Physics

John D. Cutnell, Kenneth W. Johnson

Chapter 25

The Reflection of Light: Mirrors - all with Video Answers

Educators

Chapter Questions

Problem 1

Review Conceptual Example $2 .$ Suppose that in Figure $25.9 b$ the two perpendicular plane mirrors are represented by the $-x$ and $-y$ axes of an $x, y$ coordinate system; mirror 1 is the $-x$ axis, and mirror 2 is the $-y$ axis. An object is in front of these mirrors at a point whose coordinates are $x=-2.0 \mathrm{~m}$ and $y=-1.0 \mathrm{~m} .$ Find the coordinates that locate each of the three images.

Darman Khan

Darman Khan

Numerade Educator

Problem 2

On the $+y$ axis a laser is located at $y=+3.0 \mathrm{cm} .$ The coordinates of a small target are $x=+9.0 \mathrm{cm}$ and $y=+6.0 \mathrm{cm} .$ The $+x$ axis represents the edge-on view of a plane mirror. At what point on the $+x$ axis should the laser be aimed in order for the laser light to hit the target after reflection?

Darman Khan

Numerade Educator

Problem 3

You are trying to photograph a bird sitting on a tree branch, but a tall hedge is blocking your view. However, as the drawing shows, a plane mirror reflects light from the bird into your camera. For what distance must you set the focus of the camera lens in order to snap a sharp picture of the bird’s image?

Darman Khan

Numerade Educator

Problem 4

Suppose that you are walking perpendicularly with a velocity of $+0 . \overline{90} \mathrm{m} / \mathrm{s} \mathrm{t}$ toward a stationary plane mirror. What is the velocity of your image relative to you? The direction in which you walk is the positive direction.

Susan Hallstrom

Susan Hallstrom

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Problem 5

Two plane mirrors are separated by $120^{\circ},$ as the drawing illustrates. If a ray strikes mirror $M_{1}$ at a $65^{\circ}$ angle of incidence, at what angle $\theta$ does it leave mirror $M_{2} ?$

Darman Khan

Numerade Educator

Problem 6

The drawing shows a laser beam shining on a plane mirror that is perpendicular to the floor. The beam's angle of incidence is $33.0^{\circ}$. The beam emerges from the laser at a point that is $1.10 \mathrm{~m}$ from the mirror and $1.80 \mathrm{~m}$ above the floor. After reflection, how far from the base of the mirror does the beam strike the floor?

Darman Khan

Numerade Educator

Problem 7

Review Conceptual Example 1 as an aid in understanding this problem. The drawings show two arrows, A and B, that are located in front of a plane mirror. A person at point P is viewing the image of each arrow. Which images can be seen in their entirety? Determine your answers by drawing a ray from the head and foot of each arrow that reflects from the mirror according to the law of reflection and reaches point P. Only if both rays reach point P after reflection can the image of that arrow be seen in its entirety.

Darman Khan

Numerade Educator

Problem 8

A small mirror is attached to a vertical wall, and it hangs a distance of 1.80 m above the floor. The mirror is facing due east, and a ray of sunlight strikes the mirror early in the morning and then again later in the morning. The incident and reflected rays lie in a plane that is perpendicular to both the wall and the floor. Early in the morning, the reflected ray strikes the floor at a distance of 3.86 m from the base of the wall. Later on in the morning, the ray is observed to strike the floor at a distance of 1.26 m from the wall. The earth rotates at a rate of 15.0 per hour. How much time (in hours) has elapsed between the two observations?

Shoukat Ali

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Problem 9

In an experiment designed to measure the speed of light, a laser is aimed at a mirror that is 50.0 km due north. A detector is placed 117 m due east of the laser. The mirror is to be aligned so that light from the laser reflects into the detector. (a) When properly aligned, what angle should the normal to the surface of the mirror make with due south? (b) Suppose the mirror is misaligned, so that the actual angle between the normal to the surface and due south is too large by 0.004. By how many meters (due east) will the reflected ray miss the detector?

Shoukat Ali

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Problem 10

The drawing shows two plane mirrors that intersect at an angle of $50^{\circ} .$ An incident light ray reflects from one mirror and then the other. What is the angle $\theta$ between the incident and outgoing rays?

