Light of a single wavelength is incident on a diffraction gratingwith 500 slits/mm

The frequency of a light wave in air is 5.3 X I 0 14 Hz. Is the fre quency of this wave higher, lower, or the same after the light enters a piece of glass?

Rank in order the fo llowing 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.

The wavelength of a light wave is 700 nm in air; this ligbt appears red. If this wave enters a pool of water, its wavelength becomes Aai/n = 530 nm. If you were swimming underwater, the light would sti ll appear red. Given this, what property of a wave determines its color?

A double-slit interference experiment shows fringes on a screen. T he enti re experiment is then immersed in water. Do the fringes on the screen get closer together, farther apart, remain the same, or disappear entirely? Explain.

Figure Q I 7.5 shows the fringes observed in a double-slit interfe rence experiment when the two sli ts 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 c olo1ful. What is special about the central maximum that makes it white? Explain the presence of colors in the outlying fringe s.

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.

Figure Q l7.7 shows the view- A B c o E ing 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 wi ll 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 wavele ngth 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 Q l7.7 is the inte1ference 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 Q I7.9 shows the light inte nsity on a viewi ng screen behind a single slit of width a. The light's wavelength is A. Is A< a, A = a, A> a, or is it not possible to te ll? Explain

Figure Ql7. IO 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 wi ll the screen appear if the aperture diameter is less than the light wavelength?

Light with a wavelength of 600 nm is incident on a diffraction grating that has 100 slits. The first-order maximum is observed at a point P on a distant screen. How much farther does the light travel from the fi rst slit of the grat ing to poi nt P than does the light from the IOOth slit?

White light is incident on a di ffraction grating. What color is the central maximum of the interference pattern?

Figure QI 7. 13 shows a light wave incident on and passing through a thin soap film. Reflections from the front and back surfaces of the film create smaller waves (not shown in the figure) that travel to the left of the fi lm, where they interfere. Is the interference constructive, destructive, or something in between? Explain.

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

An oil film on top of water has one patch that is much thinner than the wavelength of visi ble light. T he index of refraction of the oil is less than that of water. Will the reflection from that extremely thin part of the fi lm be bright or dark? Explain.

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?

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. ln Example 17.5, 11n1m < l1g1ass If a quarter-wave thickness film with l1n11n > flg1ass were used instead, would the film still serve as an antireflection coating? Explain.

You are standing against the wall near a corner of a large bui !ding. A friend is standing against the wall that is around the corner from you. You can't see your fri end. How is it that you can hear her when she talks to you?

Light of wavelength 500 nm in air enters a glass block with index of refract ion 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 freq uency of the light C. The wavelength of the light

The frequency of a light wave in air is 4.6 X 1014 Hz. What is the wavelength of th is wave after it enters a pool of water? A. 300 nm B. 490 nm C. 650 nm D. 870 nm

Light passes through a di ffraction 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 fi rstorder maximum appear? A. 5 cm B. 25 cm C. 50 cm D. 100 cm

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 wal l. How many bright fringes wi ll be seen? A. I B. 3 C. 5 D. 7

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

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

Reflected light from a thin film of oil gives constructive interference for light with a wavelength inside the film of Arnm By how much would the film thickness need to be increased to give destructive interference? A 2Ar.1m B. Arn 111 C. Arnm/2 D. Arnm/4

You want to estimate the diameter of a very small circular pinhole that you've made in a piece of aluminum foil. To do so, you shine a red laser pointer (A = 632 nm) at the hole and observe the diffraction l?attern on a screen 3.5 m behind the foil. You measure the width of the central maximum to be 15 mm. What is the diameter of the hole? A. 0.1 8 mm B. 0.29 mm C. 0.36 mm D. I.I mm

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?

A helium-neon laser (A = 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 sl it?

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 (A = 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?

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?

The second minimum in the diffraction pattern of a O. L0-111111-wide sl it occurs at 0.70. What is the wavelength of the light?

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

A 0.50-111111-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 sl it?

Light from a helium-neon laser (A = 633 nm) passes through a circular aperture and is observed on a screen 4.0 111 behind the aperture. The width of the central maximum is 2.5 cm. What is the diameter (in mm) of the hole?

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

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

An advanced computer sends information to its various parts via infrared light pulses traveling through si licon 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 uni t can be from the central processing unit?

Figure P 17 .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?

Figure P l7.38 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?

