A double-slit interference experiment shows fringes on a

Problem 1CQ The frequency of a light wave in air is . Is the frequency of this wave higher, lower, or the same after the light enters a piece of glass?

Problem 1P a. How long does it take light to travel through a 3.0-mmthick piece of window glass? b. Through what thickness of water could light travel in the same amount of time?

Problem 2CQ Rank in order the following according to their speeds, from slowest to fastest: (i) 425-nm-wavelength light through a pane of glass, (ii) 500-nm-wavelength light through air, (iii) 540-nmwavelength light through water, (iv) 670-nm-wavelength light through a diamond, and (v) 670-nm-wavelength light through a vacuum.

Problem 2P a. How long (in ns) does it take light to travel 1.0 m in a vacuum? b. What distance does light travel in water, glass, and diamond during the time that it travels 1.0 m in a vacuum?

Problem 3CQ The wavelength of a light wave is 700 nm in air; this light appears red. If this wave enters a pool of water, its wavelength becomes . If you were swimming underwater, the light would still appear red. Given this, what property of a wave determines its color?

Problem 3P A 5.0-cm-thick layer of oil (n = 1.46) is sandwiched between a 1.0-cm-thick sheet of glass and a 2.0-cm-thick sheet of polystyrene plastic (n = 1.59) . How long (in ns) does it take light incident perpendicular to the glass to pass through this 8.0-cmthick sandwich?

Problem 4CQ A double-slit interference experiment shows fringes on a screen. The entire experiment is then immersed in water. Do the fringes on the screen get closer together, farther apart, remain the same, or disappear entirely? Explain.

Problem 4P A light wave has a 670 nm wavelength in air. Its wavelength in a transparent solid is 420 nm. a. What is the speed of light in this solid? b. What is the light’s frequency in the solid?

Problem 5CQ Figure Q17.5 shows the fringes observed in a double-slit interference experiment when the two slits are illuminated by white light. The central maximum is white, but as we move away from the central maximum, the fringes become less distinct and more colorful. What is special about the central maximum that makes it white? Explain the presence of colors in the outlying fringes.

Problem 5P How much time does it take a pulse of light to travel through 150 m of water?

Problem 6CQ In a double-slit interference experiment, interference fringes are observed on a distant screen. The width of both slits is then doubled without changing the distance between their centers. a. What happens to the spacing of the fringes? Explain. b. What happens to the intensity of the bright fringes? Explain.

Problem 6P A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.38 ns for the light to travel through 30.0 cm of an unknown liquid. What is the wavelength of the laser beam in the liquid?

Problem 7P Two narrow slits 50 ?m apart are illuminated with light of wavelength 500 nm. What is the angle of the m = 2 bright fringe in radians? In degrees?

Problem 7CQ Figure Q17.7 shows the viewing screen in a double-slit experiment with monochromatic light. Fringe C is the central maximum. a. What will happen to the fringe spacing if the wavelength of the light is decreased? b. What will happen to the fringe spacing if the spacing between the slits is decreased? c. What will happen to the fringe spacing if 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?

Problem 8CQ Figure Q17.7 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?

Problem 8P Light from a sodium lamp (l = 589 nm) 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?

Problem 9CQ Figure Q17.9 shows the light intensity on a viewing screen behind a single slit of width a . The light’s wavelength is ??. Is ?? < a, ?? = a, ?? > a, or is it not possible to tell? Explain.

Problem 9P Two narrow slits are illuminated by light of wavelength l . The slits are spaced 20 wavelengths apart. What is the angle, in radians, between the central maximum and the m = 1 bright fringe?

Problem 10CQ Figure Q17.10 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 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?

Problem 10P A double-slit experiment is performed with light of wavelength 600 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 400 nm?

Problem 11CQ Why does light reflected from peacock feathers change color when you sce the feathers at a different angle?

Problem 11P Light from a helium-neon laser (?? = 633 nm) is used to illuminate two narrow slits. The interference pattern is observed on a screen 3.0 m behind the slits. Eleven bright fringes are seen, spanning a distance of 52 mm. What is the spacing (in mm) between the slits?

