Answer: An object with a height of 46 cm is placed 2.4 m

Alaser beam is reected by a plane mirror. It is observed that the angle between the incident and reected beams is 28. If the mirror is now rotated so that the angle of incidence increases by 5.0, what is the new angle between the incident and reected beams?

The reecting surfaces of two mirrors form a vertex with an angle of 120. If a ray of light strikes mirror 1 with an angle of incidence of 55, nd the angle of reection of the ray when it leaves mirror 2.

A ray of light reects from a plane mirror with an angle of incidence of 37. If the mirror is rotated by an angle , through what angle is the reected ray rotated?

A small vertical mirror hangs on the wall, 1.40 m above the oor. Sunlight strikes the mirror, and the reected beam forms a spot on the oor 2.50 m from the wall. Later in the day, you notice that the spot has moved to a point 3.75 m from the wall.(a)Were your two observations made in the morning or in the afternoon? Explain. (b) What was the change in the Suns angle of elevation between your two observations?

Sunlight enters a room at an angle of 32 above the horizontal and reects from a small mirror lying at on the oor. The reected light forms a spot on a wall that is 2.0 m behind the mirror, as shown in Figure 2642. If you now place a pencil under the

You stand 1.50 m in front of a wall and gaze downward at a small vertical mirror mounted on it. In this mirror you can see the reection of your shoes. If your eyes are 1.85 m above your feet, through what angle should the mirror be tilted for you to see your eyes reected in the mirror? (The location of the mirror remains the same, only its angle to the vertical is changed.)

Standing 2.3 m in front of a small vertical mirror, you see the reection of your belt buckle, which is 0.72 m below your eyes. (a) What is the vertical location of the mirror relative to the level of your eyes? (b) What angle do your eyes make with the horizontal when you look at the buckle? (c) If you now move backward until you are 6.0 m from the mirror, will you still see the buckle, or will you see a point on your body that is above or below the buckle? Explain.

How many times does the light beam shown in Figure 2643 reect from (a) the top and (b) the bottom mirror?

If you view a clock in a mirror, do the hands rotate clockwise or counterclockwise?

A12.5-foot-long, nearsighted python is stretched out perpendicular to a plane mirror, admiring its reected image. If the greatest distance to which the snake can see clearly is 26.0 ft, how close must its head be to the mirror for it to see a clear image of its tail?

(a) How rapidly does the distance between you and your mirror image decrease if you walk directly toward a mirror with a speed of 2.6 m/s? (b)Repeat part (a) for the case in which you walk toward a mirror but at an angle of 38to its normal.

You are 1.9 m tall and stand 3.2 m from a plane mirror that extends vertically upward from the oor. On the oor 1.5 m in front of the mirror is a small table, 0.80 m high. What is the minimum height the mirror must have for you to be able to see the top of the table in the mirror?

The rear window in a car is approximately a rectangle, 1.3 m wide and 0.30 m high. The inside rearview mirror is 0.50 m from the drivers eyes, and 1.50 m from the rear window. What are the minimum dimensions for the rearview mirror if the driver is to be able to see the entire width and height of the rear window in the mirror without moving her head?

You hold a small plane mirror 0.50 m in front of your eyes, as shown in Figure 2644 (not to scale). The mirror is 0.32 cm high, and in it you see the image of a tall building behind you. (a) If the building is 95 m behind you, what vertical height of the building, H, can be seen in the mirror at any one time?(b)If you move the mirror closer to your eyes, does your answer to part (a) increase, decrease, or stay the same? Explain.

Two rays of light converge toward each other, as shown in Figure 2645, forming an angle of 27. Before they intersect, however, they are reected from a circular plane mirror with a diameter of 11 cm. If the mirror can be moved horizontally to the left or right, what is the greatest possible distance dfrom the mirror to the point where the reected rays meet?

For a corner reector to be effective, its surfaces must be precisely perpendicular. Suppose the surfaces of a corner reector left on the Moons surface by the Apollo astronauts formed a 90.001angle with each other. If a laser beam is bounced back to Earth from this reector, how far (in kilometers) from its starting point will the reected beam strike Earth? For simplicity, assume the beam reects from only two sides of the reector, and that it strikes the rst surface at precisely 45.

Astronomers often use large mirrors in their telescopes to gather as much light as possible from faint distant objects. Should the mirror in their telescopes be concave or convex? Explain.

