Moving mirror M2 of a Michelson interferometer a distance

What is light?

What is diffraction?

Does light exhibit interference?

What is a diffraction grating?

How is interference used?

Suppose the viewing screen in Figure 33.4 is moved closer to the double slit. What happens to the interference fringes? a. They get brighter but otherwise do not change. b. They get brighter and closer together. c. They get brighter and farther apart. d. They get out of focus. e. They fade out and disappear

A double-slit interference pattern is observed on a screen 1.0 m behind two slits spaced 0.30 mm apart. Ten bright fringes span a distance of 1.7 cm. What is the wavelength of the light?

Light of wavelength l1 illuminates a double slit, and interference fringes are observed on a screen behind the slits. When the wavelength is changed to l2, the fringes get closer together. Is l2 larger or smaller than l1?

Light from a sodium lamp passes through a diffraction grating having 1000 slits per millimeter. The interference pattern is viewed on a screen 1.000 m behind the grating. Two bright yellow fringes are visible 72.88 cm and 73.00 cm from the central maximum. What are the wavelengths of these two fringes?

White light passes through a diffraction grating and forms rainbow patterns on a screen behind the grating. For each rainbow, a. The red side is on the right, the violet side on the left. b. The red side is on the left, the violet side on the right. c. The red side is closest to the center of the screen, the violet side is farthest from the center. d. The red side is farthest from the center of the screen, the violet side is closest to the center.

Light from a helium-neon laser 1l = 633 nm2 passes through a narrow slit and is seen on a screen 2.0 m behind the slit. The first minimum in the diffraction pattern is 1.2 cm from the central maximum. How wide is the slit?

Light passes through a 0.12-mm-wide slit and forms a diffraction pattern on a screen 1.00 m behind the slit. The width of the central maximum is 0.85 cm. What is the wavelength of the light?

The figure shows two single-slit diffraction patterns. The distance between the slit and the viewing screen is the same in both cases. Which of the following (perhaps more than one) could be true? a. The slits are the same for both; l1 7 l2. b. The slits are the same for both; l2 7 l1. c. The wavelengths are the same for both; a1 7 a2. d. The wavelengths are the same for both; a2 7 a1. e. The slits and the wavelengths are the same for both; p1 7 p2. f. The slits and the wavelengths are the same for both; p2 7 p1.

Light with a wavelength of 500 nm passes through a 150@mm@wide slit and is viewed on a screen 2.5 m behind the slit. At what distance from the center of the diffraction pattern is the intensity 50% of maximum?

A Michelson interferometer using light of wavelength l has been adjusted to produce a bright spot at the center of the interference pattern. Mirror M1 is then moved distance l toward the beam splitter while M2 is moved distance l away from the beam splitter. How many bright-dark-bright fringe shifts are seen? a. 0 b. 1 c. 2 d. 4 e. 8 f. Its not possible to say without knowing l.

Light from a helium-neon laser 1l = 633 nm2 passes through a 0.50-mm-diameter hole. How far away should a viewing screen be placed to observe a diffraction pattern whose central maximum is 3.0 mm in diameter?

An experimenter uses a Michelson interferometer to measure one of the wavelengths of light emitted by neon atoms. She slowly moves mirror M2 until 10,000 new bright central spots have appeared. (In a modern experiment, a photodetector and computer would eliminate the possibility of experimenter error while counting.) She then measures that the mirror has m

A Michelson interferometer uses a helium-neon laser with wavelength lvac = 633 nm. In one arm, the light passes through a 4.00-cm-thick glass cell. Initially the cell is evacuated, and the interferometer is adjusted so that the central spot is a bright fringe. The cell is then slowly filled to atmospheric pressure with a gas. As the cell fills, 43 bright-dark-bright fringe shifts are seen and counted. What is the index of refraction of the gas at this wavelength?

FIGURE Q33.1 shows light waves passing through two closely spaced, narrow slits. The graph shows the intensity of light on a screen behind the slits. Reproduce these graph axes, including the zero and the tick marks locating the double-slit fringes, then draw a graph to show how the light-intensity pattern will appear if the right slit is blocked, allowing light to go through only the left slit. Explain your reasoning.

