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Principles of Physics a Calculus Based Text

Raymond A. Serway, John W. Jewett, Jr.

Chapter 25

Reflection and Refraction of Light - all with Video Answers

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Chapter Questions

01:52

Problem 1

A prism that has an apex angle of $50.0^{\circ}$ is made of cubic zirconia. What is its minimum angle of deviation?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
03:12

Problem 2

Two flat, rectangular mirrors, both perpendicular to a horizontal sheet of paper, are set edge to edge with their reflecting surfaces perpendicular to each other. (a) A light ray in the plane of the paper strikes one of the mirrors at an arbitrary angle of incidence $\theta_{1}$, Prove that the final direction of the ray, after reflection from both mirrors, is opposite its initial direction. (b) What If? Now assume the paper is replaced with a third flat mirror, touching edges with the other two and perpendicular to both, creating a corner-cube retroreflector. A ray of light is incident from any direction
within the octant of space bounded by the reflecting surfaces. Argue that the ray will reflect once from each mirror and that its final direction will be opposite its original direction. The $A$ pollo 11 astronauts placed a panel of cornercube retroreflectors on the Moon. Analysis of timing data taken with it reveals that the radius of the Moon's orbit is increasing at the rate of $3.8 \mathrm{cm} / \mathrm{yr}$ as it loses kinetic energy because of tidal friction.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
04:27

Problem 3

The two mirrors illustrated in Figure P25.3 meet at a right angle. The beam of light in the vertical plane indicated by the dashed lines strikes mirror 1 as shown. (a) Determine the distance the reflected light beam travels before striking mirror $2 .$ (b) In what direction does the light beam travel after being reflected from mirror 2 ?

Jillian Rae Villa
Jillian Rae Villa
Numerade Educator
06:42

Problem 4

A plane sound wave in air at $20^{\circ} \mathrm{C},$ with wavelength $589 \mathrm{mm},$ is incident on a smooth surface of water at $25^{\circ} \mathrm{C}$ at an angle of incidence of $13.0^{\circ} .$ Determine (a) the angle of refraction for the sound wave and (b) the wavelength of the sound in water. A narrow beam of sodium yellow light, with wavelength 589 nm in vacuum, is incident from air onto a smooth water surface at an angle of incidence of $13.0^{\circ} .$ Determine (c) the angle of refraction and (d) the wavelength of the light in water. (e) Compare and contrast the behavior of the sound and light waves in this problem.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
04:21

Problem 5

How many times will the incident beam shown in Figure $\mathrm{P} 25.5$ be reflected by each of the parallel mirrors?

Jillian Rae Villa
Jillian Rae Villa
Numerade Educator
08:38

Problem 6

A submarine is $300 \mathrm{m}$ horizontally from the shore of a freshwater lake and $100 \mathrm{m}$ beneath the surface of the water. A laser beam is sent from the submarine so that the beam strikes the surface of the water $210 \mathrm{m}$ from the shore. A building stands on the shore, and the laser beam hits a target at the top of the building. The goal is to find the height of the target above sea level. (a) Draw a diagram of the situation, identifying the two triangles that are important in finding the solution. (b) Find the angle of incidence of the beam striking the water-air interface. (c) Find the angle of refraction. (d) What angle does the refracted beam make with the horizontal? (e) Find the height of the target above sea level.

Bethany Campbell
Bethany Campbell
Numerade Educator
04:39

Problem 7

The wavelength of red helium-neon laser light in air is $632.8 \mathrm{nm}$. (a) What is its frequency? (b) What is its wavelength in glass that has an index of refraction of 1.50 ?
(c) What is its speed in the glass?