Asection of a sphere has a radius of curvature of 0.86 m. If this section is painted with a reective coating on both sides, what is the focal length of (a) the convex side and (b) the concave side?

Amirrored-glass gazing globe in a garden is 31.9 cm in diameter. What is the focal length of the globe?

Sunlight reects from a concave piece of broken glass, converging to a point 15 cm from the glass. What is the radius of curvature of the glass?

You hold a shiny tablespoon at arms length and look at the back side of the spoon. (a) Is the image you see of yourself upright or inverted? (b)Is the image enlarged or reduced? (c)Is the image real or virtual?

You hold a shiny tablespoon at arms length and look at the front side of the spoon. (a) Is the image you see of yourself upright or inverted? (b)Is the image enlarged or reduced? (c)Is the image real or virtual?

An object is placed in front of a convex mirror whose radius of curvature is R. What is the greatest distance behind the mirror that the image can be formed?

An object is placed to the left of a concave mirror, beyond its focal point. In which direction will the image move when the object is moved farther to the left?

An object is placed to the left of a convex mirror. In which direction will the image move when the object is moved farther to the left?

Asmall object is located 30.0 cm in front of a concave mirror with a radius of curvature of 40.0 cm. Where will the image be formed?

Use ray diagrams to show whether the image formed by a convex mirror increases or decreases in size as an object is brought closer to the mirrors surface.

An object with a height of 46 cm is placed 2.4 m in front of a concave mirror with a focal length of 0.50 m. (a) Determine the approximate location and size of the image using a ray diagram. (b) Is the image upright or inverted?

Find the location and magnication of the image produced by the mirror in Problem 28 using the mirror and magnication equations.

An object with a height of 46 cm is placed 2.4 m in front of a convex mirror with a focal length of . (a)Determine the approximate location and size of the image using a ray diagram. (b) Is the image upright or inverted?

Find the location and magnication of the image produced by the mirror in Problem 30 using the mirror and magnication equations.

During a daytime football game you notice that a players reective helmet forms an image of the Sun 4.8 cm behind the surface of the helmet. What is the radius of curvature of the helmet, assuming it to be roughly spherical?

Amagician wishes to create the illusion of a 2.74-m-tall elephant. He plans to do this by forming a virtual image of a 50.0cm-tall model elephant with the help of a spherical mirror. (a)Should the mirror be concave or convex? (b)If the model must be placed 3.00 m from the mirror, what radius of curvature is needed? (c) How far from the mirror will the image be formed?

Aperson 1.7 m tall stands 0.66 m from a reecting globe in a garden. (a) If the diameter of the globe is 18 cm, where is the image of the person, relative to the surface of the globe? (b)How large is the persons image?

Shaving/makeup mirrors typically have one at and one concave (magnifying) surface. You nd that you can project a magnied image of a lightbulb onto the wall of your bathroom if you hold the mirror 1.8 m from the bulb and 3.5 m from the wall.(a)What is the magnication of the image? (b)Is the image erect or inverted? (c) What is the focal length of the mirror?

The Hale Telescope The 200-inch-diameter concave mirror of the Hale telescope on Mount Palomar has a focal length of 16.9 m. An astronomer stands 20.0 m in front of this mirror. (a) Where is her image located? Is it in front of or behind the mirror? (b) Is her image real or virtual? How do you know? (c) What is the magnication of her image?

A concave mirror produces a virtual image that is three times as tall as the object. (a)If the object is 28 cm in front of the mirror, what is the image distance? (b) What is the focal length of this mirror?

Aconcave mirror produces a real image that is three times as large as the object. (a)If the object is 22 cm in front of the mirror, what is the image distance? (b) What is the focal length of this mirror?

The virtual image produced by a convex mirror is onequarter the size of the object. (a)If the object is 36 cm in front of the mirror, what is the image distance? (b) What is the focal length of this mirror?

A5.7-ft-tall shopper in a department store is 17 ft from a convex security mirror. The shopper notices that his image in the mirror appears to be only 6.4 in. tall. (a) Is the shoppers image upright or inverted? Explain. (b)What is the mirrors radius of curvature?

You view a nearby tree in a concave mirror. The inverted image of the tree is 3.8 cm high and is located 7.0 cm in front of the mirror. If the tree is 23 m from the mirror, what is its height?

Ashaving/makeup mirror produces an erect image that is magnied by a factor of 2.2 when your face is 25 cm from the mirror. What is the mirrors radius of curvature?