Shoukat Ali

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Problem 11

Two plane mirrors are facing each other. They are parallel, 3.00 cm apart, and 17.0 cm in length, as the drawing indicates. A laser beam is directed at the top mirror from the left edge of the bottom mirror. What is the smallest angle of incidence with respect to the top mirror, such that the laser beam (a) hits only one of the mirrors and (b) hits each mirror only once?

Shoukat Ali

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Problem 12

The drawing shows a top view of a square room. One wall is missing, and the wall on the right is a mirror. From point P in the center of the open side, a laser is pointed at the mirrored wall. At what angle of incidence must the light strike the right-hand wall so that, after being reflected, the light hits the left corner of the back wall?

Vishal Gupta

Numerade Educator

Problem 13

When an object is located very far away from a convex mirror, the image of the object is 18 cm behind the mirror. Using a ray diagram drawn to scale, determine where the image is located when the object is placed 9.0 cm in front of the mirror. Note that the mirror must be drawn to scale also. In your drawing, assume that the height of the object is 3.0 cm.

Shoukat Ali

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Problem 14

The image of a very distant car is located 12 cm behind a convex mirror. (a) What is the radius of curvature of the mirror? (b) Draw a ray diagram to scale showing this situation.

Shoukat Ali

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Problem 15

An object is placed 11 cm in front of a concave mirror whose focal length is 18 cm. The object is 3.0 cm tall. Using a ray diagram drawn to scale, measure (a) the location and (b) the height of the image. The mirror must be drawn to scale.

Shoukat Ali

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Problem 16

A 2.0-cm-high object is situated 15.0 cm in front of a concave mirror that has a radius of curvature of 10.0 cm. Using a ray diagram drawn to scale, measure (a) the location and (b) the height of the image. The mirror must be drawn to scale.

Shoukat Ali

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Problem 17

A convex mirror has a focal length of 40.0 cm. A 12.0-cm-tall object is located 40.0 cm in front of this mirror. Using a ray diagram drawn to scale, determine the (a) location and (b) size of the image. Note that the mirror must be drawn to scale.

Shoukat Ali

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Problem 18

A plane mirror and a concave mirror $(f=8.0 \mathrm{cm})$ are facing each other and are separated by a distance of 20.0 $\mathrm{cm} .$ An object is placed between the mirrors and is 10.0 $\mathrm{cm}$ from each mirror. Consider the light from the object that reflects first from the plane mirror and then from the concave mirror. Using a ray diagram drawn to scale, find the location of the image that this light produces in the concave mirror. Specify this distance relative to the concave mirror.

Shoukat Ali

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Problem 19

The image produced by a concave mirror is located 26 cm in front of the mirror. The focal length of the mirror is 12 cm. How far in front of the mirror is the object located?

Rob Ball

Numerade Educator

Problem 20

The image behind a convex mirror (radius of curvature 68 cm) is located 22 cm from the mirror. (a) Where is the object located and (b) what is the magnification of the mirror? Determine whether the image is (c) upright or inverted and (d) larger or smaller than the object.

Shoukat Ali

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Problem 21

A concave mirror (R 56.0 cm) is used to project a transparent slide onto a wall. The slide is located at a distance of 31.0 cm from the mirror, and a small flashlight shines light through the slide and onto the mirror. The setup is similar to that in Figure 25.18a. (a) How far from the wall should the mirror be located? (b) The height of the object on the slide is 0.95 cm. What is the height of the image? (c) How should the slide be oriented, so that the picture on the wall looks normal?

Shoukat Ali

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Problem 22

A small statue has a height of 3.5 cm and is placed in front of a concave mirror. The image of the statue is inverted, 1.5 cm tall, and located 13 cm in front of the mirror. Find the focal length of the mirror.

Shoukat Ali

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Problem 23

A mirror produces an image that is located 34.0 cm behind the mirror when the object is located 7.50 cm in front of the mirror. What is the focal length of the mirror, and is the mirror concave or convex?

Shoukat Ali

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Problem 24

A concave mirror $(f=45 \mathrm{cm})$ produces an image whose distance from the mirror is one-third the object distance. Determine (a) the object distance and (b) the (positive) image distance.

Shoukat Ali

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Problem 25

The outside mirror on the passenger side of a car is convex and has a focal length of 7.0 m. Relative to this mirror, a truck traveling in the rear has an object distance of 11 m. Find (a) the image distance of the truck and (b) the magnification of the mirror.