Problem 12CQ White light is incident on a diffraction grating. What color is the central maximum of the interference pattern?

Problem 12P Two narrow slits are 0.12 mm apart. Light of wavelength 550 nm illuminates the slits, causing an interference pattern on a screen 1.0 m away. Light from each slit travels to the m = 1 maximum on the right side of the central maximum. How much farther did the light from the left slit travel than the light from the right slit?

Problem 13CQ A soap bubble usually pops because some part of it becomes too thin due to evaporation or drainage of fluid. The change in thickness also changes the color of light the bubble reflects. Why?

Problem 13P Consider a point P on the viewing screen of a double-slit interference experiment. This point is 75% of the way from the center of the 3rd bright fringe to the center of the 4th bright fringe. If the wavelength of the light is 600 nm, what is the extra distance that the wave from one slit traveled compared to the wave from the other?

Problem 14CQ An oil film on top of water has one patch that is much thinner than the wavelength of visible light. The index of refraction of the oil is less than that of water. Will the reflection from that extremely thin part of the film be bright or dark? Explain.

Problem 14P A diffraction grating with 750 slits/mm is illuminated by light that gives a first-order diffraction angle of 34.0°. What is the wavelength of the light?

Problem 15CQ Should the antireflection coating of a microscope objective lens designed for use with ultraviolet light be thinner, thicker, or the same thickness as the coating on a lens designed for visible light?

Problem 15P A 1.0-cm-wide diffraction grating has 1000 slits. It is illuminated by light of wavelength 550 nm. What are the angles of the first two diffraction orders?

Problem 16CQ If the thin wedge of air between the two plates of glass in Figure 17.21 were replaced by water, would the distance between the fringes increase, decrease, or remain the same? Explain.

Problem 16P Light of wavelength 600 nm illuminates a diffraction grating. The second-order maximum is at angle 39.5°. How many lines per millimeter does this grating have?

Problem 17CQ Example 17.5 showed that a thin film whose thickness is onequarter of the wavelength of light in the film serves as an antireflection coating when coated on glass. In Example 17.5, were used instead, would the film still serve as an antireflection coating? Explain.

Problem 17P A lab technician uses laser light with a wavelength of 670 nm to test a diffraction grating. When the grating is 40.0 cm from the screen, the first-order maxima appear 6.00 cm from the center of the pattern. How many lines per millimeter does this grating have?

Problem 18P The human eye can readily detect wavelengths from about 400 nm to 700 nm. If white light illuminates a diffraction grating having 750 lines/mm, over what range of angles does the visible m = 1 spectrum extend?

Problem 18CQ You are standing against the wall near a corner of a large building. A friend is standing against the wall that is around the corner from you. You can’t see your friend. How is it that you can hear her when she talks to you?

Problem 19MCQ Light of wavelength 500 nm in air enters a glass block with index of refraction n = 1.5. When the light enters the block, which of the following properties of the light will not change? A. The speed of the light B. The frequency of the light C. The wavelength of the light

Problem 19P A diffraction grating with 600 lines/mm is illuminated with light of wavelength 500 nm. A very wide viewing screen is 2.0 m behind the grating. a. What is the distance between the two m = 1 fringes? b. How many bright fringes can be seen on the screen?

Problem 20MCQ The frequency of a light wave in air is . What is the wavelength of this wave after it enters a pool of water? A. 300 nm B. 490 nm C. 650 nm D. 870 nm

Problem 20P A 500 line/mm diffraction grating is illuminated by light of wavelength 510 nm. How many diffraction orders are seen, and what is the angle of each?

Problem 21MCQ Light passes through a diffraction grating with a slit spacing of 0.001 mm. A viewing screen is 100 cm behind the grating. If the light is blue, with a wavelength of 450 nm, at about what distance from the center of the interference pattern will the first order maximum appear? A. 5 cm B. 25 cm C. 50 cm D. 100 cm

Problem 21P What is the thinnest film of on glass that produces a strong reflection for orange light with a wavelength of 600 nm?