In a double-slit interference experiment, which of the following actions (perhaps more than one) would cause the fringe spacing to increase? (a) Increasing the wavelength of the light. (b) Increasing the slit spacing. (c) Increasing the distance to the viewing screen. (d) Submerging the entire experiment in water

FIGURE Q33.3 shows the viewing screen in a double-slit experiment. Fringe C is the central maximum. What will happen to the fringe spacing if a. The wavelength of the light is decreased? b. The spacing between the slits is decreased? c. The distance to the screen is decreased? d. Suppose the wavelength of the light is 500 nm. How much farther is it from the dot on the screen in the center of fringe E to the left slit than it is from the dot to the right slit?

FIGURE Q33.3 is the interference pattern seen on a viewing screen behind 2 slits. Suppose the 2 slits were replaced by 20 slits having the same spacing d between adjacent slits. a. Would the number of fringes on the screen increase, decrease, or stay the same? b. Would the fringe spacing increase, decrease, or stay the same? c. Would the width of each fringe increase, decrease, or stay the same? d. Would the brightness of each fringe increase, decrease, or stay the same?

FIGURE Q33.5 shows the light intensity on a viewing screen behind a single slit of width a. The lights wavelength is l. Is l 6 a, l = a, l 7 a, or is it not possible to tell? Explain.

FIGURE Q33.6 shows the light intensity on a viewing screen behind a circular aperture. What happens to the width of the central maximum if a. The wavelength of the light is increased? b. The diameter of the aperture is increased? c. How will the screen appear if the aperture diameter is less than the light wavelength?

Narrow, bright fringes are observed on a screen behind a diffraction grating. The entire experiment is then immersed in water. Do the fringes on the screen get closer together, get farther apart, remain the same, or disappear? Explain

a. Green light shines through a 100-mm-diameter hole and is observed on a screen. If the hole diameter is increased by 20%, does the circular spot of light on the screen decrease in diameter, increase in diameter, or stay the same? Explain. b. Green light shines through a 100@mm-diameter hole and is observed on a screen. If the hole diameter is increased by 20%, does the circular spot of light on the screen decrease in diameter, increase in diameter, or stay the same? Explain

A Michelson interferometer using 800 nm light is adjusted to have a bright central spot. One mirror is then moved 200 nm forward, the other 200 nm back. Afterward, is the central spot bright, dark, or in between? Explain.

A Michelson interferometer is set up to display constructive interference (a bright central spot in the fringe pattern of Figure 33.25) using light of wavelength l. If the wavelength is changed to l/2, does the central spot remain bright, does the central spot become dark, or do the fringes disappear? Explain. Assume the fringes are viewed by a detector sensitive to both wavelengths.

A double slit is illuminated simultaneously with orange light of wavelength 620 nm and light of an unknown wavelength. The m = 4 bright fringe of the unknown wavelength overlaps the m = 3 bright orange fringe. What is the unknown wavelength?

Two narrow slits 80 mm apart are illuminated with light of wavelength 620 nm. What is the angle of the m = 3 bright fringe in radians? In degrees?

A double-slit experiment is performed with light of wavelength 630 nm. The bright interference fringes are spaced 1.8 mm apart on the viewing screen. What will the fringe spacing be if the light is changed to a wavelength of 420 nm?

Light of wavelength 550 nm illuminates a double slit, and the interference pattern is observed on a screen. At the position of the m = 2 bright fringe, how much farther is it to the more distant slit than to the nearer slit?

Light of 630 nm wavelength illuminates two slits that are 0.25 mm apart. FIGURE EX33.5 shows the intensity pattern seen on a screen behind the slits. What is the distance to the screen?

In a double-slit experiment, the slit separation is 200 times the wavelength of the light. What is the angular separation (in degrees) between two adjacent bright fringes?

Light from a sodium lamp 1l = 589 nm2 illuminates two narrow slits. The fringe spacing on a screen 150 cm behind the slits is 4.0 mm. What is the spacing (in mm) between the two slits?

A double-slit interference pattern is created by two narrow slits spaced 0.25 mm apart. The distance between the first and the fifth minimum on a screen 60 cm behind the slits is 5.5 mm. What is the wavelength (in nm) of the light used in this experiment?

The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656 nm (red) and 486 nm (blue). Light from a hydrogen lamp illuminates a diffraction grating with 500 lines/mm, and the light is observed on a screen 1.50 m behind the grating. What is the distance between the first-order red and blue fringes?

A helium-neon laser 1l = 633 nm2 illuminates a diffraction grating. The distance between the two m = 1 bright fringes is 32 cm on a screen 2.0 m behind the grating. What is the spacing between slits of the grating?

