Solved: Why does an oil slick show colored bands

A prism bends blue light more than red. Is the same true of a diffraction grating?

Why does an oil slick show colored bands?

Why does a soap bubble turn colorless just before it dries up and pops?

Why dont you see interference effects between the front and back of your eyeglasses?

You can hear around corners, but you cant see around corners. Why?

In deriving the intensity in double-slit interference, why cant you simply add the intensities from the two slits?

The primary maxima in multiple-slit interference are in the same angular positions as those in double-slit interference. Why, then, do diffraction gratings have thousands of slits instead of just two?

When the Moon passes in front of a star, the starlight intensity fluctuates before going to zero instead of dropping abruptly. Explain.

Sketch roughly the diffraction pattern you would expect for light passing through a square hole a few wavelengths wide.

A double-slit system is used to measure the wavelength of light. The system has slit spacing d = 15m and slit-to-screen distance L = 2.2m. If the m = 1 maximum in the interference pattern occurs 7.1 cm from screen center, whats the wavelength?

A double-slit experiment with d = 0.025mm and L = 75 cm uses 550-nm light. Find the spacing between adjacent bright fringes.

A double-slit experiment has slit spacing 0.12 mm. (a) What should be the slit-to-screen distance L if the bright fringes are to be 5.0 mm apart when the slits are illuminated with 633-nm laser light? (b) What will be the fringe spacing with 480-nm light?

The interference pattern from two slits separated by 0.37 mm has bright fringes with angular spacing 0.065. Find the lights wavelength.

The 546-nm green line of gaseous mercury falls on a double-slit apparatus. If the fifth dark fringe is at 0.113 from the centerline, whats the slit separation?

In a five-slit system, how many minima lie between the zerothorder and first-order maxima?

In a three-slit system, the first minimum occurs at angular position 5. Where is the next maximum?

A five-slit system with 7.5@m slit spacing is illuminated with 633-nm light. Find the angular positions of (a) the first two maxima and (b) the third and sixth minima.

Green light at 520 nm is diffracted by a grating with 3000 lines/cm. Through what angle is the light diffracted in (a) first and (b) fifth order?

Light is incident normally on a grating with 10,000 lines/cm. Find the maximum order in which (a) 450-nm and (b) 650-nm light will be visible

Find the second-order angular separation of the two wavelengths in Example 32.2.

Find the minimum thickness of a soap film 1n = 1.3332 in which 550-nm light will undergo constructive interference.

Light of unknown wavelength shines on a precisely machined glass wedge with refractive index 1.52. The closest point to the apex of the wedge where reflection is enhanced occurs where the wedge is 98 nm thick. Find the wavelength.

Monochromatic light shines on a glass wedge with refractive index 1.65, and enhanced reflection occurs where the wedge is 450 nm thick. Find all possible values for the wavelength in the visible range.

White light shines on a 75.0-nm-thick sliver of fluorite 1n = 1.432. What wavelength is most strongly reflected?

For the soap film described in Conceptual Example 32.1s Making the Connection, what portion of the film will appear dark when its illuminated with white light?

For what ratio of slit width to wavelength will the first minima of a single-slit diffraction pattern occur at {90 ?

Light with wavelength 633 nm is incident on a 2.50@m@wide slit. Find the angular width of the central peak in the diffraction pattern, taken as the angular separation between the first minima.

Youre inside a metal building that blocks radio waves, but youre trying to make a call with your cell phone, which broadcasts at a frequency of 950 MHz. Down the hall from you is a narrow window measuring 35 cm wide. Whats the horizontal angular width of the beam (i.e., the angle between the first minima) from your phone as it emerges from the window?

Find the intensity as a fraction of the central peak intensity for the second secondary maximum in single-slit diffraction, assuming the peak lies midway between the second and third minima.

Find the minimum angular separation resolvable with 633-nm laser light passing through a circular aperture of diameter 2.1 cm.

Find the minimum telescope aperture that could resolve an object with angular diameter 0.35 arcsecond, observed at 520-nm wavelength. (Note: 1 arcsec = 1/3600.)

Whats the longest wavelength of light you could use to resolve a structure with angular diameter 0.44 mrad, using a microscope with a 1.2-mm-diameter objective lens?

In bright light, the human eyes pupil diameter is about 2 mm. If diffraction were the limiting factor, whats the eyes minimum angular resolution under these conditions, assuming 550-nm light?

Find the angular position of the second-order bright fringe in a double- slit system whose slit spacing is 1.5m for (a) red light at 640 nm, (b) yellow light at 580 nm, and (c) violet light at 410 nm.

A double-slit experiment has slit spacing 0.035 mm, slit-toscreen distance 1.5 m, and wavelength 490 nm. Whats the phase difference between two waves arriving at a point 0.56 cm from the center line of the screen?