Problem 22MCQ Blue light of wavelength 450 nm passes through a diffraction grating with a slit spacing of 0.001 mm and makes an interference pattern on the wall. How many bright fringes will be seen? A. 1 B. 3 C. 5 D. 7

Problem 22P A very thin oil film (n = 1.25) floats on water (n = 1.33). What is the thinnest film that produces a strong reflection for green light with a wavelength of 500 nm?

Problem 23MCQ Yellow light of wavelength 590 nm passes through a diffraction grating and makes an interference pattern on a screen 80 cm away. The first bright fringes are 1.9 cm from the central maximum. How many lines per mm does this grating have? A. 20 B. 40 C. 80 D. 200

Problem 23P A film with n = 1.60 is deposited on glass. What is the thinnest film that will produce constructive interference in the reflection of light with a wavelength of 550 nm?

Problem 24MCQ Light passes through a 10-?m-wide slit and is viewed on a screen 1 m behind the slit. If the width of the slit is narrowed, the band of light on the screen will A. Become narrower. B. Become wider. C. Stay about the same.

Problem 24P Antireflection coatings can be used on the inner surfaces of eyeglasses to reduce the reflection of stray light into the eye, thus reducing eyestrain. a. A 90-nm-thick coating is applied to the lens. What must be the coating’s index of refraction to be most effective at 480 nm? Assume that the coating’s index of refraction is less than that of the lens. b. If the index of refraction of the coating is 1.38, what thickness should the coating be so as to be most effective at 480 nm? The thinnest possible coating is best.

Problem 25P Solar cells are given antireflection coatings to maximize their efficiency. Consider a silicon solar cell (n = 3.50) coated with a layer of silicon dioxide (n = 1.45). What is the minimum coating thickness that will minimize the reflection at the wavelength of 700 nm, where solar cells are most efficient?

Problem 25MCQ Blue light of wavelength 450 nm passes through a 0.20-mm-wide slit and illuminates a screen 1.2 m away. How wide is the centrai maximum of the diffraction pattern? A. 1.2 mm B. 2.0 mm C. 2.7 mm D. 5.4 mm

Problem 26MCQ A green laser beam of wavelength 540 nm passes through a pinhole and illuminates a dartboard 3.0 m past the pinhole. The first minimum in the intensity coincides with the ring surround-ing the bull’s-eye, 12 mm in diameter. What is the diameter of the pinhole? A. 0.14 mm B. 0.33 mm C. 0.59 mm D. 1.2 mm

Problem 26P A thin film of coats a piece of glass. Constructive interference is observed for the reflection of light with wavelengths of 500 nm and 625 nm. What is the thinnest film for which this can occur?

Problem 27P Looking straight downward into a rain puddle whose surface is covered with a thin film of gasoline, you notice a swirling pattern of colors caused by interference inside the gasoline film. The point directly beneath you is colored a beautiful iridescent green. You happen to remember that the index of refraction of gasoline is 1.38 and that the wavelength of green light is about 540 nm. What is the minimum possible thickness of the gasoline layer directly beneath you?

Problem 27P Styrofoam has a density of 300 kg/m3. What is the maximum mass that can hang without sinking from a 50-cm-diameter Styrofoam sphere in water? Assume the volume of the mass is negligible compared to that of the sphere.

Problem 28P A helium-neon laser (?? = 633 nm) illuminates a single slit and is observed on a screen 1.50 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?

Problem 29P For a demonstration, a professor uses a razor blade to cut a thin slit in a piece of aluminum foil. When she shines a laser pointer (?? = 680 nm) through the slit onto a screen 5.5 m away, a diffraction pattern appears. The bright band in the center of the pattern is 8.0 cm wide. What is the width of the slit?

Problem 30P A 0.50-mm-wide slit is illuminated by light of wavelength 500 nm. What is the width of the central maximum on a screen 2.0 m behind the slit?

Problem 31P The second minimum in the diffraction pattern of a 0.10-mm-wide slit occurs at 0.70°. What is the wavelength of the light?