Aconcave mirror with a focal length of 36 cm produces an image whose distance from the mirror is one-third the object distance. Find the object and image distances.

Predict/Explain When a ray of light enters a glass lens surrounded by air, it slows down. (a)As it leaves the glass, does its speed increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. Its speed increases because the ray is now propagating in a medium with a smaller index of refraction. II. The speed decreases because the speed of light decreases whenever light moves from one medium to another. III. The speed will stay the same because the speed of light is a universal constant.

Samurai Fishing Ahumorous scene in Akira Kurosawas classic lm The Seven Samurai shows the young samurai Kikuchiyo wading into a small stream and plucking a sh from it for his dinner. (a)As Kikuchiyo looks through the water to the sh, does he see it in the general direction of point 1 or point 2 in Figure 2646? (b) If the sh looks up at Kikuchiyo, does it see Kikuchiyos head in the general direction of point 3 or point 4?

When color Aand color B are sent through a prism, color Ais bent more than color B. Which color travels more rapidly in the prism? Explain.

Day Versus Night (a) Imagine for a moment that the Earth has no atmosphere. Over the period of a year, is the number of daylight hours at your home greater than, less than, or equal to the number of nighttime hours? (b) Repeat part (a), only this time take into account the Earths atmosphere.

Predict/Explain A kitchen has twin side-by-side sinks. One sink is lled with water, the other is empty. (a) Does the sink with water appear to be deeper, shallower, or the same depth as the empty sink? (b) Choose the best explanation from among the following: I. The sink with water appears deeper because you have to look through the water to see the bottom. II. Water bends the light, making an object under the water appear to be closer to the surface. Thus the water-lled sink appears shallower. III. The sinks are identical, and therefore have the same depth. This doesnt change by putting water in one of them.

Alight beam undergoes total internal reection at the interface between medium A, in which it propagates, and medium B, on the other side of the interface. Which medium has the greater index of refraction? Explain.

Light travels a distance of 0.960 m in 4.00 ns in a given substance. What is the index of refraction of this substance?

Find the ratio of the speed of light in water to the speed of light in diamond.

Ptolemys Optics One of the many works published by the Greek astronomer Ptolemy (A.D. ca. 100170) was Optics. In this book Ptolemy reports the results of refraction experiments he conducted by observing light passing from air into water. His results are as follows: angle of , angle of ; angle of , angle of . Find the percentage error in the calculated index of refraction of water for each of Ptolemys measurements.

Light enters a container of benzene at an angle of 43 to the normal; the refracted beam makes an angle of 27 with the normal. Calculate the index of refraction of benzene.

The angle of refraction of a ray of light traveling into an ice cube from air is 38. Find the angle of incidence.

(a) Referring to Problem 54, suppose the ice melts, but the angle of refraction remains the same. Is the corresponding angle of incidence greater than, less than, or the same as it was for ice? Explain. (b)Calculate the angle of incidence for part (a).

Asubmerged scuba diver looks up toward the calm surface of a freshwater lake and notes that the Sun appears to be 35 from the vertical. The divers friend is standing on the shore of the lake. At what angle above the horizon does the friend see the sun?

Apond with a total depth of 3.25 m is covered by a transparent layer of ice, with a thickness of 0.38 m. Find the time required for light to travel vertically from the surface of the ice to the bottom of the pond.

Light is refracted as it travels from a point Ain medium 1 to a point B in medium 2. If the index of refraction is 1.33 in medium 1 and 1.51 in medium 2, how long does it take light to go from A to B, assuming it travels 331 cm in medium 1 and 151 cm in medium 2?

You have a semicircular disk of glass with an index of refraction of . Find the incident angle for which the beam of light in Figure 2647 will hit the indicated point on the screen.

The observer in Figure 2648 is positioned so that the far edge of the bottom of the empty glass (not to scale) is just visible. When the glass is lled to the top with water, the center of the bottom of the glass is just visible to the observer. Find the height, H, of the glass, given that its width is .

Acoin is lying at the bottom of a pool of water that is 6.5 feet deep. Viewed from directly above the coin, how far below the surface of the water does the coin appear to be? (The coin is assumed to be small in diameter; therefore, we can use the smallangle approximations

A ray of light enters the long side of a 45-90-45 prism and undergoes two total internal reections, as indicated in Figure 2649. The result is a reversal in the rays direction of propagation. Find the minimum value of the prisms index of refraction, n, for these internal reections to be total.

