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College Physics

Raymond A. Serway, Jerry S. Faughn, Chris Vuille

Chapter 24

Wave Optics - all with Video Answers

Educators

Chapter Questions

01:03

Problem 1

A laser beam is incident on two slits with a separation of $0.200 \mathrm{~mm}$, and a screen is placed $5.00 \mathrm{~m}$ from the slits. If the bright interference fringes on the screen are separated by $1.58 \mathrm{~cm}$, what is the wavelength of the laser light?

Salamat Ali
Salamat Ali
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01:35

Problem 2

In a Young's double-slit experiment, a set of parallel slits with a separation of $0.100 \mathrm{~mm}$ is illuminated by light having a wavelength of $589 \mathrm{~nm}$, and the interference pattern is observed on a screen $4.00 \mathrm{~m}$ from the slits. (a) What is the difference in path lengths from each of the slits to the location of a third-order bright fringe on the screen?
(b) What is the difference in path lengths from the two slits to the location of the third dark fringe on the screen, away from the center of the pattern?

Prabhu Ramji
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01:52

Problem 3

A pair of narrow, parallel slits separated by $0.250 \mathrm{~mm}$ is illuminated by the green component from a mercury vapor lamp $(\lambda=546.1 \mathrm{~nm}) .$ The interference pattern is observed on a screen $1.20 \mathrm{~m}$ from the plane of the parallel slits. Calculate the distance (a) from the central maximum to the first bright region on either side of the central maximum and (b) between the first and second dark bands in the interference pattern.

Prabhu Ramji
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01:22

Problem 4

Light of wavelength $5.30 \times 10^{2} \mathrm{~nm}$ illuminates a pair of slits separated by $0.300 \mathrm{~mm}$. If a screen is placed $2.00 \mathrm{~m}$ from the slits, determine the distance between the first and second dark fringes.

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02:49

Problem 5

In a location where the speed of sound is $354 \mathrm{~m} / \mathrm{s}$. a $2000-\mathrm{Hz}$ sound wave impinges on two slits $30.0 \mathrm{~cm}$ apart.
(a) At what angle is the first maximum located? (b) If the sound wave is replaced by $3.00-\mathrm{cm}$ microwaves, what slit separation gives the same angle for the first maximum?
(c) If the slit separation is $1.00 \mu \mathrm{m}$, what frequency of light gives the same first maximum angle?

Suzanne W.
Suzanne W.
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02:08

Problem 6

Two slits separated by $0.0500 \mathrm{~mm}$ and located $1.50 \mathrm{~m}$ from a viewing screen are illuminated with monochromatic light. The third-order bright fringe is $5.30 \mathrm{~cm}$ from the zeroth-order bright fringe. Find the (a) wavelength of the light and (b) separation between adjacent bright fringes.

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03:37

Problem 7

Two radio antennas separated by $300 \mathrm{~m}$, as shown $\mathrm{P} 24.7$, simultaneously transmit identical signals of the same wavelength. A radio in a car traveling due north receives the signals. (a) If the car is at the position of the second maximum, what is the wavelength of the signals?
(b) How much farther must the car travel to encounter the next minimum in reception? Hint: Determine the path difference between the two signals at the two locations of the car.

Prabhu Ramji
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01:18

Problem 8

Light of wavelength $6.0 \times 10^{2} \mathrm{~nm}$ falls on a double slit, and the first bright fringe of the interference pattern is observed to make an angle of $12^{\circ}$ with the horizontal. Find the separation between the slits.

Zachary Warner
Zachary Warner
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01:22

Problem 9

A Young's double-slit interference experiment is performed with blue-green argon laser light. The separation between the slits is $0.500 \mathrm{~mm}$, and the screen is located $3.30 \mathrm{~m}$ from the slits. The first bright fringe is located $3.40 \mathrm{~mm}$ from the center of the interference pattern. What is the wavelength of argon laser light?