Problem 32P What is the width of a slit for which the first minimum is at 45° when the slit is illuminated by a helium-neon laser (??= 633 nm)? Hint: The small-angle approximation is not valid at 45°.

Problem 33P A 0.50-mm-diameter hole is illuminated by light of wavelength 500 nm. What is the width of the central maximum on a screen 2.0 m behind the slit?

Problem 34P Light from a helium-neon laser (?? = 633 nm) 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?

Problem 35P You want to photograph a circular diffraction pattern whose central maximum has a diameter of 1.0 cm. You have a heliumneon laser (??= 633 nm) and a 0.12-mm-diameter pinhole. How far behind the pinhole should you place the viewing screen?

Problem 36P Infrared light of wavelength 2.5 ?m illuminates a 0.20-mmdiameter hole. What is the angle of the first dark fringe in radians? In degrees?

Problem 37GP An advanced computer sends information to its various parts via infrared light pulses traveling through silicon fibers (n = 3.50). To acquire data from memory, the central processing unit sends a light-pulse request to the memory unit. The memory unit processes the request, then sends a data pulse back to the central processing unit. The memory unit takes 0.50 ns to process a request. If the information has to be obtained from memory in 2.00 ns, what is the maximum distance the memory unit can be from the central processing unit?

Problem 38GP Figure P17.38 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 600 nm. What is the distance from the slits to the screen?

Problem 39GP Figure P17.38 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 of the light?

Problem 40GP Your friend has been given a laser for her birthday. Unfortunately, she did not receive a manual with it and so she doesn’t know the wavelength that it emits. You help her by performing a double-slit experiment, with slits separated by 0.36 mm. You find that the two bright fringes are 5.5 mm apart on a screen 1.6 m from the slits. What is the wavelength the laser emits?

Problem 41GP A double slit is illuminated simultaneously with orange light of wavelength 600 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?

Problem 42GP A laser beam, with a wavelength of 532 nm, is directed exactly perpendicular to a screen having two narrow slits spaced 0.15 mm apart. Interference fringes, including a central maximum, are observed on a screen 1.0 m away. The direction of the beam is then slowly rotated around an axis parallel to the slits to an angle of 1.0°. By what distance does the central maximum on the screen move?

Problem 43GP A laser beam of wavelength 670 nm shines through a diffraction grating that has 750 lines/mm. Sketch the pattern that appears on a screen 1.0 m behind the grating, noting distances on your drawing and explaining where these numbers come from.

Problem 44GP 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?

Problem 45GP A triple-slit experiment illuminates three equally spaced, narrow slits with light of wavelength A. The intensity of the wave from each slit is I1. Consider a point on a distant screen at an angle such that the path-length difference between any two adjacent slits is ?/2. What is the intensity at this point? Give your answer as a multiple of I1.

Problem 46GP A diffraction grating consists of 100 slits. If the number of slits is increased to 200, with the same spacing, by what factor does the maximum intensity of the bright fringes on the screen increase?

Problem 47GP A diffraction grating produces a first-order maximum at an angle of 20.0°. What is the angle of the second-order maximum?

Problem 48GP A diffraction grating is illuminated simultaneously with red light of wavelength 660 nm and light of an unknown wavelength. The fifth-order maximum of the unknown wavelength exactly overlaps the third-order maximum of the red light. What is the unknown wavelength?

Problem 49GP White light (400–700 nm) is incident on a 600 line/mm diffraction grating. What is the width of the first-order rainbow on a screen 2.0 m behind the grating?

Problem 50GP For your science fair project you need to design a diffraction grating that will disperse the visible spectrum (400-700 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 (? = 589 nm)?

Problem 51GP Figure P17.49 shows the interference pattern on a screen 1.0 m behind an 800 line/mm diffraction grating. What is the wavelength of the light?

Problem 52GP Figure P17.49 shows the interference pattern on a screen 1.0 m behind a diffraction grating. The wavelength of the light is 600 nm. How many lines per millimeter does the grating have?