When the prism in Problem 62 is immersed in a uid with an index of refraction of 1.21, the internal reections shown in Figure 2649 are still total. The reections are no longer total, however, when the prism is immersed in a uid with . Use this information to set upper and lower limits on the possible values of the prisms index of refraction.

Aglass paperweight with an index of refraction nrests on a desk, as shown in Figure 2650. An incident ray of light enters the horizontal top surface of the paperweight at an angle to the vertical. (a) Find the minimum value of n for which the internal reection on the vertical surface of the paperweight is total. (b)If is decreased, is the minimum value of n increased or decreased? Explain.

Suppose the glass paperweight in Figure 2650 has an index of refraction . (a) Find the value of for which the reection on the vertical surface of the paperweight exactly satises the condition for total internal reection. (b) If is increased, is the reection at the vertical surface still total? Explain.

Consider the physical system shown in Figure 2647and described in Problem 59. (a) If the index of refraction of the glass is increased, will the desired value of increase or decrease? Explain. (b)Find the value of for the case of int glass

While studying physics at the library late one night, you notice the image of the desk lamp reected from the varnished tabletop. When you turn your Polaroid sunglasses sideways, the reected image disappears. If this occurs when the angle between the incident and reected rays is 110, what is the index of refraction of the varnish?

Ahorizontal beam of light enters a 45-90-45prism at the center of its long side, as shown in Figure 2651. The emerging ray moves in a direction that is 34 below the horizontal. What is the index of refraction of this prism?

Alaser beam enters one of the sloping faces of the equilateral glass prism in Figure 2652 and refracts through the prism. Within the prism the light travels horizontally. What is the angle between the direction of the incident ray and the direction of the outgoing ray?

(a) Use a ray diagram to determine the approximate location of the image produced by a concave lens when the object is at a distance from the lens. (b) Is the image upright or inverted? (c) Is the image real or virtual? Explain.

(a) Use a ray diagram to determine the approximate location of the image produced by a concave lens when the object is at a distance from the lens. (b) Is the image upright or inverted? (c) Is the image real or virtual? Explain.

An object is a distance from a convex lens. (a) Use a ray diagram to nd the approximate location of the image. (b) Is the image upright or inverted? (c) Is the image real or virtual? Explain.

An object is a distance 2f from a convex lens. (a) Use a ray diagram to nd the approximate location of the image. (b) Is the image upright or inverted? (c)Is the image real or virtual? Explain.

Two lenses that are 35 cm apart are used to form an image, as shown in Figure 2653. Lens 1 is converging and has a focal length ; lens 2 is diverging and has a focal length . The object is placed 24 cm to the left of lens 1. (a) Use a ray diagram to nd the approximate location of the image. (b) Is the image upright or inverted? (c) Is the image real or virtual? Explain.

Two lenses that are 35 cm apart are used to form an image, as shown in Figure 2654. Lens 1 is diverging and has a focal length ; lens 2 is converging and has a focal length . The object is placed 24 cm to the left of lens 1. (a)Use a ray diagram to nd the approximate location of the image. (b) Is the image upright or inverted? (c)Is the image real or virtual? Explain.

A convex lens is held over a piece of paper outdoors on a sunny day. When the paper is held 26 cm below the lens, the sunlight is focused on the paper and the paper ignites. What is the focal length of the lens?

Aconcave lens has a focal length of . Find the image distance and magnication that result when an object is placed 29 cm in front of the lens.

When an object is located 46 cm to the left of a lens, the image is formed 17 cm to the right of the lens. What is the focal length of the lens?

An object with a height of 2.54 cm is placed 36.3 mm to the left of a lens with a focal length of 35.0 mm. (a) Where is the image located? (b) What is the height of the image?

A lens for a 35-mm camera has a focal length given by . (a) How close to the lm should the lens be placed to form a sharp image of an object that is 5.0 m away? (b) What is the magnication of the image on the lm?

An object is located to the left of a convex lens whose focal length is 34 cm. The magnication produced by the lens is . (a) To increase the magnication to 4.0, should the object be moved closer to the lens or farther away? Explain. (b)Calculate the distance through which the object should be moved.