In a single-slit experiment, the slit width is 200 times the wavelength of the light. What is the width (in mm) of the central maximum on a screen 2.0 m behind the slit?

A helium-neon laser 1l = 633 nm2 illuminates a single slit and is observed on a screen 1.5 m behind the slit. The distance between the first and second minima in the diffraction pattern is 4.75 mm. What is the width (in mm) of the slit?

Light of 630 nm wavelength illuminates a single slit of width 0.15 mm. FIGURE EX33.17 shows the intensity pattern seen on a screen behind the slit. What is the distance to the screen?

A 0.50-mm-wide slit is illuminated by light of wavelength 500 nm. What is the width (in mm) of the central maximum on a screen 2.0 m behind the slit?

You need to use your cell phone, which broadcasts an 800 MHz signal, but youre behind two massive, radio-waveabsorbing buildings that have only a 15 m space between them. What is the angular width, in degrees, of the electromagnetic wave after it emerges from between the buildings?

For what slit-width-to-wavelength ratio does the first minimum of a single-slit diffraction pattern appear at (a) 30, (b) 60, and (c) 90?

Light from a helium-neon laser 1l = 633 nm2 is incident on a single slit. What is the largest slit width for which there are no minima in the diffraction pattern?

A laser beam illuminates a single, narrow slit, and the diffraction pattern is observed on a screen behind the slit. The first secondary maximum is 26 mm from the center of the diffraction pattern. How far is the first minimum from the center of the diffraction pattern?

Two 50@mm@wide slits spaced 0.25 mm apart are illuminated by blue laser light with a wavelength of 450 nm. The interference pattern is observed on a screen 2.0 m behind the slits. How many bright fringes are seen in the central maximum that spans the distance between the first missing order on one side and the first missing order on the other side?

A laser beam with a wavelength of 480 nm illuminates two 0.12-mm-wide slits separated by 0.30 mm. The interference pattern is observed on a screen 2.3 m behind the slits. What is the light intensity, as a fraction of the maximum intensity I0, at a point halfway between the center and the first minimum?

A 0.50-mm-diameter hole is illuminated by light of wavelength 550 nm. What is the width (in mm) of the central maximum on a screen 2.0 m behind the slit?

Infrared light of wavelength 2.5 mm illuminates a 0.20-mmdiameter hole. What is the angle of the first dark fringe in radians? In degrees?

You want to photograph a circular diffraction pattern whose central maximum has a diameter of 1.0 cm. You have a heliumneon laser 1l = 633 nm2 and a 0.12-mm-diameter pinhole. How far behind the pinhole should you place the screen thats to be photographed?

Your artist friend is designing an exhibit inspired by circularaperture diffraction. A pinhole in a red zone is going to be illuminated with a red laser beam of wavelength 670 nm, while a pinhole in a violet zone is going to be illuminated with a violet laser beam of wavelength 410 nm. She wants all the diffraction patterns seen on a distant screen to have the same size. For this to work, what must be the ratio of the red pinholes diameter to that of the violet pinhole?

Light from a helium-neon laser 1l = 633 nm2 passes through a circular aperture and is observed on a screen 4.0 m behind the aperture. The width of the central maximum is 2.5 cm. What is the diameter (in mm) of the hole?

A Michelson interferometer uses red light with a wavelength of 656.45 nm from a hydrogen discharge lamp. How many brightdark-bright fringe shifts are observed if mirror M2 is moved exactly 1 cm?

Moving mirror M2 of a Michelson interferometer a distance of 100 mm causes 500 bright-dark-bright fringe shifts. What is the wavelength of the light?

A Michelson interferometer uses light from a sodium lamp. Sodium atoms emit light having wavelengths 589.0 nm and 589.6 nm. The interferometer is initially set up with both arms of equal length 1L1 = L22, producing a bright spot at the center of the interference pattern. How far must mirror M2 be moved so that one wavelength has produced one more new maximum than the other wavelength?

FIGURE P33.33 shows the light intensity on a screen 2.5 m behind an aperture. The aperture is illuminated with light of wavelength 620 nm. a. Is the aperture a single slit or a double slit? Explain. b. If the aperture is a single slit, what is its width? If it is a double slit, what is the spacing between the slits?

