.

Problem 3SL Describe why the various colors of visible light appear as they do in Fig. 24–16, where red is at the top and violet at the bottom, and in Fig. 24–26, where violet is closest to the central maximum and red is farthest from the central maximum.

Problem 4MCQ A double-slit experiment yields an interference pattern due to the path length difference from light traveling through one slit versus the other. Why does a single slit show a diffraction pattern? (a) There is a path length difference from waves originating at different parts of the slit. (b) The wavelength of the light is shorter than the slit. (c) The light passing through the slit interferes with light that does not pass through. (d) The single slit must have something in the middle of it, causing it to act like a double slit.

Problem 4P (II) If 720-nm and 660-nm light passes through two slits 0.62 mm apart, how far apart are the second-order fringes for these two wavelengths on a screen 1.0 m away?

Problem 4Q Two rays of light from the same source destructively interfere if their path lengths differ by how much?

Problem 4SL When can we use geometric optics as in Chapter 23, and when do we need to use the more complicated wave model of light discussed in Chapter 24? In particular, what are the physical characteristics that matter in making this decision?

If you hold two fingers very close together and look at a bright light, you see lines between the fingers.What is happening? (a) You are holding your fingers too close to your eye to be able to focus on it. (b) You are seeing a diffraction pattern. (c) This is a quantum-mechanical tunneling effect. (d) The brightness of the light is overwhelming your eye.

Problem 5P (II) Water waves having parallel crests 4.5 cm apart pass through two openings 7.5 cm apart in a board. At a point 3.0 m beyond the board, at what angle relative to the “straight-through” direction would there be little or no wave action?

Problem 5Q Monochromatic red light is incident on a double slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe pattern would change if the red light source is replaced by a blue light source.

A parallel beam of light containing two wavelengths, \(420 \mathrm{~nm} \text { and } 650 \mathrm{~nm}\), enters a borate flint glass equilateral prism (Fig. 24–63). (a) What is the angle between the two beams leaving the prism? (b) Repeat part (a) for a diffraction grating with (c) Discuss two advantages of a diffraction grating, including one that you see from your results. FIGURE 24–63 Search and Learn 5 Equation Transcription: Text Transcription: 420 nm and 650 nm 45.0° 60° 60° 60° \theta_2 \theta_1

Problem 6MCQ 6. Light passes through a slit that is about 5 X 10-3 m high and 5 x 10-7 m wide. The central bright light visible on a distant screen will be (a) about 5 X 10-3 m high and about 5 X 10-7 m wide. (b) about 5 X 10-3 m high and wider than 5 X 10-7 m. (c) about 5 X 10-3 m high and narrower than 5 X 10-7 m. (d) taller than 5 X 10-3 m high and wider than 5 X 10-7 m. (e) taller than 5 X 10-3 m high and about 5 X 10-7 m wide.

Problem 6P (II) A red laser from the physics lab is marked as producing 632.8-nm light. When light from this laser falls on two closely spaced slits, an interference pattern formed on a wall several meters away has bright red fringes spaced 5.00mm apart near the center of the pattern. When the laser is replaced by a small laser pointer, the fringes are 5.14 mm apart. What is the wavelength of light produced by the laser pointer?

Problem 6Q If Young’s double-slit experiment were submerged in water, how would the fringe pattern be changed?

Suppose you viewed the light transmitted through a thin coating layered on a flat piece of glass. Draw a diagram, similar to Fig. 24–30 or 24–36, and describe the conditions required for maxima and minima. Consider all possible values of index of refraction. Discuss the relative intensity of the minima compared to the maxima and to zero.

Blue light of wavelength \(\lambda\) passes through a single slit of width \(d\) and forms a diffraction pattern on a screen. If we replace the blue light by red light of wavelength \(2 \lambda\) we can retain the original diffraction pattern if we change the slit width (a) to \(d / 4\) (b) to \(d / 2\) (c) not at all. (d) to \(2 d\) (e) to \(4 d\) Equation Transcription: Text Transcription: \lambda 2 \lambda 2 d/4 d/2 2d 4d

(II) Light of wavelength 680 nm falls on two slits and produces an interference pattern in which the third-order bright red fringe is 38 mm from the central fringe on a screen 2.8 m away. What is the separation of the two slits?

Problem 7Q Why doesn’t the light from the two headlights of a distant car produce an interference pattern?

Problem 7SL What percent of visible light is reflected from plain glass? Assume your answer refers to transmission through each surface, front and back. How does the presence of multiple lenses in a good camera degrade the image? What is suggested in Section 24–8 to reduce this reflection? Explain in words, and sketch how this solution works. For a glass lens in air, about how much improvement does this solution provide?

Imagine holding a circular disk in a beam of monochromatic light (Fig. 24–56). If diffraction occurs at the edge of the disk, the center of the shadow is (a) darker than the rest of the shadow. (b) a bright spot. (c) bright or dark, depending on the wavelength. (d) bright or dark, depending on the distance to the screen. FIGURE 24–56 MisConceptual Question 8.

(II) Light of wavelength \(\lambda\) passes through a pair of slits separated by 0.17 mm, forming a double-slit interference pattern on a screen located a distance 37 cm away. Suppose that the image in Fig. 24–9a is an actual-size reproduction of this interference pattern. Use a ruler to measure a pertinent distance on this image; then utilize this measured value to determine \(\lambda\) (nm).

Problem 8Q Why are interference fringes noticeable only for a thin film like a soap bubble and not for a thick piece of glass?

Problem 9MCQ If someone is around a corner from you, what is the main reason you can hear him speaking but can’t see him? (a) Sound travels farther in air than light does. (b) Sound can travel through walls, but light cannot. (c) Sound waves have long enough wavelengths to bend around a corner; light wavelengths are too short to bend much. (d) Sound waves reflect off walls, but light cannot.

Problem 9P (II) A parallel beam of light from a He–Ne laser, with a wavelength 633 nm, falls on two very narrow slits 0.068mm apart. How far apart are the fringes in the center of the pattern on a screen 3.3 m away?