Prabhu Ramji
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03:13

Problem 10

A pair of slits, separated by $0.150 \mathrm{~mm}$, is illuminated by light having a wavelength of $\lambda=643 \mathrm{~nm}$. An interference pattern is observed on a screen $140 \mathrm{~cm}$ from the slits. Consider a point on the screen located at $y=1.80 \mathrm{~cm}$ from
the central maximum of this pattern. (a) What is the path difference $\delta$ for the two slits at the location $y^{2}$ (b) Express this path difference in terms of the wavelength. (c) Will the interference correspond to a maximum, a minimum. or an intermediate condition?

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01:35

Problem 11

A riverside warehouse has two open doors, as P24.11. Its interior is lined with a sound-absorbing material. A boat on the river sounds its horn. To person $A$, the sound is loud and clear. To person $\mathrm{B}$, the sound is barely audible. The principal wavelength of the sound waves is $3.00 \mathrm{~m}$. Assuming person $\mathrm{B}$ is at the position of the first minimum, determine the distance between the doors,
center to center.

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07:34

Problem 12

A student sets up a double-slit experiment using monochromatic light of wavelength $\lambda$. The distance between the slits is equal to $25 \lambda$. (a) Find the angles at which the $m=1,2$, and 3 maxima occur on the viewing screen. (b) At what angles do the first three dark fringes occur? (c) Why are the answers so evenly spaced? Is the spacing even for all orders? Explain.

Zachary Warner
Zachary Warner
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06:03

Problem 13

Radio waves from a star, of wavelength $250 \mathrm{~m}$, reach a radio telescope by two separate paths, as shown in Figure P24.13. One is a direct path to the receiver, which is situated on the edge of a cliff by the ocean. The second is by reflection off the water. The first minimum of destructive interference occurs when the star is $25.0^{\circ}$ above the horizon. Find the height of the cliff. (Assume no phase change on reflection.)

Supratim Pal
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06:37

Problem 14

Monochromatic light of wavelength $\lambda$ is incident on a pair of slits separated by $2.40 \times 10^{-4} \mathrm{~m}$, and forms an interference pattern on a screen is placed $1.80 \mathrm{~m}$ away from the slits. The first-order bright fringe is $4.52 \mathrm{~mm}$ from the center of the central maximum. (a) Draw a picture, labeling the angle $\theta$ and the legs of the right triangle associated with the first-order bright fringe. (b) Compute the tangent of the angle $\theta$ associated with the first-order bright fringe. (c) Find the angle corresponding to the first-order bright fringe and compute the sine of that angle. Are the sine and tangent of the angle comparable in value? Does your answer always hold true? (d) Calculate the wavelength of the light. (e) Compute the angle of the fifth-order bright fringe. (f) Find its position on the screen.

Zachary Warner
Zachary Warner
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01:37

Problem 15

Waves from a radio station have a wavelength of $300 \mathrm{~m}$. They uravel by two paths to a home receiver $20.0 \mathrm{~km}$ from the transmitter. One path is a direct path, and the second is by reflection from a mountain directly behind the home receiver. What is the minimum distance from the mountain to the receiver that produces destructive interference at the receiver? (Assume that no phase change occurs on reflection from the mountain.)Waves from a radio station have a wavelength of $300 \mathrm{~m}$. They uravel by two paths to a home receiver $20.0 \mathrm{~km}$ from the transmitter. One path is a direct path, and the second is by reflection from a mountain directly behind the home receiver. What is the minimum distance from the mountain to the receiver that produces destructive interference at the receiver? (Assume that no phase change occurs on reflection from the mountain.)

Prabhu Ramji
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04:39

Problem 16

A soap bubble $(n=1.33)$ having a wall thickness of $120 \mathrm{~nm}$ is floating in air. (a) What is the wavelength of the visible light that is most strongly reflected? (b) Explain how a bubble of different thickness could also strongly reflect light of this same wavelength. (c) Find the two smallest film thicknesses larger than the one given that can produce strongly reflected light of this same wavelength.