For a double-slit system with slit spacing 0.0525 mm and wavelength 633 nm, at what angular position is the path difference a quarter wavelength?

A screen 1.0 m wide is 2.0 m from a pair of slits illuminated by 633-nm laser light, with the screens center on the centerline of the slits. Find the highest-order bright fringe that will appear on the screen if the slit spacing is (a) 0.10 mm and (b) 10m.

A tube of glowing gas emits light at 550 nm and 400 nm. In a double-slit apparatus, whats the lowest-order 550-nm bright fringe that will fall on a 400-nm dark fringe, and what are the fringes corresponding orders?

On the screen of a multiple-slit system, the interference pattern shows bright maxima separated by 0.86 and seven minima between each bright maximum. (a) How many slits are there? (b) Whats the slit separation if the incident light has wavelength 656.3 nm?

Youre designing a spectrometer whose specifications call for a minimum of 5 separation between the red hydrogen@a line at 656 nm and the yellow sodium line at 589 nm when the two are observed in third order with a grating spectrometer. Available gratings have 2500 lines/cm, 3500 lines/cm, or 4500 lines/cm. Whats the coarsest grating you can use?

For visible light with wavelengths from 400 nm to 700 nm, show that the first-order spectrum is the only one that doesnt overlap with the next higher order

Find the total number of lines in a 2.5-cm-wide diffraction grating whose third-order spectrum puts the 656-nm hydrogen@a spectral line 37 from the central maximum.

What order is necessary to resolve 647.98-nm and 648.07-nm spectral lines using a 4500-line grating?

A thin film of toluene 1n = 1.492 floats on water. Find the minimum film thickness if the most strongly reflected light has wavelength 460 nm

NASA asks you to assess the feasibility of a single-mirror spacebased optical telescope that could resolve an Earth-size planet 5 light-years away. What do you conclude?

In the second-order spectrum from a diffraction grating, yellow light at 588 nm overlaps violet light (wavelength range 390 nm 450 nm) diffracted in a different order. Whats the exact wavelength of the violet light, and whats the order of its diffraction?

X-ray diffraction in potassium chloride (KCl) results in a firstorder maximum when 97-pm-wavelength X rays graze the crystal plane at 8.5. Find the spacing between crystal planes

As a soap bubble with n = 1.333 evaporates and thins, reflected colors gradually disappear. What are (a) the bubble thickness just as the last vestige of color vanishes and (b) the last color seen?

An oil film with refractive index 1.25 floats on water. The film thickness varies from 0.80m to 2.1m. If 630-nm light is incident normally on the film, at how many locations will it undergo enhanced reflection?

The table below lists the angular positions of the bright fringes that result when monochromatic laser light shines through a diffraction grating, as a function of order m. The spacing between lines of the grating is d = 3.2m. Determine a quantity that, when plotted against m, should give a straight line. Plot the data, determine a best-fit line, and use the result to find the wavelength of the light. Order, m 0 1 2 3 4 5 Angular position 0.0 9.2 22 30 48 64

Two perfectly flat glass plates are separated at one end by a sheet of paper 0.065 mm thick. 550-nm light illuminates the plates from above, as shown in Fig. 32.28. How many bright bands appear to an observer looking down on the plates?

An air wedge like that of Fig. 32.28 shows N bright bands when illuminated from above. Find an expression for the number of bands if the air is replaced by a liquid of refractive index n different from that of the glass

A Michelson interferometer uses light from glowing hydrogen at 486.1 nm. As you move one mirror, 530 bright fringes pass a fixed point in the viewer. How far did the mirror move?

Find the wavelength of light used in a Michelson interferometer if 550 bright fringes go by a fixed point when the mirror moves 0.150 mm.

One arm of a Michelson interferometer is 42.5 cm long and is enclosed in a box that can be evacuated. The box initially contains air, which is gradually pumped out. In the process, 388 bright fringes pass a point in the viewer. If the interferometer uses light with wavelength 641.6 nm, whats the airs refractive index?

Your stereo is in a dead spot caused by direct reception from an FM radio station at 89.5 MHz interfering with the signal reflecting off a wall behind you. How much farther from the wall should you move so that the interference is fully constructive?

A proposed star wars antimissile laser is to focus infrared light with 2.8@m wavelength to a 50-cm-diameter spot on a missile 2500 km distant. Find the minimum diameter for a concave mirror that can achieve this spot size, given the diffraction limit. (Your answer suggests one of many technical difficulties faced by antimissile defense systems.)