Why are the fringes of Newton’s rings (Fig. 24–31) closer together as you look farther from the center?

Problem 10MCQ When a CD is held at an angle, the reflected light contains many colors. What causes these colors? (a) An anti-theft encoding intended to prevent copying of the CD. (b) The different colors correspond to different data bits. (c) Light reflected from the closely spaced grooves adds constructively for different wavelengths at different angles. (d) It is part of the decorative label on the CD.

Problem 10P (II) A physics professor wants to perform a lecture demonstration of Young’s double-slit experiment for her class using the 633-nm light from a He–Ne laser. Because the lecture hall is very large, the interference pattern will be projected on a wall that is 5.0 m from the slits. For easy viewing by all students in the class, the professor wants the distance between the m=0 and m =1 maxima to be 35 cm. What slit separation is required in order to produce the desired interference

Problem 10Q Some coated lenses appear greenish yellow when seen by reflected light. What reflected wavelengths do you suppose the coating is designed to eliminate completely?

If a thin film has a thickness that is (a) \(\frac{1}{4}\) of a wavelength, constructive interference will always occur. (b) \(\frac{1}{4}\) of a wavelength, destructive interference will always occur. (c) \(\frac{1}{2}\) of a wavelength, constructive interference will always occur. (d) \(\frac{1}{2}\) of a wavelength, destructive interference will always occur. (e) None of the above is always true. Equation Transcription: Text Transcription: \frac1 4 \frac1 4 \frac1 2 \frac1 2

\(\text { (II) }\) Suppose a thin piece of glass is placed in front of the lower slit in Fig. 24–7 so that the two waves enter the slits \(180^{\circ}\) out of phase (Fig.24–58). Draw in detail the interference pattern seen on the screen. Equation Transcription: Text Transcription: (II) 180°

Problem 11Q A drop of oil on a pond appears bright at its edges, where its thickness is much less than the wavelengths of visible light.What can you say about the index of refraction of the oil compared to that of water?

If unpolarized light is incident from the left on three polarizers as shown in Fig. 24–57, in which case will some light get through? (a) Case 1 only. (b) Case 2 only. (c) Case 3 only. (d) Cases 1 and 3. (e) All three cases.

Problem 12P (II) In a double-slit experiment it is found that blue light of wavelength 480 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a minimum at the same location?

Problem 12Q Radio waves and visible light are both electromagnetic waves. Why can a radio receive a signal behind a hill when we cannot see the transmitting antenna?

Problem 13P (II) Two narrow slits separated by 1.0 mm are illuminated by 544-nm light. Find the distance between adjacent bright fringes on a screen 4.0 m from the slits.

Problem 13Q Hold one hand close to your eye and focus on a distant light source through a narrow slit between two fingers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

\(\text { (II) }\) Assume that light of a single color, rather than white light, passes through the two-slit setup described in Example 24–3. If the distance from the central fringe to a first-order fringe is measured to be \(2.9 \mathrm{~mm}\) on the screen, determine the light’s wavelength (in nm) and color (see Fig. 24–12). Equation Transcription: Text Transcription: (II) 2.9 mm

Problem 15P (II) In a double-slit experiment, the third-order maximum for light of wavelength 480 nm is located 16 mm from the central bright spot on a screen 1.6 m from the slits. Light of wavelength 650 nm is then projected through the same slits. How far from the central bright spot will the second-order maximum of this light be located?

Problem 15Q Describe the single-slit diffraction pattern produced when white light falls on a slit having a width of (a) 60 nm, (b) 60,000 nm.

Problem 16P (II) Light of wavelength 470 nm in air shines on two slits 6. 00 X 10-2 mm apart. The slits are immersed in water, as is a viewing screen 40.0 cm away. How far apart are the fringes on the screen?

Problem 16Q What happens to the diffraction pattern of a single slit if the whole apparatus is immersed in (a) water, (b) a vacuum, instead of in air.

Problem 17Q What is the difference in the interference patterns formed by two slits 10-4 apart as compared to a diffraction grating containing 104 slits_cm?

Problem 18Q For a diffraction grating, what is the advantage of (a) many slits, (b) closely spaced slits?

\(\text { (I) }\) By what percent is the speed of blue light \(\text { (450 nm) }\) less than the speed of red light \(\text { (680 nm) }\), in silicate flint glass (see Fig. 24–14)? Equation Transcription: Text Transcription: (I) (450 nm) (680 nm)

Problem 19P (II) A light beam strikes a piece of glass at a 65.00° incident angle. The beam contains two wavelengths, 450.0 nm and 700.0 nm, for which the index of refraction of the glass is 1.4831 and 1.4754, respectively. What is the angle between the two refracted beams?

Problem 19Q White light strikes (a) a diffraction grating and (b) a prism. A rainbow appears on a wall just below the direction of the horizontal incident beam in each case.What is the color of the top of the rainbow in each case? Explain.

Problem 20Q What does polarization tell us about the nature of light?

Problem 22P (I) Monochromatic light falls on a slit that is 2.60 X 10-3 mm wide. If the angle between the first dark fringes on either side of the central maximum is 28.0° (dark fringe to dark fringe), what is the wavelength of the light used?

Problem 22Q How can you tell if a pair of sunglasses is polarizing or not?

Problem 23P (II) When blue light of wavelength 440 nm falls on a single slit, the first dark bands on either side of center are separated by 51.0°. Determine the width of the slit.

Problem 24EA A light beam in air with wavelength = 500 nm. Frequency = 6.0 X 1014 Hz., and speed = 3.0 X 108 m/s goes into glass which has an index of refraction = 1.5. What are the wavelength, frequency, and speed of the light in the glass?