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00:45

Problem 17

A thin layer of liquid methylene iodide $(n=1.756)$ is sandwiched between two flat, parallel plates of glass $(n=1.50)$. What is the minimum thickness of the liquid layer if normally incident light with $\lambda=6.00 \times 10^{2} \mathrm{~nm}$ in air is to be strongly reflected?

Salamat Ali
Salamat Ali
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04:08

Problem 18

A thin film of oil $(n=1.25)$ is located on smooth, wet pavement. When viewed from a direction perpendicular to the pavement, the film reflects most strongly red light at $640 \mathrm{~nm}$ and reflects no green light at $512 \mathrm{~nm}$. (a) What is the minimum thickness of the oil film? (b) Let $m_{1}$ correspond to the order of the constructive interference and $m_{2}$ to the order of the destructive interference. Obtain a relationship between $m_{1}$ and $m_{2}$ that is consistent with the given data.

Prabhu Ramji
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01:47

Problem 19

A coating is applied to a lens to minimize reflections. The index of refraction of the coating is $1.55$ and that of the lens is $1.48 .$ If the coating is $177.4 \mathrm{~nm}$ thick, what wavelength is minimally reflected for normal incidence in the lowest order?

Prabhu Ramji
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01:27

Problem 20

A transparent oil with index of refraction $1.29$ spills on the surface of water (index of refraction 1.33), producing a maximum of reflection with normally incident orange light (wavelength $600 \mathrm{~nm}$ in air). Assuming the maximum occurs in the first order, determine the thickness of the oil slick.

Prabhu Ramji
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01:16

Problem 21

A possible means for making an airplane invisible to radar is to coat the plane with an antireflective polymer. If radar waves have a wavelength of $3.00 \mathrm{~cm}$ and the index of refraction of the polymer is $n=1.50$, how thick would you make the coating?

Suzanne W.
Suzanne W.
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03:51

Problem 22

An oil film $(n=1.45)$ floating on water is illuminated by white light at normal incidence. The film is $2.80 \times 10^{2} \mathrm{~nm}$ thick. Find (a) the wavelength and color of the light in the visible spectrum most strongly reflected and (b) the wavelength and color of the light in the visible spectrum most strongly transmitted. Explain your reasoning.

Zachary Warner
Zachary Warner
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01:21

Problem 23

Astronomers observe the chromosphere of the Sun with a filter that passes the red hydrogen spectral line of wavelength $656.3 \mathrm{~nm}$, called the $\mathrm{H}_{\alpha}$ line. The filter consists of a transparent dielectric of thickness $d$ held between two partially aluminized glass plates. The filter is kept at a constant temperature. (a) Find the minimum value of $d$ that will produce maximum transmission of perpendicular $\mathrm{H}_{\text { light }}$ if the dielectric has an index of refraction of $1.378 .$ (b) If the temperature of the filter increases above the normal value increasing its thickness, what happens to the transmitted wavelength? (c) The dielectric will also pass what near-visible wavelength? One of the glass plates is colored red to absorb this light.

Salamat Ali
Salamat Ali
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02:04

Problem 24

Two rectangular optically flat plates $(n=1.52)$ are in contact along one end and are separated along the other end by a $2.00-\mu \mathrm{m}$ -thick spacer (Fig. P24.24). The top plate is illuminated by monochromatic light of wavelength $546.1 \mathrm{~nm}$. Calculate the number of dark parallel bands crossing the top plate (including the dark band at zero thickness along the edge of contact between the plates).

Prabhu Ramji
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01:08

Problem 25

An air wedge is formed between two glass plates separated at one edge by a very fine wire, as shown in Figure $\mathrm{P} 24.24$. When the wedge is illuminated from above by $600-\mathrm{nm}$ light, 30 dark fringes are observed. Calculate the radius of the wire.

Suzanne W.
Suzanne W.
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01:03

Problem 26

A plano-convex lens with radius of curvature $R=3.0 \mathrm{~m}$ is in contact with a flat plate of glass. A light source and the observer's eye are both close to the normal, as shown in Figure $24.8$. The radius of the 50 th bright Newton's ring is found to be $9.8 \mathrm{~mm}$. What is the wavelength of the light produced by the source?