FIGURE P33.34 shows the light intensity on a screen 2.5 m behind an aperture. The aperture is illuminated with light of wavelength 620 nm. a. Is the aperture a single slit or a double slit? Explain. b. If the aperture is a single slit, what is its width? If it is a double slit, what is the spacing between the slits?

Light from a helium-neon laser 1l = 633 nm2 is used to illuminate two narrow slits. The interference pattern is observed on a screen 3.0 m behind the slits. Twelve bright fringes are seen, spanning a distance of 52 mm. What is the spacing (in mm) between the slits?

FIGURE P33.36 shows the light intensity on a screen behind a double slit. The slit spacing is 0.20 mm and the wavelength of the light is 620 nm. What is the distance from the slits to the screen?

FIGURE P33.36 shows the light intensity on a screen behind a double slit. The slit spacing is 0.20 mm and the screen is 2.0 m behind the slits. What is the wavelength (in nm) of the light?

FIGURE P33.36 shows the light intensity on a screen behind a double slit. Suppose one slit is covered. What will be the light intensity at the center of the screen due to the remaining slit?

A diffraction grating having 500 lines/mm diffracts visible light at 30. What is the lights wavelength?

Helium atoms emit light at several wavelengths. Light from a helium lamp illuminates a diffraction grating and is observed on a screen 50.00 cm behind the grating. The emission at wavelength 501.5 nm creates a first-order bright fringe 21.90 cm from the central maximum. What is the wavelength of the bright fringe that is 31.60 cm from the central maximum?

A triple-slit experiment consists of three narrow slits, equally spaced by distance d and illuminated by light of wavelength l. Each slit alone produces intensity I1 on the viewing screen at distance L. a. Consider a point on the distant viewing screen such that the path-length difference between any two adjacent slits is l. What is the intensity at this point? b. What is the intensity at a point where the path-length difference between any two adjacent slits is l/2?

Because sound is a wave, its possible to make a diffraction grating for sound from a large board of sound-absorbing material with several parallel slits cut for sound to go through. When 10 kHz sound waves pass through such a grating, listeners 10 m from the grating report loud spots 1.4 m on both sides of center. What is the spacing between the slits? Use 340 m/s for the speed of sound.

A diffraction grating with 600 lines/mm is illuminated with light of wavelength 510 nm. A very wide viewing screen is 2.0 m behind the grating. a. What is the distance between the two m = 1 bright fringes? b. How many bright fringes can be seen on the screen?

A 500 line/mm diffraction grating is illuminated by light of wavelength 510 nm. How many bright fringes are seen on a 2.0-m-wide screen located 2.0 m behind the grating?

White light (400700 nm) incident on a 600 line/mm diffraction grating produces rainbows of diffracted light. What is the width of the first-order rainbow on a screen 2.0 m behind the grating?

A chemist identifies compounds by identifying bright lines in their spectra. She does so by heating the compounds until they glow, sending the light through a diffraction grating, and measuring the positions of first-order spectral lines on a detector 15.0 cm behind the grating. Unfortunately, she has lost the card that gives the specifications of the grating. Fortunately, she has a known compound that she can use to calibrate the grating. She heats the known compound, which emits light at a wavelength of 461 nm, and observes a spectral line 9.95 cm from the center of the diffraction pattern. What are the wavelengths emitted by compounds A and B that have spectral lines detected at positions 8.55 cm and 12.15 cm, respectively?

a. Find an expression for the positions y1 of the first-order fringes of a diffraction grating if the line spacing is large enough for the small-angle approximation tan u sin u u to be valid. Your expression should be in terms of d, L, and l. b. Use your expression from part a to find an expression for the separation y on the screen of two fringes that differ in wavelength by l. c. Rather than a viewing screen, modern spectrometers use detectorssimilar to the one in your digital camerathat are divided into pixels. Consider a spectrometer with a 333 line/mm grating and a detector with 100 pixels/mm located 12 cm behind the grating. The resolution of a spectrometer is the smallest wavelength separation lmin that can be measured reliably. What is the resolution of this spectrometer for wavelengths near 550 nm, in the center of the visible spectrum? You can assume that the fringe due to one specific wavelength is narrow enough to illuminate only one column of pixels

For your science fair project you need to design a diffraction grating that will disperse the visible spectrum (400700 nm) over 30.0 in first order. a. How many lines per millimeter does your grating need? b. What is the first-order diffraction angle of light from a sodium lamp 1l = 589 nm2?