You have two lenses at your disposal, one with a focal length , the other with a focal length . (a) Which of these two lenses would you use to project an image of a lightbulb onto a wall that is far away? (b)If youwant to produce an image of the bulb that is enlarged by a factor of 2.00, how far from the wall should the lens be placed?

(a) Determine the distance from lens 1 to the nal image for the system shown in Figure 2653. (b) What is the magnication of this image?

(a) Determine the distance from lens 1 to the nal image for the system shown in Figure 2654. (b) What is the magnication of this image?

An object is located to the left of a concave lens whose focal length is . The magnication produced by the lens is . (a) To decrease the magnication to , should the object be moved closer to the lens or farther away? (b)Calculate the distance through which the object should be moved.

Albert is nearsighted, and without his eyeglasses he can focus only on objects less than 2.2 m away. (a)Are Alberts eyeglasses concave or convex? Explain. (b) To correct Alberts nearsightedness, his eyeglasses must produce a virtual, upright image at a distance of 2.2 m when viewing an innitely distant object. What is the focal length of Alberts eyeglasses?

Asmall insect viewed through a convex lens is 1.4 cm from the lens and appears twice its actual size. What is the focal length of the lens?

Afriend tells you that when he takes off his eyeglasses and holds them 23 cm above a printed page the image of the print is erect but reduced to 0.67 of its actual size. (a) Is the image real or virtual? How do you know? (b) What is the focal length of your friends glasses? (c)Are the lenses in the glasses concave or convex? Explain.

Afriend tells you that when she takes off her eyeglasses and holds them 23 cm above a printed page the image of the print is erect but enlarged to 1.5 times its actual size. (a) Is the image real or virtual? How do you know? (b) What is the focal length of your friends glasses? (c)Are the lenses in the glasses concave or convex? Explain.

Predict/Explain You take a picture of a rainbow with an infrared camera, and your friend takes a picture at the same time with visible light. (a)Is the height of the rainbow in the infrared picture greater than, less than, or the same as the height of the rainbow in the visible-light picture? (b) Choose the best explanation from among the following: I. The height will be greater because the top of a rainbow is red, and so infrared light would be even higher. II. The height will be less because infrared light is below the visible spectrum. III. A rainbow is the same whether seen in visible light or infrared; therefore the height is the same.

The index of refraction for red light in a certain liquid is 1.320; the index of refraction for violet light in the same liquid is 1.332. Find the dispersion for red and violet light when both are incident on the at surface of the liquid at an angle of 45.00 to the normal.

Ahorizontal incident beam consisting of white light passes through an equilateral prism, like the one shown in Figure 2652. What is the dispersion of the outgoing beam if the prisms index of refraction is for violet light and for red light?

The focal length of a lens is inversely proportional to the quantity , where n is the index of refraction of the lens material. The value of n, however, depends on the wavelength of the light that passes through the lens. For example, one type of int glass has an index of refraction of for red light and in violet light. Now, suppose a white object is placed 24.00 cm in front of a lens made from this type of glass. If the red light reected from this object produces a sharp image 55.00 cm from the lens, where will the violet image be found?

Jurassic Park A T. rex chases the heroes of Steven Spielbergs Jurassic Park as they desperately try to escape in their Jeep. The T. rex is closing in fast, as they can see in the outside rearview mirror. Near the bottom of the mirror they also see the following helpful message: OBJECTS IN THE MIRROR ARE CLOSER THAN THEY APPEAR. Is this mirror concave or convex? Explain

The receiver for a dish antenna is placed in front of the concave surface of the dish. If the radius of curvature of the dish is R, how far in front of the dish should the receiver be placed? Explain.

Predict/Explain If a lens is immersed in water, its focal length changes, as discussed in Conceptual Checkpoint 265. (a) If a spherical mirror is immersed in water, does its focal length increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. The focal length will increase because the water will cause more bending of light. II. Water will refract the light. This, combined with the reection due to the mirror, will result in a decreased focal length. III. The focal length stays the same because it depends on the fact that the angle of incidence is equal to the angle of reection for a mirror. This is unaffected by the presence of the water.

Predict/Explain Aglass slab surrounded by air causes a sideways displacement in a beam of light. (a) If the slab is now placed in water, does the displacement it causes increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. The displacement of the beam increases because of the increased refraction due to the water. II. The displacement of the beam is decreased because with water surrounding the slab there is a smaller difference in index of refraction between the slab and its surroundings. III. The displacement stays the same because it is determined only by the properties of the slab; in particular, the material it is made of and its thickness.