Aatish Gupta
Aatish Gupta
Numerade Educator
02:31

Problem 8

An underwater scuba diver sees the Sun at an apparent angle of $45.0^{\circ}$ above the horizontal. What is the actual elevation angle of the Sun above the horizontal?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:43

Problem 9

A digital video disc (DVD) records information in a spiral track approximately $1 \mu \mathrm{m}$ wide. The track consists of a seFies of pits in the information layer (Fig. P25.9a) that scatter light from a laser beam sharply focused on them. The laser shines in from below through transparent plastic of thickness $t=1.20 \mathrm{mm}$ and index of refraction 1.55 (Fig. P25.9b ) . Assume the width of the laser beam at the information layer must be $a=1.00 \mu \mathrm{m}$ to read from only one track and not from its neighbors. Assume the width of the beam as it enters the transparent plastic is $w=0.700 \mathrm{mm}$. A lens makes the beam converge into a cone with an apex angle $2 \theta_{1}$ before it enters the DVD. Find the incidence angle $\theta_{1}$ of the light at the edge of the conical beam. This design is relatively immune to small dust particles degrading the video quality.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
03:07

Problem 10

When you look through a window, by what time interval is the light you see delayed by having to go through glass instead of air? Make an order-of-magnitude estimate on the basis of data you specify. By how many wavelengths is it delayed?

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
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02:46

Problem 11

A ray of light is incident on a flat surface of a block of crown glass that is surrounded by water. The angle of refraction is $19.6^{\circ} .$ Find the angle of reflection.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:54

Problem 12

A laser beam is incident at an angle of $30.0^{\circ}$ from the vertical onto a solution of corn syrup in water. The beam is refracted to $19.24^{\circ}$ from the vertical. (a) What is the index of refraction of the corn syrup solution? Assume that the light is red, with vacuum wavelength $632.8 \mathrm{nm}$ Find its (b) wavelength, (c) frequency, and (d) speed in the solution.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
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01:25

Problem 13

A laser beam with vacuum wavelength $632.8 \mathrm{nm}$ is incident from air onto a block of Lucite as shown in Active Figure $25.8 \mathrm{b}$. The line of sight of the photograph is perpendicular to the plane in which the light moves. Find (a) the speed, (b) the frequency, and (c) the wavelength of the light in the Lucite. Suggestion: Use a protractor.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
03:33

Problem 14

A light ray initially in water enters a transparent substance at an angle of incidence of $37.0^{\circ},$ and the transmitted ray is refracted at an angle of $25.0^{\circ} .$ Calculate the speed of light in the transparent substance.

Bethany Campbell
Bethany Campbell
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01:51

Problem 15

Find the speed of light in (a) flint glass, (b) water, and (c) cubic zirconia.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:31

Problem 16

A ray of light strikes a flat block of glass $(n=1.50)$ of thickness $2.00 \mathrm{cm}$ at an angle of $30.0^{\circ}$ with the normal. Trace the light ray through the glass and find the angles of incidence and refraction at each surface.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
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01:51

Problem 17

An opague cylindrical tank with an open top has a diameter of $3.00 \mathrm{m}$ and is completely filled with water. When the afternoon Sun reaches an angle of $28.0^{\circ}$ above the horizon, sunlight ceases to illuminate any part of the bottom of the tank. How deep is the tank?

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
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02:46

Problem 18

The reflecting surfaces of two intersecting flat mirrors are at an angle $\theta\left(0^{\circ} < \theta < 90^{\circ}\right)$ as shown in Figure $\mathrm{P} 25.18$. For a light ray that strikes the horizontal mirror, show that the emerging ray will intersect the incident ray at an angle $\beta=180^{\circ}-2 \theta$.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
02:46

Problem 19

Unpolarized light in vacuum is incident onto a sheet of glass with index of refraction $n$. The reflected and refracted rays are perpendicular to each other. Find the angle of incidence. This angle is called Brewster's angle or the polarizing angle. In this situation, the reflected light is linearly polarized, with its electric field restricted to be perpendicular to the plane containing the rays and the normal.