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 petforming a double-slit experiment, with slits separated by 0. 18 mm. You find that two adjacent bright fringes are 5.5 mm apart on a screen 1.6 m from the slits. What is the wavelength the laser emits?

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 over laps the 111 = 3 bright orange fringe. What is the unknown wavelength?

Figure Pl7.42 shows the light intensity on a screen 2.5 m behind a double slit. The wavelength of the light is 532 nm. What is the spacing between the slits?

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.

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 diffraction grating produces a first-order maximum at an angle of 20.0. What is the angle of the second-order maximum?

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?

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?

A miniature spectrometer used for chemical analysis has a diffraction grating with 800 slits/mm set 25.0 mm in front of the detector "screen." The detector can barely distinguish two bright lines that are 30 m apart in the first-order spectrum. What is the resolution of the spectrometer at a wavelength of 600 nm? That is, if two distinct wavelengths can barely be distinguished, one of them being 600.0 nm, what is the wavelength difference ~A between the two?

Figure Pl7.49 shows the interference pattern on a screen 1.0 m behind an 800 line/mm diffraction grating. What is the wavelength of the light?

Figure P 17.49 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?

Because sound is a wave, it is possible to make a diffract.ion grating for sound from a large board with several parallel slots for the sound to go through. When IO kHz sound waves pass through such a grating, listeners I 0 m from the grating report "loud spots" 1.4 m on both sides of center. What is the spacing between the slots? Use 340 mis for the speed of sound.

The shi ny 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 A = 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 ci rcles on the CD's surface?

If sunlight shines straight onto a peacock feather, the feather appears bright blue when viewed from 15 on e ither side of the incident beam of s unlight. The blue color is due to diffract.ion 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?

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 wi ng. If the melanin lines on the wing are spaced 2.0 m apart, what is the first-order diffraction angle for green I ight (A= 550 nm)?

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

Light emitted by element X passes through a diffraction grating that has 1200 slits/mm. The interference pattern is observed on a screen 75.0 cm behind the grating. First-order maxima are observed at distances of 56.2 cm, 65.9 cm, and 93.5 cm from the central maximum. What are the wavelengths of light emitted by elementX?

Light of a single wavelength is incident on a diffraction grating with 500 slits/mm. Several bright fri nges are observed on a screen behind the grating, including one at 45.7 and one next to it at 72.6. What is the wavelength of the light?

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?

A soap bubble is essentia lly 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?

A laboratory dish, 20 cm in diameter, is half filled with M water. One at a time, 0.50 ,L drops of oil from a micropipette are dropped onto the surface of the water, where they spread out into a uniform thin film. After the first drop is added, the intensity of 600 nm light reflected from the surface is very low. As more drops are added, the reflected intensity increases, then decreases- agai n to a minimum after a total of 13 drops have been added. What is the index of refraction of the oil?

You need to use your cell phone, which broadcasts an 830MHz signal, but you' re in an alley between two massive, radiowave- absorbing buildi ngs thaf 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?

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

The opening to a cave is a tall, 30-cm-wide crack. A bat that INT is preparing to leave the cave emits a 30 kHz ultrasonic chirp. How wide is the "sound beam" I 00 m outside the cave opening? Use Vsound = 340 mis.

A diffraction grating has 500 slits/mm. What is the longest wavelength of light for which there will be a third-order maximum?

Figure Pl7.65 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?

Figure Pl7.65 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?

Figure P 17.67 shows the light intensity on a screen 2.5 m behind an aperture. The aperture is illuminated with light of wavelength 600 nm. a. ls 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 Pl7.68 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?

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 li ght on the far wall. Having recently studied optics in your physics c lass, you're not too surprised to see that the patch of light seems to be a circular di ffracti on 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 sunli ght is about 500 nm, estimate the diameter of the pinhole.

A radar for tracking aircraft broadcasts a 12 GHz microwave beam from a 2.0-m-diameter circular radar ante nna. 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 IOO kW of power, what is the average microwave intensity at 30 km?

A helium-neon laser (A = 633 nm), shown in Figure P 17 .7 1, 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 perspecti ve, the laser beam is a light wave that diffracts out through a J .0-mm-diameter circular opening. a. Explain why a laser beam can't be pe1fectly parallel, with no spreading. b. The angle 01 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?

In the laser range-finding experiments of Example 17.10, the laser beam fi red toward the moon spreads out as it travels because it diffracts through a ci rcular 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 I km in diameter. Staying within this diameter is accomplished by using a special large-diameter laser. If A= 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.