For the setup in Example 24–3, how far from the central white fringe is the first-order fringe for green light \(\lambda=500 \mathrm{~nm}\)? Equation Transcription: Text Transcription: \lambda=500 nm

In Example 24–5, red light \((\lambda=750 \mathrm{~nm})\) was used. If instead yellow light \((\lambda=550 \mathrm{~nm})\) had been used, would the central maximum be wider or narrower? Equation Transcription: Text Transcription: ( \lambda = 750 nm) ( \lambda = 550 nm)

You are shown the spectra produced by red light shining through two different gratings. The maxima in spectrum A are farther apart than those in spectrum B. Which grating has more slits/cm?

Return to the Chapter-Opening Question, page 679, and answer it again now. Try to explain why you may have answered differently the first time.

Problem 24EF How much light would pass through if the 45° polarizer in Example 24–14 was placed not between the other two polarizers but (a) before the vertical (first) polarizer, or (b) after the horizontal polarizer?

Problem 24P (II) A single slit 1.0 mm wide is illuminated by 450-nm light. What is the width of the central maximum (in cm) in the diffraction pattern on a screen 6.0 m away?

Problem 24Q If the Earth’s atmosphere were 50 times denser than it is, would sunlight still be white, or would it be some other color?

Problem 25P (II) How wide is the central diffraction peak on a screen 2.30m behind a 0.0348-mm-wide slit illuminated by 558-nm light?

Problem 26P (II) Consider microwaves which are incident perpendicular to a metal plate which has a 1.6-cm slit in it. Discuss the angles at which there are diffraction minima for wavelengths of (a) 0.50 cm, (b) 1.0 cm, and (c) 3.0 cm.

Problem 27P (II) (a) For a given wavelength ? what is the minimum slit width for which there will be no diffraction minima? (b) What is the minimum slit width so that no visible light exhibits a diffraction minimum?

Problem 28P (II) Light of wavelength 620 nm falls on a slit that is 3.80 X 10-3 mm wide. Estimate how far the first bright diffraction fringe is from the strong central maximum if the screen is 10.0 m away

Problem 29P (II) Monochromatic light of wavelength 633 nm falls on a slit. If the angle between the first two bright fringes on either side of the central maximum is 32°, estimate the slit width.

Problem 30P (II) Coherent light from a laser diode is emitted through a rectangular area 3.0 µm X 1.5 µm (horizontal-by-vertical). If the laser light has a wavelength of 780 nm, determine the angle between the first diffraction minima (a) above and below the central maximum, (b) to the left and right of the central maximum.

Problem 31P (III) If parallel light falls on a single slit of width D at a 28.0° angle to the normal, describe the diffraction pattern.

Problem 32P (I) At what angle will 510-nm light produce a second-order maximum when falling on a grating whose slits are 1.35 X 10-3 cm apart?

Problem 33P (I) A grating that has 3800 slits per cm produces a third-order fringe at a 22.0° angle. What wavelength of light is being used?

Problem 34P (I) A grating has 7400 slits/cm. How many spectral orders can be seen (400 to 700 nm) when it is illuminated by white light?

Problem 35P (II) Red laser light from a He–Ne laser (? = 632.8nm) creates a second-order fringe at 53.2° after passing through the grating. What is the wavelength of light that creates a first-order fringe at 20.6°?

Problem 36P (II) How many slits per centimeter does a grating have if the third order occurs at a 15.0° angle for 620-nm light?

Problem 37P (II) A source produces first-order lines when incident normally on a 9800-slit/cm diffraction grating at angles 28.8°, 36.7°, 38.6°, and 41.2°. What are the wavelengths?

Problem 38P (II) White light containing wavelengths from 410 nm to 750 nm falls on a grating with 7800 slits/cm. How wide is the first-order spectrum on a screen 3.40 m away?

Problem 39P (II) A diffraction grating has 6.5 X 105 slits/m Find the angular spread in the second-order spectrum between red light of wavelength 7.0 X 10-7 m and blue light of wavelength 4.5 X 10-7 m.

Problem 40P (II) Two first-order spectrum lines are measured by a spectroscope at angles, on each side of center, +26°38, +41°02 and -26°18 -40°27 and Calculate the wavelengths based on these data.

Problem 41P (II) What is the highest spectral order that can be seen if a grating with 6500 slits per cm is illuminated with 633-nm laser light? Assume normal incidence.

Problem 42P (II) The first-order line of 589-nm light falling on a diffraction grating is observed at a 14.5° angle. How far apart are the slits? At what angle will the third order be observed?

Problem 43P (II) Two (and only two) full spectral orders can be seen on either side of the central maximum when white light is sent through a diffraction grating. What is the maximum number of slits per cm for the grating?

Problem 44P (I) If a soap bubble is 120 nm thick, what wavelength is most strongly reflected at the center of the outer surface when illuminated normally by white light? Assume that n =1.32.

Problem 45P (I) How far apart are the dark bands in Example 24–10 if the glass plates are each 21.5 cm long?

Problem 46P (II) (a) What is the smallest thickness of a soap film (N =1.33) that would appear black if illuminated with 480-nm light? Assume there is air on both sides of the soap film. (b) What are two other possible thicknesses for the film to appear black? (c) If the thickness was much less than ? why would the film also appear black?

Problem 47P (II) A lens appears greenish yellow (? =570 NM is strongest) when white light reflects from it. What minimum thickness of coating (N =1.25) do you think is used on such a glass lens (N =1.52) , and why?

\(\text { (II) }\) A thin film of oil \(\left(n_{o}=1.50\right)\) with varying thickness floats on water \(\left(n_{w}=1.33\right)\) When it is illuminated from above by white light, the reflected colors are as shown in Fig. In air, the wavelength of yellow light is \(580 \mathrm{~nm}\). (a) Why are there no reflected colors at point A? (b) What is the oil's thickness \(t\) at point B? Equation Transcription: Text Transcription: (II) (n0=1.50) (nw=1.33) 580 nm t n0=1.50 nw=1.33

Problem 49P (II) How many uncoated thin lenses in an optical instrument would reduce the amount of light passing through the instrument to 50%or less? (Assume the same transmission percent at each of the two surfaces

\(\text { (II) }\) A total of 35 bright and 35 dark Newton’s rings (not counting the dark spot at the center) are observed when \(560-\mathrm{nm}\) light falls normally on a planoconvex lens resting on a flat glass surface (Fig. 24–31). How much thicker is the lens at the center than the edges? Equation Transcription: Text Transcription: (II) 560-nm

Problem 51P (II) If the wedge between the glass plates of Example 24–10 is filled with some transparent substance other than air— say, water—the pattern shifts because the wavelength of the light changes. In a material where the index of refraction is n, the wavelength is ?n =?/n, where is the wavelength in vacuum (Eq. 24–1). How many dark bands would there be if the wedge of Example 24–10 were filled with water?