Problem 53GP Because sound is a wave, it is possible to make a diffraction grating for sound from a large board with several parallel slots for the 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 slots? Use 340 m/s for the speed of sound

Problem 54GP The shiny surface of a CD is imprinted with millions of tiny pits, arranged in a pattern of thousands of essentially concentric circles that act like a reflection grating when light shines on them. You decide to determine the distance between those circles by aiming a laser pointer (with ?? = 680 nm) perpendicular to the disk and measuring the diffraction pattern reflected onto a screen 1.5 m from the disk. The central bright spot you expected to see is blocked by the laser pointer itself. You do find two other bright spots separated by 1.4 m, one on either side of the missing central spot. The rest of the pattern is apparently diffracted at angles too great to show on your screen. What is the distance between the circles on the CD’s surface?

Problem 55GP 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 sunlight. The blue color is due to diffraction from the melanin bands in the feather barbules, as was shown in the photograph on page 549. Blue light with a wavelength of 470 nm is diffracted at 15° by these bands (this is the firstorder diffraction) while other wavelengths in the sunlight are diffracted at different angles. What is the spacing of the melanin bands in the feather?

Problem 56GP 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 (??= 550 nm)?

Problem 57GP A diffraction grating having 500 lines/mm diffracts visible light at 30°. What is the light’s wavelength?

Problem 58GP Light emitted by Element X passes through a diffraction grating having 1200 lines/mm. The interference pattern is observed on a screen 75.0 cm behind the grating. Bright fringes are seen on the screen at distances of 56.2 cm, 65.9 cm, and 93.5 cm from the central maximum. No other fringes are seen. a. What is the value of m for each of these diffracted wavelengths? Explain why only one value is possible. ________________ b. What are the wavelengths of light emitted by Element X?

Problem 59GP 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?

Problem 60GP A sheet of glass is coated with a 500-nm-thick layer of oil (n = 1.42). a. For what visible wavelengths of light do the reflected waves interfere constructively? b. For what visible wavelengths of light do the reflected waves interfere destructively? c. What is the color of reflected light? What is the color of transmitted light?

Problem 61GP A soap bubble is essentially a thin film of water surrounded by air. The colors you see in soap bubbles are produced by interference. What visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble? What color would such a soap bubble appear to be?

Problem 63GP You need to use your cell phone, which broadcasts an 830 MHz signal, but you’re in an alley between two massive, radiowave- absorbing 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?

Problem 62GP In a single-slit experiment, the slit width is 200 times the wavelength of the light. What is the width of the central maximum on a screen 2.0 m behind the slit?

Problem 64GP Light from a sodium lamp (?? = 589 nm) illuminates a narrow slit and is observed on a screen 75 cm behind the slit. The distance between the first and third dark fringes is 7.5 mm. What is the width (in mm) of the slit?

Problem 65GP The opening to a cave is a tall, 30-cm-wide crack. A bat that is preparing to leave the cave emits a 30 kHz ultrasonic chirp. How wide is the “sound beam” 100 m outside the cave opening? Use .

Problem 66GP 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°? Hint: The small-angle approximation is not valid.

Problem 68GP Figure P17.65 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?

Problem 67GP Figure P17.65 shows the light intensity on a screen behind a single slit. The wavelength of the light is 500 nm and the screen is 1.0 m behind the slit. What is the width (in mm) of the slit?

Problem 69GP Figure P17.67 shows the light intensity on a screen 2.5 m behind an aperture. The aperture is illuminated with light of wavelength 600 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?

Problem 70GP Figure P17.68 shows the light intensity on a screen 2.5 m behind an aperture. The aperture is illuminated with light of wavelength 600 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?

Problem 71GP 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, you’re 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 3 cm across, and you estimate that the distance from the window shade to the wall is about 3 m. Knowing that the average wavelength of sunlight is about 500 nm, estimate the diameter of the pinhole.

Problem 72GP 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?

Problem 73GP Problem A helium-neon laser (?? = 633 nm), shown in Figure P17.71, is built with a glass tube of inside diameter 1.0 mm. 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. Explain why a laser beam can’t be perfectly parallel, with no spreading. b. The angle 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?