FIGURE P33.49 shows the interference pattern on a screen 1.0 m behind an 800 line/mm diffraction grating. What is the wavelength (in nm) of the light?

The wings of some beetles have closely spaced parallel lines of melanin, causing the wing to act as a reflection grating. Suppose sunlight shines straight onto a beetle wing. If the melanin lines on the wing are spaced 2.0 mm apart, what is the first-order diffraction angle for green light 1l = 550 nm2?

If sunlight shines straight onto a peacock feather, the feather appears bright blue when viewed from 15 on either side of the incident beam of light. The blue color is due to diffraction from parallel rods of melanin in the feather barbules, as was shown in the photograph on page 940. Other wavelengths in the incident light are diffracted at different angles, leaving only the blue light to be seen. The average wavelength of blue light is 470 nm. Assuming this to be the first-order diffraction, what is the spacing of the melanin rods in the feather?

Youve found an unlabeled diffraction grating. Before you can use it, you need to know how many lines per mm it has. To find out, you illuminate the grating with light of several different wavelengths and then measure the distance between the two first-order bright fringes on a viewing screen 150 cm behind the grating. Your data are as follows: Wavelength (nm) Distance (cm) 430 109.6 480 125.4 530 139.8 580 157.2 630 174.4 680 194.8 Use the best-fit line of an appropriate graph to determine the number of lines per mm.

A diffraction grating has slit spacing d. Fringes are viewed on a screen at distance L. Find an expression for the wavelength of light that produces a first-order fringe on the viewing screen at distance L from the center of the screen

FIGURE P33.56 shows the light intensity on a screen behind a single slit. The slit width is 0.20 mm and the screen is 1.5 m behind the slit. What is the wavelength (in nm) of the light?

FIGURE P33.56 shows the light intensity on a screen behind a single slit. The wavelength of the light is 600 nm and the slit width is 0.15 mm. What is the distance from the slit to the screen?

FIGURE P33.56 shows the light intensity on a screen behind a circular aperture. The wavelength of the light is 500 nm and the screen is 1.0 m behind the slit. What is the diameter (in mm) of the aperture?

A student performing a double-slit experiment is using a green laser with a wavelength of 530 nm. She is confused when the m = 5 maximum does not appear. She had predicted that this bright fringe would be 1.6 cm from the central maximum on a screen 1.5 m behind the slits. a. Explain what prevented the fifth maximum from being observed. b. What is the width of her slits?

Scientists shine a laser beam on a 35@mm@wide slit and produce a diffraction pattern on a screen 70 cm behind the slit. Careful measurements show that the intensity first falls to 25% of maximum at a distance of 7.2 mm from the center of the diffraction pattern. What is the wavelength of the laser light? Hint: Use the trial-and-error technique demonstrated in Example 33.5 to solve the transcendental equation

Light from a helium-neon laser 1l = 633 nm2 illuminates a circular aperture. It is noted that the diameter of the central maximum on a screen 50 cm behind the aperture matches the diameter of the geometric image. What is the apertures diameter (in mm)?

A helium-neon laser 1l = 633 nm2 is built with a glass tube of inside diameter 1.0 mm, as shown in FIGURE P33.62. One mirror is partially transmitting to allow the laser beam out. An electrical discharge in the tube causes it to glow like a neon light. From an optical perspective, the laser beam is a light wave that diffracts out through a 1.0-mm-diameter circular opening. a. Can a laser beam be perfectly parallel, with no spreading? Why or why not? b. The angle u1 to the first minimum is called the divergence angle of a laser beam. What is the divergence angle of this laser beam? c. What is the diameter (in mm) of the laser beam after it travels 3.0 m? d. What is the diameter of the laser beam after it travels 1.0 km?

One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch of light on the far wall. Having recently studied optics in your physics class, youre not too surprised to see that the patch of light seems to be a circular diffraction pattern. It appears that the central maximum is about 1 cm across, and you estimate that the distance from the window shade to the wall is about 3 m. Estimate (a) the average wavelength of the sunlight (in nm) and (b) the diameter of the pinhole (in mm).

A radar for tracking aircraft broadcasts a 12 GHz microwave beam from a 2.0-m-diameter circular radar antenna. From a wave perspective, the antenna is a circular aperture through which the microwaves diffract. a. What is the diameter of the radar beam at a distance of 30 km? b. If the antenna emits 100 kW of power, what is the average microwave intensity at 30 km?