Aatish Gupta
Aatish Gupta
Numerade Educator
02:37

Problem 20

Figure $P 25.20$ shows a refracted light beam in linseed oil making an angle of $\alpha=$ $20.0^{\circ}$ with the normal line
$N N^{\prime} .$ The index of refraction of linseed oil is 1.48 Determine the angles (a) $\theta$ and (b) $\theta^{\prime}$.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
06:18

Problem 21

A narrow beam of ultrasonic waves reflects off the liver tumor illustrated in Figure $\mathrm{P} 25.21 .$ The speed of the wave is $10.0 \%$ less in the liver than in the surrounding medium. Determine the depth of the tumor.

Aatish Gupta
Aatish Gupta
Numerade Educator
03:34

Problem 22

When the light ray illustrated in Figure $\mathrm{P} 25.22$ passes through the glass block of index of refraction $n=1.50,$ it is shifted laterally by the distance $d .$ (a) Find the value of $d .(\mathrm{b})$ Find the time interval required for the light to pass through the glass block.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
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09:10

Problem 23

The index of refraction for violet light in silica flint glass is $1.66,$ and that for red light is $1.62 .$ What is the angular spread of visible light passing through a prism of apex angle $60.0^{\circ}$ if the angle of incidence is $50.0^{\circ}$ ? See Figure P25.23.

Aatish Gupta
Aatish Gupta
Numerade Educator
04:41

Problem 24

The index of refraction for violet light in silica flint glass is $n_{V},$ and that for red light is $n_{R} .$ What is the angular spread of visible light passing through a prism of apex angle $\Phi$ if the angle of incidence is $\theta$ ? See Figure P25.23.

Mayukh Banik
Mayukh Banik
Numerade Educator
03:05

Problem 25

A ray of light strikes the midpoint of one face of an equiangular glass prism $(n=1.50)$ at an angle of incidence of $30.0^{\circ} .$ Trace the path of the light ray through the glass and find the angles of incidence and refraction at each surface.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
01:15

Problem 26

The speed of a water wave is described by $v=\sqrt{g d}$, where $d$ is the water depth, assumed to be small compared to the wavelength. Because their speed changes, water waves refract when moving into a region of different depth. (a) Sketch a map of an ocean beach on the eastern side of a landmass. Show contour lines of constant depth under water, assuming a reasonably uniform slope. (b) Suppose waves approach the coast from a storm far away to the north-northeast. Demonstrate that the waves move nearly perpendicular to the shoreline when they reach the beach. (c) Sketch a map of a coastline with alternating bays and headlands as suggested in Figure $\mathrm{P} 25.26 .$ Again make a reasonable guess about the shape of contour lines of constant depth. (d) Suppose waves approach the coast, carrying energy with uniform density along originally straight wave fronts. Show that the energy reaching the coast is concentrated at the headlands and has lower intensity in the bays.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:39

Problem 27

For 589 -nm light, calculate the critical angle for the following materials surrounded by air: (a) cubic zirconia,
(b) flint glass, and (c) ice.

Rodger Claar
Rodger Claar
Numerade Educator
04:03

Problem 28

A room contains air in which the speed of sound is $343 \mathrm{m} / \mathrm{s}$. The walls of the room are made of concrete in which the speed of sound is $1850 \mathrm{m} / \mathrm{s}$. (a) Find the critical angle for total internal reflection of sound at the concrete air boundary. (b) In which medium must the sound be initially traveling if it is to undergo total internal reflection? (c) "A bare concrete wall is a highly efficient mirror for sound." Give evidence for or against this statement.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:46

Problem 29

A triangular glass prism with apex angle $\Phi=60.0^{\circ}$ has an index of refraction $n=1.50 \text { (Fig. } P 25.29)$ What is the smallest angle of incidence $\theta_{1}$ for which a light ray can emerge from the other side?