Referring to Conceptual Question 12, suppose the same type of glass used in an eyedropper is made into a convex lens with a focal length f. If this lens is immersed in the oil of the bottle on the left in the photo, will its focal length be 0, , 2f, or ? (Hint: See Conceptual Checkpoint 265.)

Two identical containers are lled with different transparent liquids. The container with liquid Aappears to have a greater depth than the container with liquid B. Which liquid has the greater index of refraction? Explain.

Is the image you see in a three-dimensional corner reector upright or inverted?

Inverse Lenses Suppose we mold a hollow piece of plastic into the shape of a double concave lens. The lens is watertight, and its interior is lled with air. We now place this lens in water and shine a beam of light on it. (a) Does the lens converge or diverge the beam of light? Explain. (b) If our hollow lens is double convex instead, does it converge or diverge a beam of light when immersed in water? Explain.

Suppose the separation between the two mirrors in Figure 2643 is increased by moving the top mirror upward. (a) Will this affect the number of reections made by the beam of light? If so, how? (b) What is the total number of reections made by the beam of light when the separation between the mirrors is 145 cm?

Standing 2.0 m in front of a small vertical mirror you see the reection of your belt buckle, which is 0.70 m below your eyes. If you remain 2.0 m from the mirror but climb onto a stool, how high must the stool be to allow you to see your knees in the mirror? Assume that your knees are 1.2 m below your eyes.

Apparent Size of Floats in a Termometro Lentos The Galileo thermometer, or Termometro Lentos (slow thermometer in Italian), consists of a vertical, cylindrical ask containing a uid and several glass oats of different color. The oats all have the same dimensions, but they appear to differ in size depending on their location within the cylinder. (a) Does a oat near the front surface of the cylinder (the surface closest to you) appear to be larger or smaller than a oat near the back surface? (b) Figure 2655 shows a ray diagram for a oat near the front surface of the cylinder. Draw a ray diagram for a oat at the center of the cylinder, and show that the change in apparent size agrees with your answer to part (a).

(a) Find the two locations where an object can be placed in front of a concave mirror with a radius of curvature of 39 cm such that its image is twice its size. (b) In each of these cases, state whether the image is real or virtual, upright or inverted.

A convex mirror with a focal length of is used to give a truck driver a view behind the vehicle. (a) If a person who is 1.7 m tall stands 2.2 m from the mirror, where is the persons image located? (b) Is the image upright or inverted? (c) What is the size of the image?

The three laser beams shown in Figure 2656 meet at a point at the back of a solid, transparent sphere. (a) What is the index of refraction of the sphere? (b) Is there a nite index of refraction that will make the three beams come to a focus at the center of the sphere? If your answer is yes, give the required index of refraction; if your answer is no, explain why not.

The speed of light in substance Ais xtimes greater than the speed of light in substance B. Find the ratio in terms of x.

Alm of oil, with an index of refraction of 1.48 and a thickness of 1.50 cm, oats on a pool of water, as shown in Figure 2657. Abeam of light is incident on the oil at an angle of 60.0to the vertical. (a) Find the angle the light beam makes with the vertical as it travels through the water. (b) How does your answer to part (a) depend on the thickness of the oil lm? Explain.

Consider the physical system shown in Figure 2657. For this problem we assume that the angle of incidence at the airoil interface can be varied from 0 to 90. (a) What is the maximum possible value for , the angle of refraction in the water? (b) If an oil with a larger index of refraction is used, does your answer to part (a) increase or decrease? Explain.

Consider the physical system shown in Figure 2657, only this time let the direction of the light rays be reversed. (a) Find the angle of incidence at the wateroil interface such that the condition for total internal reection at the oilair surface is exactly satised. (b) If is decreased, is the reection at the oilair interface still total? Explain.

Figure 2658shows a ray of light entering one end of an optical ber at an angle of incidence . The index of refraction of the ber is 1.62. (a) Find the angle the ray makes with the normal when it reaches the curved surface of the ber. (b)Show that the internal reection from the curved surface is total.

Suppose the persons eyes in Figure 2644 are 1.6 m above the ground and that the small plane mirror can be moved up or down. (a) Find the height of the bottom of the mirror such that the lowest point the person can see on the building is 19.6 m above the ground. (b)With the mirror held at the height found in part (a), what is the highest point on the building the person can see?