Zachary Warner
Zachary Warner
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02:36

Problem 27

A plano-convex lens rests with its curved side on a flat glass surface and is illuminated from above by light of wavelength $500 \mathrm{~nm}$. (See Fig. 24.8.) A dark spot is observed at the center, surrounded by 19 concentric dark rings (with bright rings in between). How much thicker is the air wedge at the position of the 19 th dark ring than at the center?

Prabhu Ramji
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01:47

Problem 28

Nonreflective coatings on camera lenses reduce the loss of light at the surfaces of multilens systems and prevent internal reflections that might mar the image. Find the minimum thickness of a layer of magnesium fluoride $(n=1.38)$ on flint glass $(n=1.66)$ that will cause destructive interference of reflected light of wavelength $550 \mathrm{~nm}$ near the middle of the visible spectrum.

Prabhu Ramji
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02:56

Problem 29

A thin film of $\mathrm{MgF}_{2}(n=1.38)$ with thickness $1.00 \times$ $10^{-5} \mathrm{~cm}$ is used to coat a camera lens. Are any wave- lengths in the visible spectrum intensified in the reflected light?

Prabhu Ramji
Prabhu Ramji
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02:07

Problem 30

A beam of light of wavelength $580 \mathrm{~nm}$ passes through two closely spaced glass plates, as shown in Figure P24.30. For what minimum nonzero value of the plate separation $\bar{d}$ will the transmitted light be bright? This arrangement is often used to measure the wavelength of light and is called a Fabry-Perot interferometer.

Prabhu Ramji
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02:38

Problem 31

Light of wavelength $5.40 \times 10^{2} \mathrm{~nm}$ passes through a slit of width $0.200 \mathrm{~mm}$. (a) Find the width of the central maximum on a screen located $1.50 \mathrm{~m}$ from the slit. (b) Determine the width of the first-order bright fringe.

Salamat Ali
Salamat Ali
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02:53

Problem 32

Light of wavelength $600 \mathrm{~nm}$ falls on a $0.40-\mathrm{mm}$ -wide slit and forms a diffraction pattern on a screen $1.5 \mathrm{~m}$ away,
(a) Find the position of the first dark band on each side of the central maximum. (b) Find the width of the central maximum.

Prabhu Ramji
Prabhu Ramji
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01:10

Problem 33

Light of wavelength $587.5 \mathrm{~nm}$ illuminates a slit of width $0.75 \mathrm{~mm}$. (a) At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be $0.85 \mathrm{~mm}$ from the central maximum? (b) Calculate the width of the central maximum.

Salamat Ali
Salamat Ali
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01:30

Problem 34

Microwaves of wavelength $5.00 \mathrm{~cm}$ enter a long, narrow window in a building that is otherwise essentially opaque to the incoming waves. If the window is $36.0 \mathrm{~cm}$ wide, what is the distance from the central maximum to the firstorder minimum along a wall $6.50 \mathrm{~m}$ from the window?

Prabhu Ramji
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00:55

Problem 35

A beam of monochromatic light is diffracted by a slit of width $0.600 \mathrm{~mm}$. The diffraction pattern forms on a wall $1.30 \mathrm{~m}$ beyond the slit. The width of the central maximum is $2.00 \mathrm{~mm}$. Calculate the wavelength of the light.

Salamat Ali
Salamat Ali
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01:56

Problem 36

A screen is placed $50.0 \mathrm{~cm}$ from a single slit that is illuminated with light of wavelength $680 \mathrm{~nm}$. If the distance between the first and third minima in the diffraction pattern is $3.00 \mathrm{~mm}$, what is the width of the slit?

Prabhu Ramji
Prabhu Ramji
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02:16

Problem 37

A slit of width $0.50 \mathrm{~mm}$ is illuminated with light of wavelength $500 \mathrm{~nm}$, and a screen is placed $120 \mathrm{~cm}$ in front of the slit. Find the widths of the first and second maxima on each side of the central maximum.