Narayan Hari
Narayan Hari
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00:00

Problem 30

A triangular glass prism with apex angle $\Phi$ has an index of refraction $n$ (Fig. $P 25.29$ ). What is the smallest angle of incidence $\theta_{1}$ for which a light ray can emerge from the other side?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:41

Problem 31

Consider a common mirage formed by superheated air immediately above a roadway. A truck driver whose eyes are $2.00 \mathrm{m}$ above the road, where $n=1.000293,$ looks forward. She perceives the illusion of a patch of water ahead on the road. The road appears wet only beyond a point on the road at which her line of sight makes an angle of $1.20^{\circ}$ below the horizontal. Find the index of refraction of the air immediately above the road surface.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
06:36

Problem 32

Around $1965,$ engineers at the Toro Company invented a gasoline gauge for small engines diagrammed in Figure $\mathrm{P} 25.32 .$ The gauge has no moving parts. It consists of a flat slab of transparent plastic fitting vertically into a slot in the cap on the gas tank. None of the plastic has a reflective coating. The plastic projects from the horizontal top down nearly to the bottom of the opaque tank. Its lower edge is cut with facets making angles of $45^{\circ}$ with the horizontal. A lawn mower operator looks down from above and sees a boundary between bright and dark on the gauge. The location of the boundary, across the width of the plastic, indicates the quantity of gasoline in the tank. (a) Explain how the gauge works. (b) Explain the design requirements, if any, for the index of refraction of the plastic.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
01:24

Problem 33

A glass optical fiber $(n=1.50)$ is submerged in water $(n=$ 1.33). What is the critical angle for light to stay inside the fiber?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:52

Problem 34

Why is the following situation impossible? A laser beam strikes one end of a slab of material of length $L=42.0 \mathrm{cm}$ and thickness $t=3.10 \mathrm{mm}$ as shown in Figure $\mathrm{P} 25.34$ (not to scale $) .$ It enters the material at the center of the left end, striking it at an angle of incidence of $\theta=50.0^{\circ} .$ The index of refraction of the slab is $n=1.48 .$ The light makes 85

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
01:19

Problem 35

Assume a transparent rod of diameter $d=2.00 \mu \mathrm{m}$ has an index of refraction of $1.36 .$ Determine the maximum angle $\theta$ for which the light rays incident on the end of the rod in Figure $P 25.35$ are subject to total internal reflection along the walls of the rod. Your answer defines the size of the cone of acceptance for the rod.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
03:40

Problem 36

An optical fiber has an index of refraction $n$ and diameter $d .$ It is surrounded by vacuum. Light is sent into the fiber along its axis as shown in Figure $\mathrm{P} 25.36 .$ (a) Find the smallest outside radius $R_{\text {min }}$ permitted for a bend in the fiber if no light is to escape. (b) What If? What result does part (a) predict as $d$ approaches zero? Is this behavior reasonable? Explain. $(c)$ As $n$ increases? $(d)$ As $n$ approaches $1 ?(\mathrm{e})$ Evaluate $R_{\min }$ assuming the fiber diameter is $100 \mu \mathrm{m}$ and its index of refraction is 1.40

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
03:11

Problem 37

A small light fixture on the bottom of a swimming pool is $1.00 \mathrm{m}$ below the surface. The light emerging from the still water forms a circle on the water surface. What is the diameter of this circle?

Aatish Gupta
Aatish Gupta
Numerade Educator
03:00

Problem 38

One technique for measuring the apex angle of a prism is shown in Figure $\mathrm{P} 25.38 .$ Two parallel rays of light are directed onto the apex of the prism so that the rays reflect from opposite faces of the prism. The angular separation $\gamma$ of the two reflected rays can be measured. Show that $\phi=\frac{1}{2} \gamma$.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
01:01