An arrow 2.00 cm long is located 75.0 cm from a lens that has a focal length . (a) If the arrow is perpendicular to the principal axis of the lens, as in Figure 2659 (a), what is its lateral magnication, dened as ? (b) Suppose, instead, that the arrow lies along the principal axis, extending from 74.0 cm to 76.0 cm from the lens, as indicated in Figure 2659 (b). What is the longitudinal magnication of the arrow, dened as ? (Hint: Use the thin-lens equation to locate the image of each end of the arrow.)

Repeat Problem 114, this time for a diverging lens with a focal length

Aconvex lens with is mounted 40.0 cm to the left of a concave lens. When an object is placed 30.0 cm to the left of the convex lens, a real image is formed 60.0 cm to the right of the concave lens. What is the focal length of the concave lens?

Two thin lenses, with focal lengths and , are placed in contact. What is the effective focal length of the double lens?

When an object is placed a distance in front of a curved mirror, the resulting image has a magnication m. Find an expression for the focal length of the mirror, f, in terms of and m.

A Slab of Glass Give a symbolic expression for the sideways displacement d of a light ray passing through the slab of glass shown in Figure 2660. The thickness of the glass is t, its index of refraction is n, and the angle of incidence is .

Referring to Figure 2658, show that the internal reection from the curved surface of the ber is always total for any incident angle , provided the index of refraction of the ber exceeds

Least Time A beam of light propagates from point A in medium 1 to point B in medium 2, as shown in Figure 2661. The index of refraction is different in these two media; therefore, the light follows a refracted path that obeys Snells law. (a) Calculate the time required for light to travel from Ato B along the refracted path.(b)Compare the time found in part (a) with the time it takes for light to travel from Ato B along a straight-line path. (Note that the time on the straight-line path is longer than the time on the refracted path. In general, the shortest time between two points in different media is along the path given by Snells law.)

The ray of light shown in Figure 2662 passes from medium 1 to medium 2 to medium 3. The index of refraction in medium 1 is , in medium 2 it is , and in medium 3 it is . Show that medium 2 can be ignored when calculating the angle of refraction in medium 3; that is, show that

A beam of light enters the sloping side of a 45-90-45 glass prism with an index of refraction . The situation is similar to that shown in Figure 2651, except that the angle of incidence of the incoming beam can be varied. (a)Find the angle of incidence for which the reection on the vertical side of the prism exactly satises the condition for total internal reection. (b) If the angle of incidence is increased, is the reection at the vertical surface still total? Explain. (c) What is the minimum value of n such that a horizontal beam like that in Figure 2651 undergoes total internal reection at the vertical side of the prism?

Aconverging lens with a focal length in air of cm is made from ice. What is the focal length of this lens if it is immersed in benzene? (Refer to Table 262.) A. B. C. D

Adiverging lens with is made from ice. What is the focal length of this lens if it is immersed in ethyl alcohol? (Refer to Table 262.) A. 102 cm B. 105 cm C. 118 cm D.

Calculate the focal length of a lens in water, given that the index of refraction of the lens is and its focal length in air is 25.0 cm. (Refer to Table 262.) A. 57.8 cm B. 66.0 cm C. 91.0 cm D.

Suppose a lens is made from fused quartz (glass), and that its focal length in air is . What is the focal length of this lens if it is immersed in benzene? (Refer to Table 262.) A. B. 134 cm C. 141 cm D.

Referring to Example 263Suppose the radius of curvature of the mirror is 5.0 cm. (a) Find the object distance that gives an upright image with a magnication of 1.5. (b)Find the object distance that gives an inverted image with a magnication of .

Referring to Example 263 An object is 4.5 cm in front of the mirror. (a)What radius of curvature must the mirror have if the image is to be 2.2 cm in front of the mirror? (b)What is the magnication of the image? (c) If the object is moved closer to the mirror, does the magnication of the image increase in magnitude, decrease in magnitude, or stay the same?

Referring to Example 267(a)What object distance is required to give an image with a magnication of ? Assume that the focal length of the lens is . (b) What is the location of the image in this case?

Referring to Example 267Suppose the convex lens is replaced with a concave lens with a focal length of . (a)Where must the object be placed to form an image with a magnication of 0.50? (b) What is the location of the image in this case? (c) If we now move the object closer to the lens, does the magnication of the image increase, decrease, or stay the same?