Prabhu Ramji
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01:39

Problem 38

A helium-neon laser $(\lambda=632.8 \mathrm{~nm})$ is used to calibrate a diffraction grating. If the first-order maximum occurs at $20.5^{\circ}$, what is the spacing between adjacent grooves in the grating?

Aja S
Aja S
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04:35

Problem 39

Three discrete spectral lines occur at angles of $10.1^{\circ}$, $13.7^{\circ}$, and $14.8^{\circ}$, respectively, in the first-order spectrum of a diffraction-grating spectrometer. (a) If the grating has 3660 slits $/ \mathrm{cm}$, what are the wavelengths of the light?
(b) At what angles are these lines found in the secondorder spectra:

Prabhu Ramji
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02:55

Problem 40

Intense white light is incident on a diffraction grating that has 600 lines/mm. (a) What is the highest order in which the complete visible spectrum can be seen with this grating? (b) What is the angular separation between the violet edge $(400 \mathrm{~nm})$ and the red edge $(700 \mathrm{~nm})$ of the first-order spectrum produced by the grating?

Zachary Warner
Zachary Warner
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02:09

Problem 41

The hydrogen spectrum has a red line at $656 \mathrm{~nm}$ and a violet line at $434 \mathrm{~nm}$. What angular separation between these two spectral lines is obtained with a diffraction grating that has 4500 lines $/ \mathrm{cm} ?$

Prabhu Ramji
Prabhu Ramji
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01:56

Problem 42

A grating with 1500 slits per centimeter is illuminated with light of wavelength $500 \mathrm{~nm}$. (a) What is the highest-order number that can be observed with this grating?
(b) Repeat for a grating of 15000 slits per centimeter.

Prabhu Ramji
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03:14

Problem 43

A light source emits two major spectral lines: an orange line of wavelength $610 \mathrm{~nm}$ and a blue-green line of wavelength $480 \mathrm{~nm}$. If the spectrum is resolved by a diffraction grating having 5000 lines $/ \mathrm{cm}$ and viewed on a screen $2.00 \mathrm{~m}$ from the grating, what is the distance (in centimeters) between the two spectral lines in the second-order spectrum?

Prabhu Ramji
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01:11

Problem 44

White light is spread out into its spectral components by a diffraction grating. If the grating has 2000 lines per centimeter, at what angle does red light of wavelength $640 \mathrm{~nm}$ appear in the first-order spectrum?

Prabhu Ramji
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04:36

Problem 45

Light from an argon laser strikes a diffraction grating that has 5310 grooves per centimeter. The central and first-order principal maxima are separated by $0.488 \mathrm{~m}$ on a wall $1.72 \mathrm{~m}$ from the grating. Determine the wavelength of the laser light.

Khoobchandra Agrawal
Khoobchandra Agrawal
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01:20

Problem 46

ecp Take red light at $700 \mathrm{~nm}$ and violet at $400 \mathrm{~nm}$ as the ends of the visible specurum and consider the continuous spectrum of white light formed by a diffraction grating with a spacing of $d$ meters between adjacent lines. Show that the interval $\theta_{i 2} \leq \theta \leq \theta_{, 2}$ of the continuous spectrum in second order must overlap the interval $\theta_{\mathrm{r} 3} \leq \theta \leq \theta_{r 3}$ of the third-order spectrum. Note: $\theta_{i 2}$ is the angle of the violet light in second order, and $\theta_{r 2}$ is the angle made by red light in second order.