Problem 39

Three sheets of plastic have unknown indices of refraction. Sheet 1 is placed on top of sheet 2 , and a laser beam is directed onto the sheets from above. The laser beam enters sheet 1 and then strikes the interface between sheet 1 and sheet 2 at an angle of $26.5^{\circ}$ with the normal. The refracted beam in sheet 2 makes an angle of $31.7^{\circ}$ with the normal. The experiment is repeated with sheet 3 on top of sheet 2 , and, with the same angle of incidence on the sheet 3 -sheet 2 interface, the refracted beam makes an angle of $36.7^{\circ}$ with the normal. If the experiment is repeated again with sheet 1 on top of sheet 3 , with that same angle of incidence on the sheet 1 -sheet 3 interface, what is the expected angle of refraction in sheet 3 ?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:41

Problem 40

Consider a horizontal interface between air above and glass of index of refraction 1.55 below. (a) Draw a light ray incident from the air at angle of incidence $30.0^{\circ} .$ Determine the angles of the reflected and refracted rays and show them on the diagram. (b) What If? Now suppose the light ray is incident from the glass at an angle of $30.0^{\circ} .$ Determine the angles of the reflected and refracted rays and show all three rays on a new diagram. (c) For rays incident from the air onto the air-glass surface, determine and tabulate the angles of reflection and refraction for all the angles of incidence at $10.0^{\circ}$ intervals from $0^{\circ}$ to $90.0^{\circ} .$ (d) Do the same for light rays coming up to the interface through the glass.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
07:15

Problem 41

A light ray enters the atmosphere of the Earth and descends vertically to the surface a distance $h=100 \mathrm{km}$ below. The index of refraction where the light enters the atmosphere is 1.00 , and it increases linearly with distance to have the value $n=1.000293$ at the Earth's surface. (a) Over what time interval does the light traverse this path? (b) By what percentage is the time interval larger than that required in the absence of the Earth's atmosphere?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
04:28

Problem 42

A light ray enters the atmosphere of a planet and descends vertically to the surface a distance $h$ below. The index of refraction where the light enters the atmosphere is 1.00 , and it increases linearly with distance to have the value $n$ at the planet surface. (a) Over what time interval does the light traverse this path? (b) By what fraction is the time interval larger than that required in the absence of an atmosphere?

Prashant Bana
Prashant Bana
Numerade Educator
03:45

Problem 43

A 4.00-m-long pole stands vertically in a freshwater lake having a depth of $2.00 \mathrm{m}$. The Sun is $40.0^{\circ}$ above the horizontal. Determine the length of the pole's shadow on the bottom of the lake.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
03:55

Problem 44

Figure $P 25.44$ shows a top view of a square enclosure. The inner surfaces are plane mirrors. A ray of light enters a small hole in the center of one mirror. (a) At what angle $\theta$ must the ray enter if it exits through the hole after being reflected once by each of the other three mirrors?
(b) What If? Are there other values of $\theta$ for which the ray can exit after multiple reflections? If so, sketch one of the ray's paths.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
03:57

Problem 45

A light ray enters a rectangular block of plastic at an angle $\theta_{1}=45.0^{\circ}$ and emerges at an angle $\theta_{2}=76.0^{\circ}$ as shown in Figure $P 25.45 .$ (a) Determine the index of refraction of the plastic. (b) If the light ray enters the plastic at a point $L=50.0 \mathrm{cm}$ from the bottom edge, what time interval is required for the light ray to travel through the plastic?

Mayukh Banik
Mayukh Banik
Numerade Educator
04:29

Problem 46

The walls of an ancient shrine are perpendicular to the four cardinal compass directions. On the first day of spring, light from the rising Sun enters a rectangular window in the eastern wall. The light traverses 2.37 m horizontally to shine perpendicularly on the wall opposite the window. A tourist observes the patch of light moving across this western wall.
(a) With what speed does the illuminated rectangle move?
(b) The tourist holds a small, square mirror flat against the western wall at one corner of the rectangle of light. The mirror reflects light back to a spot on the eastern wall close beside the window. With what speed does the smaller square of light move across that wall? (c) Seen from latitude of $40.0^{\circ}$ north, the rising Sun moves through the sky along a line making a $50.0^{\circ}$ angle with the southeastern horizon. In what direction does the rectangular patch of light on the western wall of the shrine move? (d) In what direction does the smaller square of light on the eastern wall move?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:55

Problem 47

A hiker stands on an isolated mountain peak near sunset and observes a rainbow caused by water droplets in the air at a distance of $8.00 \mathrm{km}$ along her line of sight to the most intense light from the rainbow. The valley is $2.00 \mathrm{km}$ below the mountain peak and entirely flat. What fraction of the complete circular arc of the rainbow is visible to the hiker?