\(\text { (II) }\) A fine metal foil separates one end of two pieces of optically flat glass, as in Fig. 24–33. When light of wavelength \(670 \mathrm{~mm}\) is incident normally, 24 dark bands are observed (with one at each end). How thick is the foil? Equation Transcription: Text Transcription: (II) 670 nm

Problem 53P (II) How thick (minimum) should the air layer be between two flat glass surfaces if the glass is to appear bright when 450-nm light is incident normally? What if the glass is to appear dark?

Problem 54P (III) A thin oil slick (no -1.50) floats on water (nw = 1.33) When a beam of white light strikes this film at normal incidence from air, the only enhanced reflected colors are red (650 nm) and violet (390 nm). From this information, deduce the (minimum) thickness of the oil slick.

(III) A uniform thin film of alcohol (n =1.36) lies on a flat glass plate (n = 1.56) When monochromatic light, whose wavelength can be changed, is incident normally, the reflected light is a minimum for \(\lambda=525 \ \mathrm {nm}\) and a maximum for \(\lambda=655 \ \mathrm {nm}\). What is the minimum thickness of the film?

(II) How far must the mirror \(M_1\) in a Michelson interferometer be moved if 680 fringes of 589-nm light are to pass by a reference line?

Problem 57P (II) What is the wavelength of the light entering an interferometer if 362 bright fringes are counted when the movable mirror moves 0.125 mm?

Problem 58P (II) A micrometer is connected to the movable mirror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net number of bright fringes that move, compared to closing the empty micrometer, is 296. What is the thickness of the foil? The wavelength of light used is 589 nm.

(III) One of the beams of an interferometer (Fig. 24–61) passes through a small evacuated glass container 1.155 cm deep. When a gas is allowed to slowly fill the container, a total of 158 dark fringes are counted to move past a reference line. The light used has a wavelength of 632.8 nm. Calculate the index of refraction of the gas at its final density, assuming that the interferometer is in vacuum.

Problem 60P (I) Two polarizers are oriented at 72° to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?

Problem 61P (I) What is Brewster’s angle for an air–glass surface?

\((I I)\) At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light to \((a) \frac{1}{3},(b) \frac{1}{10}\)? Equation Transcription: Text Transcription: (II) (a)1 3, (b)1 10

Problem 63P (II) Two polarizers are oriented at 42.0° to one another. Light polarized at a 21.0° angle to each polarizer passes through both. What is the transmitted intensity (%)?

Problem 64P (II) Three perfectly polarizing sheets are spaced 2 cm apart and in parallel planes. The transmission axis of the second sheet is 30° relative to the first one. The transmission axis of the third sheet is 90° relative to the first one. Unpolarized light impinges on the first polarizing sheet. What percent of this light is transmitted out through the third polarizer?

Problem 65P (II) A piece of material, suspected of being a stolen diamond is submerged in oil of refractive index 1.43 and illuminated by unpolarized light. It is found that the reflected light is completely polarized at an angle of 62°. Is it diamond? Explain.

Problem 66P (II) Two Polaroids are aligned so that the initially unpolarized light passing through them is a maximum. At what angle should one of them be placed so the transmitted intensity is subsequently reduced by half?

Problem 67P (II) What is Brewster’s angle for a diamond submerged in water?

Problem 68P (II) The critical angle for total internal reflection at a boundary between two materials is 58°.What is Brewster’s angle at this boundary? Give two answers, one for each material.

Problem 69P (II) What would Brewster’s angle be for reflections off the surface of water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’s angle from above the surface.

Problem 70P (II) Unpolarized light of intensity I0 passes through six successive Polaroid sheets each of whose axis makes a 35° angle with the previous one. What is the intensity of the transmitted beam?

Problem 71P (III) Two polarizers are oriented at 48° to each other and plane-polarized light is incident on them. If only 35% of the light gets through both of them, what was the initial polarization direction of the incident light?

Problem 72P (III) Four polarizers are placed in succession with their axes vertical, at 30.0° to the vertical, at 60.0° to the vertical, and at 90.0° to the vertical. (a) Calculate what fraction of the incident unpolarized light is transmitted by the four polarizers. (b) Can the transmitted light be decreased by removing one of the polarizers? If so, which one? (c) Can the transmitted light intensity be extinguished by removing polarizers? If so, which one(s)?

Problem 73GP Light of wavelength 5.0*10-7 passes through two parallel slits and falls on a screen 5.0 m away. Adjacent bright bands of the interference pattern are 2.0 cm apart. (a) Find the distance between the slits. (b) The same two slits are next illuminated by light of a different wavelength, and the fifth-order minimum for this light occurs at

Television and radio waves reflecting from mountains or airplanes can interfere with the direct signal from the station. (a) What kind of interference will occur when \(\text { 75-MHz }\) television signals arrive at a receiver directly from a distant station, and are reflected from a nearby airplane \(122 \mathrm{~m}\) directly above the receiver? Assume \(\frac{1}{2} \lambda\) change in phase of the signal upon reflection. (b) What kind of interference will occur if the plane is \(22 \mathrm{~m}\) closer to the receiver? Equation Transcription: Text Transcription: 75-MHz 122 m 1 2 \lambda 22 m

Problem 75GP Red light from three separate sources passes through a diffraction grating with 3.60 X 105 slits/m. The wavelengths of the three lines are 6.56 X 10-7 m (hydrogen), 6.50 X 10-7m (neon), and 6.97 X 10-7 m (argon). Calculate the angles for the first-order diffraction line of each source.