Suppose one of the 10-m-diameter Keck Telescopes in Hawaii is trained on San Francisco, 3400 km away. Assuming 550-nm light, and ignoring atmospheric distortion, would it be possible to read (a) newspaper headlines or (b) a billboard sign at this distance? (c) Repeat for the case of the Keck optical interferometer, formed from the two 10-m Keck Telescopes and several smaller ones, with a 50-m effective aperture

A camera has an f/1.4 lens, meaning the ratio of focal length to lens diameter is 1.4. Find the smallest spot diameter (i.e., the diameter of the first diffraction minimum) to which this lens can focus parallel light with 580-nm wavelength.

The CIA wants your help identifying individual terrorists in a photo of a training camp taken from a spy satellite at 100-km altitude. You ask for details of the optical system used, but theyre classified. However, they do tell you that the optics are diffraction limited and can resolve facial features as small as 5 cm. Assuming a typical optical wavelength of 550 nm, what do you conclude about the size of the mirror or lens in the satellite camera?

While driving at night, your eyes irises dilate to 3.1-mm diameter. If your vision were diffraction limited, what would be the greatest distance at which you could see as distinct the two headlights of an oncoming car, spaced 1.5 m apart? Take l = 550nm

Under the best conditions, atmospheric turbulence limits groundbased telescopes resolution to about 1 arcsecond (1/3600 of a degree). For what apertures is this limitation more severe than that of diffraction at 550 nm? (Your answer shows why large ground-based telescopes dont generally produce better images than small ones, although they do gather more light.)

Youre a biologist studying rhinoviruses, which cause the common cold. These are among the smallest viruses, some 50 nm in diameter, and you cant image them with your optical microscope using visible light (average wavelength about 560 nm). A sales rep tries to sell you an expensive microscope using 280-nm ultraviolet light, saying it will resolve structures half the size thats resolvable with your current microscope. Is the rep correct? Will the new microscope resolve your rhinoviruses?

An air wedge like that of Fig. 32.28 displays 10,003 bright bands when illuminated from above. If the region between the plates is then evacuated, the number of bands drops to 10,000. Find the refractive index of the air.

A thin-walled glass tube of length L containing a gas of unknown refractive index is placed in one arm of a Michelson interferometer using light of wavelength l. The tube is then evacuated. During the process, m bright fringes pass a fixed point in the viewer. Find an expression for the refractive index of the gas.

Light is incident on a diffraction grating at angle a to the normal. Show that the condition for maximum light intensity becomes d1sin u{sina2 = ml.

An arrangement known a s L l o y d s m i r r o r (Fig. 32.29) allows interference between direct and reflected beams from the same source. Find an expression for the separation of bright fringes on the screen, given the distances d and D and the lights wavelength l.

The intensity of the single-slit diffraction pattern can be calculated by summing the amplitudes of infinitely many field amplitudes corresponding to waves from every infinitesimal part of the slit. (a) Referring to Fig. 32.20, show that the field from an element of slit width dy, a distance y from the bottom edge of the slit, is dE = 1Epdy/a2 sin1vt + f1y22, where f1y2 = 12py/l2 sin u. (b) Integrate dE over the entire slit from y = 0 to y = a, and use trig identities from Appendix A, to find the total amplitude and from there show that the average intensity is given by Equation 32.10.

Youre on an international panel charged with allocating real estate for communications satellites in geostationary orbit. The panel needs to know how many satellites could fit in geostationary orbit without receivers on the ground picking up multiple signals. Assume all satellites broadcast at 12 GHz and that receiver dishes are 45 cm in diameter. Begin by calculating the angular size of the beam associated with such a receiver dish, defined as the full width of its central diffraction peak. Use your result to find the number of satellites allowed in geostationary orbit if each receiver dish is to see just one satellite. (Hint: Consult Example 8.3.)

Youre investigating an oil spill for your state environmental protection agency. Theres a thin film of oil on water, and you know its refractive index is noil = 1.38. You shine white light vertically on the oil, and use a spectrometer to determine that the most strongly reflected wavelength is 580 nm. Assuming firstorder thin-film interference, what do you report for the thickness of the oil slick?

If the separation of two telescopes comprising an interferometer is doubled, the angular separation between two sources just barely resolvable by the interferometer will a. not change. b. decrease by a factor of 1/12. c. halve. d. double

If the separation of two telescopes comprising an interferometer is doubled, the instruments light-collecting power will a. not change. b. increase by a factor of 12. c. double. d. quadruple.

If a point source is located directly above a two-telescope interferometer, on the perpendicular bisector of the line joining the telescopes (source 1 in Fig. 32.30), electromagnetic waves reaching the two will be a. in phase. b. out of phase by 45. c. out of phase by 90. d. you cant tell without further information

If a point source is located on a line at 45 to the line joining the two telescopes (source 2 in Fig. 32.30), electromagnetic waves reaching the two will be a. in phase. b. out of phase by 45. c. out of phase by 90. d. you cant tell without further information