Mayukh Banik
Mayukh Banik
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05:02

Problem 48

A person looking into an empty container is able to see the far edge of the container's bottom as shown in Figure $\mathrm{P} 25.48$ a. The height of the container is $h$, and its width is $d .$ When the container is completely filled with a fluid of index of refraction $n$ and viewed from the same angle, the person can see the center of a coin at the middle of the container's bottom as shown in Figure P25.48b. (a) Show that the ratio $h / d$ is given by
$$\frac{h}{d}=\sqrt{\frac{n^{2}-1}{4-n^{2}}}$$
(b) Assuming the container has a width of $8.00 \mathrm{cm}$ and is filled with water, use the expression above to find the height of the container. (c) For what range of values of $n$ will the center of the coin not be visible for any values of
$h$ and $d$ ?

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
01:51

Problem 49

When light is incident normally on the interface between two transparent optical media, the intensity of the reflected light is given by the expression
$$S_{1}^{\prime}=\left(\frac{n_{2}-n_{1}}{n_{2}+n_{1}}\right)^{2} S_{1}$$
In this equation, $S_{1}$ represents the average magnitude of the Poynting vector in the incident light (the incident intensity $), S_{1}^{\prime}$ is the reflected intensity, and $n_{1}$ and $n_{2}$ are the refractive indices of the two media. (a) What fraction of the incident intensity is reflected for 589 -nm light normally incident on an interface between air and crown glass? (b) Does it matter in part (a) whether the light is in the air or in the glass as it strikes the interface?

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
03:13

Problem 50

Refer to Problem 49 for its description of the reflected intensity of light normally incident on an interface between two transparent media. (a) For light normally incident on an interface between vacuum and a transparent medium of index $n$, show that the intensity $S_{2}$ of the transmitted light is given by $S_{2} / S_{1}=4 n /(n+1)^{2}$. (b) Light travels perpendicularly through a diamond slab, surrounded by air, with parallel surfaces of entry and exit. Apply the transmission fraction in part (a) to find the approximate overall transmission through the slab of diamond, as a percentage. Ignore light reflected back and forth within the slab.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
04:50

Problem 51

This problem builds upon the results of Problems 49 and $50 .$ Light travels perpendicularly through a diamond slab, surrounded by air, with parallel surfaces of entry and exit. The intensity of the transmitted light is what fraction of the incident intensity? Include the effects of light reflected back and forth inside the slab.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
02:23

Problem 52

Why is the following situation impossible? The perpendicular distance of a light bulb from a large plane mirror is twice the perpendicular distance of a person from the mirror. Light from the light bulb reaches the person by two paths:
(1) it travels to the mirror and reflects from the mirror to the person, and (2) it travels directly to the person without reflecting off the mirror. The total distance traveled by the light in the first case is 3.10 times the distance traveled by the light in the second case.