Suzanne W.
Suzanne W.
Numerade Educator
03:29

Problem 47

Sunlight is incident on a diffraction grating that has 2750 lines $/ \mathrm{cm} .$ The second-order spectrum over the visible range $(400-700 \mathrm{~nm})$ is to be limited to $1.75 \mathrm{~cm}$ along a screen that is a distance $L$ from the grating. What is the required value of $L_{i}^{2}$

Prabhu Ramji
Prabhu Ramji
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03:50

Problem 48

A diffraction grating has $4.200 \times 10^{3}$ rulings per centimeter. The screen is $2.000 \mathrm{~m}$ from the grating. In parts
(a) through (e), round each result to four digits, using the rounded values for subsequent calculations. (a) Compute the value of $d$, the distance between adjacent rulings. Express the answer in meters. (b) Calculate the angle of the second-order maximum made by the $589.0-\mathrm{nm}$ wave-

Prabhu Ramji
Prabhu Ramji
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02:59

Problem 49

A beam of $541-n m$ light is incident on a diffraction grating that has 400 lines/mm. (a) Determine the angle of the second-order ray. (b) If the entire apparatus is immersed in water, determine the new second-order angle of diffraction. (c) Show that the two diffracted rays of parts (a) and (b) are related through the law of refraction.

Prabhu Ramji
Prabhu Ramji
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03:41

Problem 50

Light containing two different wavelengths passes through a diffraction grating with 1200 slits/cm. On a screen $15.0 \mathrm{~cm}$ from the grating, the third-order maximum of the shorter wavelength falls midway between the central maximum and the first side maximum for the longer wavelength. If the neighboring maxima of the longer wavelength are $8.44 \mathrm{~mm}$ apart on the screen, what are the wavelengths in the light? Hint: Use the small-angle approximation.

Prabhu Ramji
Prabhu Ramji
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01:17

Problem 51

The angle of incidence of a light beam in air onto a reflecting surface is continuously variable. The reflected ray is found to be completely polarized when the angle of incidence is $48.0^{\circ}$. (a) What is the index of refraction of the reflecting material? (b) If some of the incident light (at an angle of $48.0^{\circ}$ ) passes into the material below the surface, what is the angle of refraction?

Salamat Ali
Salamat Ali
Numerade Educator
03:41

Problem 52

Unpolarized light passes through two Polaroid sheets. The transmission axis of the analyzer makes an angle of $35.0^{\circ}$ with the axis of the polarizer. (a) What fraction of the original unpolarized light is transmitted through the analyzer? (b) What fraction of the original light is absorbed by the analyzer?

Zachary Warner
Zachary Warner
Numerade Educator
01:02

Problem 53

The index of refraction of a glass plate is $1.52 .$ What is the Brewster's angle when the plate is (a) in air and (b) in water? (See Problem 57 .)

Salamat Ali
Salamat Ali
Numerade Educator
01:15

Problem 54

A light beam is incident on a piece of fused quartz $(n=$ $1.458$ ) at the Brewster's angle. Find the (a) value of Brewster's angle and (b) the angle of refraction for the transmitted ray.

Salamat Ali
Salamat Ali
Numerade Educator
01:15

Problem 55

A light beam is incident on a piece of fused quartz ( $n=$ $1.458$ ) at the Brewster's angle. Find the (a) value of Brewster's angle and (b) the angle of refraction for the transmitted ray.

Salamat Ali
Salamat Ali
Numerade Educator
01:05

Problem 56

The critical angle for total internal reflection for sapphire surrounded by air is $34.4^{\circ} .$ Calculate the Brewster's angle for sapphire if the light is incident from the air.

Zachary Warner
Zachary Warner
Numerade Educator
01:31

Problem 57

Equation $24.14$ assumes the incident light is in air. If the light is incident from a medium of index $n_{1}$ onto a medium of index $n_{2}$, follow the procedure used to derive Equation $24.14$ to show that $\tan \theta_{\phi}=n_{\mathrm{g}} / n_{1}$.