Problem 76GP What is the index of refraction of a clear material if a minimum thickness of 125 nm, when laid on glass, is needed to reduce reflection to nearly zero when light of 675 nm is incident normally upon it? Do you have a choice for an answer?

Problem 77GP Light of wavelength 650 nm passes through two narrow slits 0.66 mm apart. The screen is 2.40 m away. A second source of unknown wavelength produces its second-order fringe 1.23 mm closer to the central maximum than the 650-nm light.What is the wavelength of the unknown light?

Problem 79GP Show that the second- and third-order spectra of white light produced by a diffraction grating always overlap. What wavelengths overlap?

Monochromatic light of variable wavelength is incident normally on a thin sheet of plastic film in air. The reflected light is a maximum only for \(\lambda=491.4 \mathrm{~nm} \text { and } \lambda=688.0 \mathrm{~nm}\) and in the visible spectrum. What is the thickness of the film \((n=1.58)\) ? [Hint: Assume successive values of \(m\).] Equation Transcription: Text Transcription: \lambda =491.4 nm and \lambda =688.0 nm (n=1.58) m

A radio station operating at \(90.3 M H z\) broadcasts from two identical antennas at the same elevation but separated by a \(9.0-m\) horizontal distance \(d\), Fig. 24-62 A maximum signal is found along the midline, perpendicular to \(d\) at its midpoint and extending horizontally in both directions. If the midline is taken as \(0^{\circ}\), at what other angle(s) \(\theta\) is a maximum signal detected? A minimum signal? Assume all measurements are made much farther than \(9.0 \mathrm{~m}\) from the antenna towers. Equation Transcription: Text Transcription: 90.3 MHz 9.0-m d d 0° \theta 9.0 m \theta

Problem 81GP Calculate the minimum thickness needed for an antireflective coating (n=1.38) applied to a glass lens in order to eliminate (a) blue (450 nm), or (b) red (720 nm) reflections for light at normal incidence.

Problem 82GP Stealth aircraft are designed to not reflect radar, whose wavelength is typically 2 cm, by using an antireflecting coating. Ignoring any change in wavelength in the coating, estimate its thickness.

Problem 83GP A laser beam passes through a slit of width 1.0 cm and is pointed at the Moon, which is approximately 380,000 km from the Earth. Assume the laser emits waves of wavelength 633 nm (the red light of a He–Ne laser). Estimate the width of the beam when it reaches the Moon due to diffraction.

Problem 84GP A thin film of soap (n=1.34) coats a piece of flat glass (n=1.52). How thick is the film if it reflects 643-nm red light most strongly when illuminated normally by white light?

Problem 85GP When violet light of wavelength 415 nm falls on a single slit, it creates a central diffraction peak that is 8.20 cm wide on a screen that is 3.15 m away. How wide is the slit?

Problem 86GP A series of polarizers are each rotated 10° from the previous polarizer. Unpolarized light is incident on this series of polarizers. How many polarizers does the light have to go through before it is of its original intensity?

Problem 87GP The wings of a certain beetle have a series of parallel lines across them. When normally incident 480-nm light is reflected from the wing, the wing appears bright when viewed at an angle of 56°. How far apart are the lines?

Problem 88GP A teacher stands well back from an outside doorway 0.88 m wide, and blows a whistle of frequency 950 Hz. Ignoring reflections, estimate at what angle(s) it is not possible to hear the whistle clearly on the playground outside the doorway. Assume 340 m/s for the speed of sound.

Light is incident on a diffraction grating with \(7200 \text { slits } / \mathrm{cm}\) and the pattern is viewed on a screen located \(2.5 \mathrm{~m}\) from the grating. The incident light beam consists of two wavelengths, \(\lambda_{1}=4.4 \times 10^{-7} \mathrm{~m} \text { and } \lambda_{2}=6.8 \times 10^{-7} \mathrm{~m}\) Calculate the linear distance between the first-order bright fringes of these two wavelengths on the screen. Equation Transcription: Text Transcription: 7200 slits/cm 2.5 m \lambda 1=4.4 x 10-7m and \lambda 2=6.8 x 10-7m

Problem 90GP How many slits per centimeter must a grating have if there is to be no second-order spectrum for any visible wavelength?

When yellow sodium light, \(\lambda=589 \mathrm{~mm}\), falls on a diffraction grating, its first-order peak on a screen \(72.0 \mathrm{~cm}\) away falls \(3.32 \mathrm{~cm}\) from the central peak. Another source produces a line \(3.71 \mathrm{~cm}\) from the central peak. What is its wavelength? How many slits/cm are on the grating? Equation Transcription: Text Transcription: \lambda =589 nm 72.0 cm 3.32 cm 3.71 cm

Problem 92GP Two of the lines of the atomic hydrogen spectrum have wavelengths of 656 nm and 410 nm. If these fall at normal incidence on a grating with 7700 slits/cm, what will be the angular separation of the two wavelengths in the first-order spectrum?

Problem 93GP A tungsten–halogen bulb emits a continuous spectrum of ultraviolet, visible, and infrared light in the wavelength range 360 nm to 2000 nm. Assume that the light from a tungsten–halogen bulb is incident on a diffraction grating with slit spacing d and that the first-order brightness maximum for the wavelength of 1200 nm occurs at angle ?. What other wavelengths within the spectrum of incident light will produce a brightness maximum at this same angle ?? [Optical filters are used to deal with this bothersome effect when a continuous spectrum of light is measured by a spectrometer.]

Problem 94GP At what angle above the horizon is the Sun when light reflecting off a smooth lake is polarized most strongly?

Problem 95GP Unpolarized light falls on two polarizer sheets whose axes are at right angles. (a) What fraction of the incident light intensity is transmitted? (b) What fraction is transmitted if a third polarizer is placed between the first two so that its axis makes a 56° angle with the axis of the first polarizer? (c) What if the third polarizer is in front of the other two?