Anand Jangid
Anand Jangid
Numerade Educator
02:29

Problem 53

The light beam in Figure $\mathrm{P} 25.53$ strikes surface 2 at the critical angle. Determine the angle of incidence $\theta_{1}$

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
03:07

Problem 54

A light ray of wavelength $589 \mathrm{nm}$ is incident at an angle $\theta$ on the top surface of a block of polystyrene as shown in Figure $\mathrm{P} 25.54$
(a) Find the maximum value of $\theta$ for which the refracted ray undergoes total internal reflection at the point $P$ located at the left vertical face of the block. What If? Re-
peat the calculation for the case in

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
03:36

Problem 55

A transparent cylinder of radius $R=2.00 \mathrm{m}$ has a mirrored surface on its right half as shown in Figure P25.55. A light ray traveling in air is incident on the left side of the cylinder. The incident light ray and exiting light ray are parallel and $d=2.00 \mathrm{m} .$ Determine the index of refraction of the material.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:51

Problem 56

Students allow a narrow beam of laser light to strike a water surface. They measure the angle of refraction for selected angles of incidence and record the data shown in the accompanying table. (a) Use the data to verify Snell's law of refraction by plotting the sine of the angle of incidence versus the sine of the angle of refraction. (b) Explain what the shape of the graph demonstrates. (c) Use the resulting plot to deduce the index of refraction of water, explaining how you do so.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
03:04

Problem 57

A ray of light passes from air into water. For its deviation angle $\delta=\left|\theta_{1}-\theta_{2}\right|$ to be $10.0^{\circ},$ what must its angle of incidence be?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:18

Problem 58

A mirror is often "silvered" with aluminum. By adjusting the thickness of the metallic film, one can make a sheet of glass into a mirror that reflects anything between say $3 \%$ and $98 \%$ of the incident light, transmitting the rest. Prove that it is impossible to construct a "one-way mirror" that would reflect $90 \%$ of the electromagnetic waves incident from one side and reflect $10 \%$ of those incident from the other side. ( Suggestion: Use Clausius's statement of the second law of thermodynamics.)

Dominador Tan
Dominador Tan
Numerade Educator
05:25

Problem 59

Figure $P 25.59$ shows an overhead view of a room of square floor area and side $L$ At the center of the room is a
mirror set in a vertical plane and rotating on a vertical shaft at angular speed $\omega$ about an axis coming out of the page. A bright red laser beam enters from the center point on one wall of the room and strikes the mirror. As the mirror rotates, the reflected laser beam creates a red spot sweeping across the walls of the room. (a) When the spot of light on the wall is at distance $x$ from point $O,$ what is its speed?
(b) What value of $x$ corresponds to the minimum value for the speed? (c) What is the minimum value for the speed? (d) What is the maximum speed of the spot on the wall? (e) In what time interval does the spot change from its minimum to its maximum speed?

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator
02:35

Problem 60

Why is the following situation impossible? While at the bottom of a calm freshwater lake, a scuba diver sees the Sun at an apparent angle of $38.0^{\circ}$ above the horizontal.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
03:05

Problem 61

A material having an index of refraction $n$ is surrounded by vacuum and is in the shape of a quarter circle of radius $R \text { (Fig. } P 25.61) .$ A light ray parallel to the base of the material is incident from the left at a distance $L$ above the base and emerges from the material at the angle $\theta$. Determine an expression for $\theta$ in terms of $n, R,$ and $L$

Mayukh Banik
Mayukh Banik
Numerade Educator
03:54

Problem 62

As sunlight enters the Earth's atmosphere, it changes direction due to the small difference between the speeds of light in vacuum and in air. The duration of an optical day is defined as the time interval between the instant when the top of the rising Sun is just visible above the horizon and the instant when the top of the Sun just disappears below the horizontal plane. The duration of the geometric day is defined as the time interval between the instant a mathematically straight line between an observer and the top of the Sun just clears the horizon and the instant this line just dips below the horizon. (a) Explain which is longer, an optical day or a geometric day. (b) Find the difference between these two time intervals. Model the Earth's atmosphere as uniform, with index of refraction 1.000293 a sharply defined upper surface, and depth $8614 \mathrm{m}$. Assume the observer is at the Earth's equator so that the apparent path of the rising and setting Sun is perpendicular to the horizon.

Mohamed Raafat Mohamed
Mohamed Raafat Mohamed
Numerade Educator