Prabhu Ramji
Prabhu Ramji
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01:23

Problem 58

Plane-polarized light is incident on a single polarizing disk, with the direction of $E_{0}$ parallel to the direction of the transmission axis. Through what angle should the disk be rotated so that the intensity in the transmitLed beam is reduced by a factor of (a) $2.00$, (b) 4,00, and
(c) $6.00 ?$

Prabhu Ramji
Prabhu Ramji
Numerade Educator
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Problem 59

Three polarizing plates whose planes are parallel are centered on a common axis. The directions of the transmission axes relative to the common vertical direction are shown in Figure P24.59. A linearly polarized beam of light with plane of polarization parallel to the vertical reference direction is incident from the left onto the first disk with intensity $I_{i}=10.0$ units (arbitrary). Calculate the transmitted intensity $I_{i}$ when $\theta_{1}=20.0^{\circ}, \theta_{2}=40.0^{\circ}$, and $\theta_{3}=60.0^{\circ}$. Hint: Make repeated use of Malus's law.

Prabhu Ramji
Prabhu Ramji
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01:16

Problem 60

Light of intensity $I_{0}$ and polarized parallel to the transmission axis of a polarizer is incident on an analyzer. (a) If the transmission axis of the analyzer makes an angle of $45^{\circ}$ with the axis of the polarizer, what is the intensity of the transmitted light? (b) What should the angle between the transmission axes be to make $I / I_{0}=1 / 3$ ?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:46

Problem 61

Light with a wavelength in vacuum of $546.1 \mathrm{~nm}$ falls perpendicularly on a biological specimen that is 1.000 $\mu \mathrm{m}$ thick. The light splits into two beams polarized at right angles, for which the indices of refraction are $1.320$ and $1.333$, respectively, (a) Calculate the wavelength of each component of the light while it is traversing the specimen. (b) Calculate the phase difference between the two beams when they emerge from the specimen.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:39

Problem 62

Light from a helium-neon laser $(\lambda=632.8 \mathrm{~nm})$ is incident on a single slit. What is the maximum width of the slit for which no diffraction minima are observed?

Aja S
Aja S
Numerade Educator
00:50

Problem 63

Laser light with a wavelength of $632.8 \mathrm{~nm}$ is directed through one slit or two slits and allowed to fall on a screen $2.60 \mathrm{~m}$ beyond. Figure $\mathrm{P} 24.63$ shows the pattern on the
screen, with a centimeter ruler below it. Did the light pass through one slit or two slits? Explain how you can tell. If the answer is one slit, find its width. If the answer is two slits, find the distance between their centers.

Salamat Ali
Salamat Ali
Numerade Educator
03:01

Problem 64

In a Young's interference experiment, the two slits are separated by $0.150 \mathrm{~mm}$ and the incident light includes two wavelengths: $\lambda_{1}=540 \mathrm{~nm}$ (green) and $\lambda_{2}=$ $450 \mathrm{~nm}$ (blue). The overlapping interference patterns are observed on a screen $1.40 \mathrm{~m}$ from the slits. (a) Find a relationship between the orders $m_{1}$ and $m_{2}$ that determines where a bright fringe of the green light coincides with a bright fringe of the blue light. (The order $m_{1}$ is associated with $\lambda_{1}$, and $m_{2}$ is associated with $\lambda_{2 .}$ ) (b) Find the minimum values of $m_{1}$ and $m_{2}$ such that the overlapping of the bright fringes will occur and find the position of the overlap on the screen.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:01

Problem 65

Light of wavelength $546 \mathrm{~nm}$ (the intense green line from a mercury source) produces a Young's interference pattern in which the second minimum from the central maximum is along a direction that makes an angle of $18.0 \mathrm{~min}$ of arc with the axis through the central maximum. What is the distance between the parallel slits?

Salamat Ali
Salamat Ali
Numerade Educator
04:16

Problem 66

The two speakers are placed $35.0 \mathrm{~cm}$ apart. A single oscillator makes the speakers vibrate in phase at a frequency of $2.00 \mathrm{kH}_{\mathrm{z}}$. At what angles, measured from the perpendicular bisector of the line joining the speakers, would a distant observer hear maximum sound intensity? Minimum sound intensity? (Take the speed of sound to be $340 \mathrm{~m} / \mathrm{s}$.)