Problem 96GP At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the first Polaroid cuts it in half) of (a) 4, (b) 10, (c) 100?

Monochromatic light falling on two slits 0.018 mm apart produces the fifth-order bright fringe at an 8.6 angle. What is the wavelength of the light used?

The third-order bright fringe of 610-nm light is observed at an angle of 31 when the light falls on two narrow slits. How far apart are the slits?

Monochromatic light falls on two very narrow slits 0.048 mm apart. Successive fringes on a screen 6.50 m away are 8.5 cm apart near the center of the pattern. Determine the wavelength and frequency of the light.

If 720-nm and 660-nm light passes through two slits 0.62 mm apart, how far apart are the second-order fringes for these two wavelengths on a screen 1.0 m away?

Water waves having parallel crests 4.5 cm apart pass through two openings 7.5 cm apart in a board. At a point 3.0 m beyond the board, at what angle relative to the straight-through direction would there be little or no wave action?

A red laser from the physics lab is marked as producing 632.8-nm light. When light from this laser falls on two closely spaced slits, an interference pattern formed on a wall several meters away has bright red fringes spaced 5.00 mm apart near the center of the pattern. When the laser is replaced by a small laser pointer, the fringes are 5.14 mm apart. What is the wavelength of light produced by the laser pointer?

Light of wavelength 680 nm falls on two slits and produces an interference pattern in which the third-order bright red fringe is 38 mm from the central fringe on a screen 2.8 m away. What is the separation of the two slits?

Light of wavelength passes through a pair of slits separated by 0.17 mm, forming a double-slit interference pattern on a screen located a distance 37 cm away. Suppose that the image in Fig. 249a is an actual-size reproduction of this interference pattern. Use a ruler to measure a pertinent distance on this image; then utilize this measured value to determine

A parallel beam of light from a HeNe laser, with a wavelength 633 nm, falls on two very narrow slits 0.068 mm apart. How far apart are the fringes in the center of the pattern on a screen 3.3 m away?

A physics professor wants to perform a lecture demonstration of Youngs double-slit experiment for her class using the 633-nm light from a HeNe laser. Because the lecture hall is very large, the interference pattern will be projected on a wall that is 5.0 m from the slits. For easy viewing by all students in the class, the professor wants the distance between the and maxima to be 35 cm. What slit separation is required in order to produce the desired interference pattern?

Suppose a thin piece of glass is placed in front of the lower slit in Fig. 247 so that the two waves enter the slits 180 out of phase (Fig.2458). Draw in detail the interference pattern seen on the screen.

In a double-slit experiment it is found that blue light of wavelength 480 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a minimum at the same location?

Two narrow slits separated by 1.0 mm are illuminated by 544-nm light. Find the distance between adjacent bright fringes on a screen 4.0 m from the slits.

Assume that light of a single color, rather than white light, passes through the two-slit setup described in Example 243. If the distance from the central fringe to a first-order fringe is measured to be 2.9 mm on the screen, determine the lights wavelength (in nm) and color (see Fig. 2412).

In a double-slit experiment, the third-order maximum for light of wavelength 480 nm is located 16 mm from the central bright spot on a screen 1.6 m from the slits. Light of wavelength 650 nm is then projected through the same slits. How far from the central bright spot will the secondorder maximum of this light be located?

Light of wavelength 470 nm in air shines on two slits apart. The slits are immersed in water, as is a viewing screen 40.0 cm away. How far apart are the fringes on the screen?

A very thin sheet of plastic covers one slit of a double-slit apparatus illuminated by 680-nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic?

By what percent is the speed of blue light (450 nm) less than the speed of red light (680 nm), in silicate flint glass (see Fig. 2414)?

A light beam strikes a piece of glass at a 65.00 incident angle. The beam contains two wavelengths, 450.0 nm and 700.0 nm, for which the index of refraction of the glass is 1.4831 and 1.4754, respectively. What is the angle between the two refracted beams?

A parallel beam of light containing two wavelengths, and enters the silicate flint glass of an equilateral prism as shown in Fig.2459. At what angles, does each beam leave the prism (give angle with normal to the face)? See Fig. 2414.

If 680-nm light falls on a slit 0.0425 mm wide, what is the angular width of the central diffraction peak?

Monochromatic light falls on a slit that is wide. If the angle between the first dark fringes on either side of the central maximum is 28.0 (dark fringe to dark fringe), what is the wavelength of the light used?

When blue light of wavelength 440 nm falls on a single slit, the first dark bands on either side of center are separated by 51.0. Determine the width of the slit.

A single slit 1.0 mm wide is illuminated by 450-nm light. What is the width of the central maximum (in cm) in the diffraction pattern on a screen 6.0 m away?

How wide is the central diffraction peak on a screen 2.30 m behind a 0.0348-mm-wide slit illuminated by 558-nm light?

Consider microwaves which are incident perpendicular to a metal plate which has a 1.6-cm slit in it. Discuss the angles at which there are diffraction minima for wavelengths of (a) 0.50 cm, (b) 1.0 cm, and (c) 3.0 cm.

(a) For a given wavelength what is the minimum slit width for which there will be no diffraction minima? (b) What is the minimum slit width so that no visible light exhibits a diffraction minimum?

Light of wavelength 620 nm falls on a slit that is wide. Estimate how far the first bright diffraction fringe is from the strong central maximum if the screen is 10.0 m away

Monochromatic light of wavelength 633 nm falls on a slit. If the angle between the first two bright fringes on either side of the central maximum is 32, estimate the slit width.

Coherent light from a laser diode is emitted through a rectangular area (horizontal-byvertical). If the laser light has a wavelength of 780 nm, determine the angle between the first diffraction minima (a) above and below the central maximum, (b) to the left and right of the central maximum.

If parallel light falls on a single slit of width D at a 28.0 angle to the normal, describe the diffraction pattern.