Scientists use laser range-finding to measure the distance to the moon with great accuracy. A brief laser pulse is fired at the moon, then the time interval is measured until the echo is seen by a telescope. A laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. In order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0 km in diameter. Staying within this diameter is accomplished by using a special largediameter laser. If l = 532 nm, what is the minimum diameter of the circular opening from which the laser beam emerges? The earth-moon distance is 384,000 km

Light of wavelength 600 nm passes though two slits separated by 0.20 mm and is observed on a screen 1.0 m behind the slits. The location of the central maximum is marked on the screen and labeled y = 0. a. At what distance, on either side of y = 0, are the m = 1 bright fringes? b. A very thin piece of glass is then placed in one slit. Because light travels slower in glass than in air, the wave passing through the glass is delayed by 5.0 * 10-16 s in comparison to the wave going through the other slit. What fraction of the period of the light wave is this delay? c. With the glass in place, what is the phase difference f0 between the two waves as they leave the slits? d. The glass causes the interference fringe pattern on the screen to shift sideways. Which way does the central maximum move (toward or away from the slit with the glass) and by how far?

A 600 line/mm diffraction grating is in an empty aquarium tank. The index of refraction of the glass walls is nglass = 1.50. A helium-neon laser 1l = 633 nm2 is outside the aquarium. The laser beam passes through the glass wall and illuminates the diffraction grating. a. What is the first-order diffraction angle of the laser beam? b. What is the first-order diffraction angle of the laser beam after the aquarium is filled with water 1nwater = 1.332?

A Michelson interferometer operating at a 600 nm wavelength has a 2.00-cm-long glass cell in one arm. To begin, the air is pumped out of the cell and mirror M2 is adjusted to produce a bright spot at the center of the interference pattern. Then a valve is opened and air is slowly admitted into the cell. The index of refraction of air at 1.00 atm pressure is 1.00028. How many brightdark-bright fringe shifts are observed as the cell fills with air?

Optical computers require microscopic optical switches to turn signals on and off. One device for doing so, which can be implemented in an integrated circuit, is the Mach-Zender interferometer seen in FIGURE P33.69. Light from an on-chip infrared laser 1l = 1.000 mm2 is split into two waves that travel equal distances around the arms of the interferometer. One arm passes through an electro-optic crystal, a transparent material that can change its index of refraction in response to an applied voltage. Suppose both arms are exactly the same length and the crystals index of refraction with no applied voltage is 1.522. a. With no voltage applied, is the output bright (switch closed, optical signal passing through) or dark (switch open, no signal)? Explain. b. What is the first index of refraction of the electro-optic crystal larger than 1.522 that changes the optical switch to the state opposite the state you found in part a?

To illustrate one of the ideas of holography in a simple way, consider a diffraction grating with slit spacing d. The small-angle approximation is usually not valid for diffraction gratings, because d is only slightly larger than l, but assume that the l/d ratio of this grating is small enough to make the small-angle approximation valid. a. Use the small-angle approximation to find an expression for the fringe spacing on a screen at distance L behind the grating. b. Rather than a screen, suppose you place a piece of film at distance L behind the grating. The bright fringes will expose the film, but the dark spaces in between will leave the film unexposed. After being developed, the film will be a series of alternating light and dark stripes. What if you were to now play the film by using it as a diffraction grating? In other words, what happens if you shine the same laser through the film and look at the films diffraction pattern on a screen at the same distance L? Demonstrate that the films diffraction pattern is a reproduction of the original diffraction grating.

A double-slit experiment is set up using a helium-neon laser 1l = 633 nm2. Then a very thin piece of glass 1n = 1.502 is placed over one of the slits. Afterward, the central point on the screen is occupied by what had been the m = 10 dark fringe. How thick is the glass?

The intensity at the central maximum of a double-slit interference pattern is 4I1. The intensity at the first minimum is zero. At what fraction of the distance from the central maximum to the first minimum is the intensity I1? Assume an ideal double slit.