Problem 74GP In the laser range-finding experiments of Example 17.10, the laser beam fired toward the moon 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 km in diameter. Staying within this diameter is accomplished by using a special large-diameter laser. If ?? = 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.

Problem 75PP The Blue Morpho Butterfly The brilliant blue color of a blue morpho butterfly is, like the colors of peacock feathers, due to interference. Figure P17.73a shows an easy way to demonstrate this: If a drop of the clear solvent acetone is placed on the wing of a blue morpho butterfly, the color changes from a brilliant blue to an equally brilliant green—returning to blue once the acetone evaporates. There would be no change if the color were due to pigment. A cross section of a scale from the wing of a blue morpho butterfly reveals the source of the butterfly’s color. As Figure P17.73b shows, the scales are covered with structures that look like small Christmas trees. Light striking the wings reflects from different layers of these structures, and the differing path lengths cause the reflected light to interfere constructively or destructively, depending on the wavelength. For light at normal incidence, blue light experiences constructive interference while other colors undergo destructive interference and cancel. Acetone fills the spaces in the scales with a fluid of index of refraction n = 1.38; this changes the conditions for constructive interference and results in a change in color. The coloring of the blue morpho butterfly is protective. As the butterfly flaps its wings, the angle at which light strikes the wings changes. This causes the butterfly’s color to change and makes it difficult for a predator to follow. This color change is because A. A diffraction pattern appears only at certain angles. B. The index of refraction of the wing tissues changes as the wing flexes. C. The motion of the wings causes a Doppler shift in the reflected light. D. As the angle changes, the differences in paths among light reflected from different surfaces change, resulting in constructive interference for a different color.

Problem 76PP The Blue Morpho Butterfly The brilliant blue color of a blue morpho butterfly is, like the colors of peacock feathers, due to interference. Figure P17.73a shows an easy way to demonstrate this: If a drop of the clear solvent acetone is placed on the wing of a blue morpho butterfly, the color changes from a brilliant blue to an equally brilliant green—returning to blue once the acetone evaporates. There would be no change if the color were due to pigment. A cross section of a scale from the wing of a blue morpho butterfly reveals the source of the butterfly’s color. As Figure P17.73b shows, the scales are covered with structures that look like small Christmas trees. Light striking the wings reflects from different layers of these structures, and the differing path lengths cause the reflected light to interfere constructively or destructively, depending on the wavelength. For light at normal incidence, blue light experiences constructive interference while other colors undergo destructive interference and cancel. Acetone fills the spaces in the scales with a fluid of index of refraction n = 1.38; this changes the conditions for constructive interference and results in a change in color. The change in color when acetone is placed on the wing is due to the difference between the indices of refraction of acetone and air. Consider light of some particular color. In acetone, A. The frequency of the light is less than in air. B. The frequency of the light is greater than in air. C. The wavelength of the light is less than in air. D. The wavelength of the light is greater than in air.

Problem 77PP The Blue Morpho Butterfly The brilliant blue color of a blue morpho butterfly is, like the colors of peacock feathers, due to interference. Figure P17.73a shows an easy way to demonstrate this: If a drop of the clear solvent acetone is placed on the wing of a blue morpho butterfly, the color changes from a brilliant blue to an equally brilliant green—returning to blue once the acetone evaporates. There would be no change if the color were due to pigment. A cross section of a scale from the wing of a blue morpho butterfly reveals the source of the butterfly’s color. As Figure P17.73b shows, the scales are covered with structures that look like small Christmas trees. Light striking the wings reflects from different layers of these structures, and the differing path lengths cause the reflected light to interfere constructively or destructively, depending on the wavelength. For light at normal incidence, blue light experiences constructive interference while other colors undergo destructive interference and cancel. Acetone fills the spaces in the scales with a fluid of index of refraction n = 1.38; this changes the conditions for constructive interference and results in a change in color. The scales on the butterfly wings are actually made of a transparent material with index of refraction 1.56. Light reflects from the surface of the scales because A. The scales’ index of refraction is different from that of air. B. The scales’ index of refraction is similar to that of glass. C. The scales’ density is different from that of air. D. Different colors of light have different wavelengths.