At what angle will 510-nm light produce a second-order maximum when falling on a grating whose slits are 1.35 * 103 cmapart?

A grating that has 3800 slits per cm produces a third-order fringe at a 22.0 angle. What wavelength of light is being used?

A grating has How many spectral orders can be seen (400 to 700 nm) when it is illuminated by white light?

Red laser light from a HeNe laser creates a second-order fringe at 53.2 after passing through the grating. What is the wavelength of light that creates a first-order fringe at 20.6?

How many slits per centimeter does a grating have if the third order occurs at a 15.0 angle for 620-nm light?

A source produces first-order lines when incident normally on a diffraction grating at angles 28.8, 36.7, 38.6, and 41.2. What are the wavelengths?

White light containing wavelengths from 410 nm to 750 nm falls on a grating with How wide is the first-order spectrum on a screen 3.40 m away?

A diffraction grating has Find the angular spread in the second-order spectrum between red light of wavelength and blue light of wave length 4.5 * 107 m

Two first-order spectrum lines are measured by a spectroscope at angles, on each side of center, of and Calculate the wavelengths based on these data

What is the highest spectral order that can be seen if a grating with 6500 slits per cm is illuminated with 633-nm laser light? Assume normal incidence.

The first-order line of 589-nm light falling on a diffraction grating is observed at a 14.5 angle. How far apart are the slits? At what angle will the third order be observed?

Two (and only two) full spectral orders can be seen on either side of the central maximum when white light is sent through a diffraction grating. What is the maximum number of slits per cm for the grating?

If a soap bubble is 120 nm thick, what wavelength is most strongly reflected at the center of the outer surface when illuminated normally by white light? Assume that n = 1.32.

How far apart are the dark bands in Example 2410 if the glass plates are each 21.5 cm long?

(a) What is the smallest thickness of a soap film that would appear black if illuminated with 480-nm light? Assume there is air on both sides of the soap film. (b) What are two other possible thicknesses for the film to appear black? (c) If the thickness was much less than why would the film also appear black?

A lens appears greenish yellow ( is strongest) when white light reflects from it. What minimum thickness of coating do you think is used on such a glass lens , and why?

A thin film of oil with varying thickness floats on water When it is illuminated from above by white light, the reflected colors are as shown in Fig. 2460. In air, the wavelength of yellow light is 580 nm. (a) Why are there no reflected colors at point A? (b) What is the oils thickness at point B?

(II) How many uncoated thin lenses in an optical instrument would reduce the amount of light passing through the instrument to 50%or less? (Assume the same transmission percent at each of the two surfaces—see page 697.)

A total of 35 bright and 35 dark Newtons rings (not counting the dark spot at the center) are observed when 560-nm light falls normally on a planoconvex lens resting on a flat glass surface (Fig. 2431). How much thicker is the lens at the center than the edges?

If the wedge between the glass plates of Example 2410 is filled with some transparent substance other than air say, waterthe pattern shifts because the wavelength of the light changes. In a material where the index of refraction is n, the wavelength is where is the wavelength in vacuum (Eq. 241). How many dark bands would there be if the wedge of Example 2410 were filled with water?

A fine metal foil separates one end of two pieces of optically flat glass, as in Fig. 2433. When light of wavelength 670 nm is incident normally, 24 dark bands are observed (with one at each end). How thick is the foil?

How thick (minimum) should the air layer be between two flat glass surfaces if the glass is to appear bright when 450-nm light is incident normally? What if the glass is to appear dark?

A thin oil slick floats on water (nw = 1.33). When a beam of white light strikes this film at normal incidence from air, the only enhanced reflected colors are red (650 nm) and violet (390 nm). From this information, deduce the (minimum) thickness of the oil slick

A uniform thin film of alcohol lies on a flat glass plate When monochromatic light, whose wavelength can be changed, is incident normally, the reflected light is a minimum for and a maximum for What is the minimum thickness of the film?

How far must the mirror in a Michelson interferometer be moved if 680 fringes of 589-nm light are to pass by a reference line?

What is the wavelength of the light entering an interferometer if 362 bright fringes are counted when the movable mirror moves 0.125 mm?

A micrometer is connected to the movable mirror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net number of bright fringes that move, compared to closing the empty micrometer, is 296. What is the thickness of the foil? The wavelength of light used is 589 nm

One of the beams of an interferometer (Fig. 2461) passes through a small evacuated glass container 1.155 cm deep. When a gas is allowed to slowly fill the container, a total of 158 dark fringes are counted to move past a reference line. The light used has a wavelength of 632.8 nm. Calculate the index of refraction of the gas at its final density, assuming that the interferometer is in vacuum.

(I) Two polarizers are oriented at \(72^\circ\) to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?

What is Brewsters angle for an airglass surface?

At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light to (a) (b) 1 10?

(II) Two polarizers are oriented at \(42.0^{\circ}\) to one another. Light polarized at a \(21.0^{\circ}\) angle to each polarizer passes through both. What is the transmitted intensity (%)?

Three perfectly polarizing sheets are spaced 2 cm apart and in parallel planes. The transmission axis of the second sheet is 30 relative to the first one. The transmission axis of the third sheet is 90 relative to the first one. Unpolarized light impinges on the first polarizing sheet. What percent of this light is transmitted out through the third polarizer?

(II) A piece of material, suspected of being a stolen diamond (n = 2.42), is submerged in oil of refractive index 1.43 and illuminated by unpolarized light. It is found that the reflected light is completely polarized at an angle of \(62^{\circ}\). Is it diamond? Explain.

Two Polaroids are aligned so that the initially unpolarized light passing through them is a maximum. At what angle should one of them be placed so the transmitted intensity is subsequently reduced by half?

What is Brewsters angle for a diamond submerged in water?

The critical angle for total internal reflection at a boundary between two materials is 58. What is Brewsters angle at this boundary? Give two answers, one for each material.

What would Brewsters angle be for reflections off the surface of water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewsters angle from above the surface.