FIGURE CP33.73 shows two nearly overlapped intensity peaks of the sort you might produce with a diffraction grating (see Figure 33.9b). As a practical matter, two peaks can just barely be resolved if their spacing y equals the width w of each peak, where w is measured at half of the peaks height. Two peaks closer together than w will merge into a single peak. We can use this idea to understand the resolution of a diffraction grating. a. In the small-angle approximation, the position of the m = 1 peak of a diffraction grating falls at the same location as the m = 1 fringe of a double slit: y1 = lL/d. Suppose two wavelengths differing by l pass through a grating at the same time. Find an expression for y, the separation of their first-order peaks. b. We noted that the widths of the bright fringes are proportional to 1/N, where N is the number of slits in the grating. Lets hypothesize that the fringe width is w = y1/N. Show that this is true for the double-slit pattern. Well then assume it to be true as N increases. c. Use your results from parts a and b together with the idea that ymin = w to find an expression for lmin, the minimum wavelength separation (in first order) for which the diffraction fringes can barely be resolved. d. Ordinary hydrogen atoms emit red light with a wavelength of 656.45 nm. In deuterium, which is a heavy isotope of hydrogen, the wavelength is 656.27 nm. What is the minimum number of slits in a diffraction grating that can barely resolve these two wavelengths in the first-order diffraction pattern?

FIGURE CP33.74 shows light of wavelength l incident at angle f on a reflection grating of spacing d. We want to find the angles um at which constructive interference occurs. a. The figure shows paths 1 and 2 along which two waves travel and interfere. Find an expression for the path-length difference r = r2 - r1. b. Using your result from part a, find an equation (analogous to Equation 33.15) for the angles um at which diffraction occurs when the light is incident at angle f. Notice that m can be a negative integer in your expression, indicating that path 2 is shorter than path 1. c. Show that the zeroth-order diffraction is simply a reflection. That is, u0 = f. d. Light of wavelength 500 nm is incident at f = 40 on a reflection grating having 700 reflection lines/mm. Find all angles um at which light is diffracted. Negative values of um are interpreted as an angle left of the vertical. e. Draw a picture showing a single 500 nm light ray incident at f = 40 and showing all the diffracted waves at the correct angles.

The pinhole camera of FIGURE CP33.75 images distant objects by allowing only a narrow bundle of light rays to pass through the hole and strike the film. If light consisted of particles, you could make the image sharper and sharper (at the expense of getting dimmer and dimmer) by making the aperture smaller and smaller. In practice, diffraction of light by the circular aperture limits the maximum sharpness that can be obtained. Consider two distant points of light, such as two distant streetlights. Each will produce a circular diffraction pattern on the film. The two images can just barely be resolved if the central maximum of one image falls on the first dark fringe of the other image. (This is called Rayleighs criterion, and we will explore its implication for optical instruments in Chapter 35.) a. Optimum sharpness of one image occurs when the diameter of the central maximum equals the diameter of the pinhole. What is the optimum hole size for a pinhole camera in which the film is 20 cm behind the hole? Assume l = 550 nm, an average value for visible light. b. For this hole size, what is the angle a (in degrees) between two distant sources that can barely be resolved? c. What is the distance between two street lights 1 km away that can barely be resolved?

A double-slit interference pattern is observed on a screen 1.0 m behind two slits spaced 0.30 mm apart. Ten bright fringes span a distance of 1.7 cm. What is the wavelength of the light?

Light from a sodium lamp passes through a diffraction grating having 1000 slits per millimeter. The interference pattern is viewed on a screen 1.000 m behind the grating. Two bright yellow fringes are visible 72.88 cm and 73.00 cm from the central maximum. What are the wavelengths of these two fringes?

Light from a helium-neon laser 1l = 633 nm2 passes through a narrow slit and is seen on a screen 2.0 m behind the slit. The first minimum in the diffraction pattern is 1.2 cm from the central maximum. How wide is the slit?

The figure shows two single-slit diffraction patterns. The distance between the slit and the viewing screen is the same in both cases. Which of the following (perhaps more than one) could be true? a. The slits are the same for both; l1 7 l2. b. The slits are the same for both; l2 7 l1. c. The wavelengths are the same for both; a1 7 a2. d. The wavelengths are the same for both; a2 7 a1. e. The slits and the wavelengths are the same for both; p1 7 p2. f. The slits and the wavelengths are the same for both; p2 7 p1.

A Michelson interferometer using light of wavelength l has been adjusted to produce a bright spot at the center of the interference pattern. Mirror M1 is then moved distance l toward the beam splitter while M2 is moved distance l away from the beam splitter. How many bright-dark-bright fringe shifts are seen? a. 0 b. 1 c. 2 d. 4 e. 8 f. Its not possible to say without knowing l.