Prabhu Ramji
Prabhu Ramji
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01:34

Problem 67

Interference effects are produced at point $P$ on a screen as a result of direct rays from a $500-\mathrm{nm}$ source and reflected rays off a mirror, as shown in Figure $\mathrm{P} 24.67$. If the source is $100 \mathrm{~m}$ to the left of the screen and $1.00 \mathrm{~cm}$ above the mirror, find the distance $y$ (in millimeters) to the first dark band above the mirror.

Suzanne W.
Suzanne W.
Numerade Educator
03:31

Problem 68

Many cells are transparent and colorless. Structures of great interest in biology and medicine can be practically invisible to ordinary microscopy. An interference microscope reveals a difference in refractive index as a shift in interference fringes to indicate the size and shape of cell structures. The idea is exemplified in the following problem:
An air wedge is formed between two glass plates in contact along one edge and slightly separated at the opposite edge. When the plates are illuminated with monochromatic light from above, the reflected light has 85 dark fringes. Calculate the number of dark fringes that appear if water $(n=1.33)$ replaces the air between the plates.

Zachary Warner
Zachary Warner
Numerade Educator
03:34

Problem 69

Shows a radio-wave transmitter and a receiver, both $h=50.0 \mathrm{~m}$ above the ground and $d=600 \mathrm{~m}$ apart. The receiver can receive signals directly from the transmitter and indirectly from signals that bounce off the ground. If the ground is level between the transmitter and receiver and a $\lambda / 2$ phase shift occurs upon reflection, determine the longest wavelengths that interfere
(a) constructively and (b) destructively.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
04:50

Problem 70

Three polarizers, centered on a common axis and with their planes parallel to one another, have transmission axes oriented at angles of $\theta_{1}, \theta_{2}$, and $\theta_{3}$ from the vertical, as shown in Figure $\mathrm{P} 24.59$. Light of intensity $I_{i}$, polarized with its plane of polarization oriented vertically, is incident from the left onto the first polarizer. What is the ratio $I_{f} / I_{i}$ of the final transmitted intensity to the incident intensity if (a) $\theta_{1}=45^{\circ}, \theta_{2}=90^{\circ}$, and $\theta_{3}=0^{\circ}$ ? (b) $\theta_{1}=0^{\circ}$,
$\theta_{2}=45^{\circ}$, and $\theta_{3}=90^{\circ}$ ?

Zachary Warner
Zachary Warner
Numerade Educator
01:16

Problem 71

The transmitting antenna on a submarine is $5.00 \mathrm{~m}$ above the water when the ship surfaces. The captain wishes to transmit a message to a receiver on a $90.0$ -m-tall cliff at the ocean shore. If the signal is to be completely polarized by reflection off the ocean surface, how far must the ship be from the shore?

Salamat Ali
Salamat Ali
Numerade Educator
03:11

Problem 72

A plano-convex lens (flat on one side, convex on the other) with index of refraction $n$ rests with its curved side (radius of curvature $R$ ) on a flat glass surface of the same index of refraction with a film of index $n_{\text {film }}$ between them. The lens is illuminated from above by light of wavelength $\lambda$. Show that the dark Newton rings that appear have radii of
$$
r \approx \sqrt{m \lambda R / n_{\text {film }}}
$$
where $m$ is an integer.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:02

Problem 73

A diffraction pattern is produced on a screen $140 \mathrm{~cm}$ from a single slit, using monochromatic light of wavelength $500 \mathrm{~nm}$. The distance from the center of the central maximum to the first-order maximum is $3.00 \mathrm{~mm}$. Calculate the slit width. Hint: Assume that the first-order maximum is halfway between the first- and second-order minima.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:04

Problem 74

A flat piece of glass is supported horizontally above the flat end of a $10.0$ -cm-long metal rod that has its lower end rigidly fixed. The thin film of air between the rod and the glass is observed to be bright when illuminated by light of wavelength $500 \mathrm{~nm}$. As the temperature is slowly increased by $25.0^{\circ} \mathrm{C}$, the film changes from bright to dark and back to bright 200 times. What is the coefficient of linear expansion of the metal?

Prabhu Ramji
Prabhu Ramji
Numerade Educator