Unpolarized light of intensity passes through six successive Polaroid sheets each of whose axis makes a 35 angle with the previous one. What is the intensity of the transmitted beam?

Two polarizers are oriented at 48 to each other and plane-polarized light is incident on them. If only 35% of the light gets through both of them, what was the initial polarization direction of the incident light?

Four polarizers are placed in succession with their axes vertical, at 30.0 to the vertical, at 60.0 to the vertical, and at 90.0 to the vertical. (a) Calculate what fraction of the incident unpolarized light is transmitted by the four polarizers. (b) Can the transmitted light be decreased by removing one of the polarizers? If so, which one? (c) Can the transmitted light intensity be extinguished by removing polarizers? If so, which one(s)?

Light of wavelength passes through two parallel slits and falls on a screen 5.0 m away. Adjacent bright bands of the interference pattern are 2.0 cm apart. (a) Find the distance between the slits. (b) The same two slits are next illuminated by light of a different wavelength, and the fifth-order minimum for this light occurs at the same point on the screen as the fourth-order minimum for the previous light. What is the wavelength of the second source of light?

Television and radio waves reflecting from mountains or airplanes can interfere with the direct signal from the station. (a) What kind of interference will occur when 75-MHz television signals arrive at a receiver directly from a distant station, and are reflected from a nearby airplane 122 m directly above the receiver? Assume change in phase of the signal upon reflection. (b) What kind of interference will occur if the plane is 22 m closer to the receiver?

Red light from three separate sources passes through a diffraction grating with The wavelengths of the three lines are (hydrogen), (neon), and (argon). Calculate the angles for the first-order diffraction line of each source.

What is the index of refraction of a clear material if a minimum thickness of 125 nm, when laid on glass, is needed to reduce reflection to nearly zero when light of 675 nm is incident normally upon it? Do you have a choice for an answer?

Light of wavelength 650 nm passes through two narrow slits 0.66 mm apart. The screen is 2.40 m away. A second source of unknown wavelength produces its second-order fringe 1.23 mm closer to the central maximum than the 650-nm light. What is the wavelength of the unknown light?

Monochromatic light of variable wavelength is incident normally on a thin sheet of plastic film in air. The reflected light is a maximum only for and in the visible spectrum. What is the thickness of the film [Hint: Assume successive values of m.

Show that the second- and third-order spectra of white light produced by a diffraction grating always overlap. What wavelengths overlap?

A radio station operating at 90.3 MHz broadcasts from two identical antennas at the same elevation but separated by a 9.0-m horizontal distance d, Fig. 2462. A maximum signal is found along the midline, perpendicular to d at its midpoint and extending horizontally in both directions. If the midline is taken as 0, at what other angle(s) is a maximum signal detected? A minimum signal? Assume all measurements are made much farther than 9.0 m from the antenna towers.

Calculate the minimum thickness needed for an antireflective coating applied to a glass lens in order to eliminate (a) blue (450 nm), or (b) red (720 nm) reflections for light at normal incidence.

Stealth aircraft are designed to not reflect radar, whose wavelength is typically 2 cm, by using an antireflecting coating. Ignoring any change in wavelength in the coating, estimate its thickness

A laser beam passes through a slit of width 1.0 cm and is pointed at the Moon, which is approximately 380,000 km from the Earth. Assume the laser emits waves of wavelength 633 nm (the red light of a HeNe laser). Estimate the width of the beam when it reaches the Moon due to diffraction.

A thin film of soap coats a piece of flat glass How thick is the film if it reflects 643-nm red light most strongly when illuminated normally by white light

When violet light of wavelength 415 nm falls on a single slit, it creates a central diffraction peak that is 8.20 cm wide on a screen that is 3.15 m away. How wide is the slit?

A series of polarizers are each rotated 10 from the previous polarizer. Unpolarized light is incident on this series of polarizers. How many polarizers does the light have to go through before it is of its original intensity?

The wings of a certain beetle have a series of parallel lines across them. When normally incident 480-nm light is reflected from the wing, the wing appears bright when viewed at an angle of 56. How far apart are the lines?

A teacher stands well back from an outside doorway 0.88 m wide, and blows a whistle of frequency 950 Hz. Ignoring reflections, estimate at what angle(s) it is not possible to hear the whistle clearly on the playground outside the doorway. Assume for the speed of sound

Light is incident on a diffraction grating with and the pattern is viewed on a screen located 2.5 m from the grating. The incident light beam consists of two wavelengths, and Calculate the linear distance between the first-order bright fringes of these two wavelengths on the screen

How many slits per centimeter must a grating have if there is to be no second-order spectrum for any visible wavelength?

When yellow sodium light, falls on a diffraction grating, its first-order peak on a screen 72.0 cm away falls 3.32 cm from the central peak. Another source produces a line 3.71 cm from the central peak. What is its wavelength? How many are on the grating?

Two of the lines of the atomic hydrogen spectrum have wavelengths of 656 nm and 410 nm. If these fall at normal incidence on a grating with what will be the angular separation of the two wavelengths in the first-order spectrum?

A tungstenhalogen bulb emits a continuous spectrum of ultraviolet, visible, and infrared light in the wavelength range 360 nm to 2000 nm. Assume that the light from a tungstenhalogen bulb is incident on a diffraction grating with slit spacing d and that the first-order brightness maximum for the wavelength of 1200 nm occurs at angle What other wavelengths within the spectrum of incident light will produce a brightness maximum at this same angle [Optical filters are used to deal with this bothersome effect when a continuous spectrum of light is measured by a spectrometer.]

At what angle above the horizon is the Sun when light reflecting off a smooth lake is polarized most strongly?

Unpolarized light falls on two polarizer sheets whose axes are at right angles. (a) What fraction of the incident light intensity is transmitted? (b) What fraction is transmitted if a third polarizer is placed between the first two so that its axis makes a 56 angle with the axis of the first polarizer? (c) What if the third polarizer is in front of the other two?

At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the first Polaroid cuts it in half) of (a) 4, (b) 10, (c) 100?