Shoukat Ali

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Problem 26

A convex mirror has a focal length of 27.0 cm. Find the magnification produced by the mirror when the object distance is 9.0 cm and 18.0 cm.

Shoukat Ali

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Problem 27

When viewed in a spherical mirror, the image of a setting sun is a virtual image. The image lies 12.0 cm behind the mirror. (a) Is the mirror concave or convex? Why? (b) What is the radius of curvature of the mirror?

Shoukat Ali

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Problem 28

A concave mirror has a focal length of 12 cm. This mirror forms an image located 36 cm in front of the mirror. What is the magnification of the mirror?

Shoukat Ali

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Problem 29

An object is located 14.0 cm in front of a convex mirror, the image being 7.00 cm behind the mirror. A second object, twice as tall as the first one, is placed in front of the mirror, but at a different location. The image of this second object has the same height as the other image. How far in front of the mirror is the second object located?

Shoukat Ali

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Problem 30

An object is located 14.0 cm in front of a convex mirror, the image being 7.00 cm behind the mirror. A second object, twice as tall as the first one, is placed in front of the mirror, but at a different location. The image of this second object has the same height as the other image. How far in front of the mirror is the second object located?

Shoukat Ali

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Problem 31

A tall tree is growing across a river from you. You would like to know the distance between yourself and the tree, as well as its height, but are unable to make the measurements directly. However, by using a mirror to form an image of the tree and then measuring the image distance and the image height, you can calculate the distance to the tree as well as its height. Suppose that this mirror produces an image of the sun, and the image is located 0.9000 m from the mirror. The same mirror is then used to produce an image of the tree. The image of the tree is 0.9100 m from the mirror. (a) How far away is the tree? (b) The image height of the tree has a magnitude of 0.12 m. How tall is the tree?

Shoukat Ali

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Problem 32

A spherical mirror is polished on both sides. When the concave side is used as a mirror, the magnification is $+2.0$. What is the magnification when the convex side is used as a mirror, the object remaining the same distance from the mirror?

Shoukat Ali

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Problem 33

Consult Multiple-Concept Example 7 to see a model for solving this type of problem. A concave makeup mirror is designed so the virtual image it produces is twice the size of the object when the distance between the object and the mirror is 14 cm. What is the radius of curvature of the mirror?

Shoukat Ali

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Problem 34

A concave mirror has a focal length of 30.0 cm. The distance between an object and its image is 45.0 cm. Find the object and image distances, assuming that (a) the object lies beyond the center of curvature and (b) the object lies between the focal point and the mirror.

Shoukat Ali

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Problem 35

A spacecraft is in a circular orbit about the moon, $1.22 \times 10^{5} \mathrm{m}$ above its surface. The speed of the spacecraft is $1620 \mathrm{m} / \mathrm{s},$ and the radius of the moon is $1.74 \times 10^{6} \mathrm{m} .$ If the moon were a smooth, reflective sphere, (a) how far below the moon’s surface would the image of the spacecraft appear, and (b) what would be the apparent speed of the spacecraft’s image? (Hint: Both the spacecraft and its image have the same angular speed about the center of the moon.)

Shoukat Ali

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Problem 36

An object is placed in front of a convex mirror. Draw the convex mirror (radius of curvature 15 cm) to scale, and place the object 25 cm in front of it. Make the object height 4 cm. Using a ray diagram, locate the image and measure its height. Now move the object closer to the mirror, so the object distance is 5 cm. Again, locate its image using a ray diagram. As the object moves closer to the mirror, (a) does the magnitude of the image distance become larger or smaller, and (b) does the magnitude of the image height become larger or smaller? (c) What is the ratio of the image height when the object distance is 5 cm to its height when the object distance is 25 cm? Give your answer to one significant figure.

Shoukat Ali

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Problem 37

An object that is 25 cm in front of a convex mirror has an image located 17 cm behind the mirror. How far behind the mirror is the image located when the object is 19 cm in front of the mirror?

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Problem 38

A concave mirror has a focal length of 42 cm. The image formed by this mirror is 97 cm in front of the mirror. What is the object distance?

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Problem 39

Review Conceptual Example 1 before attempting this problem. A person whose eyes are 1.70 m above the floor stands in front of a plane mirror. The top of her head is 0.12 m above her eyes. (a) What is the height of the shortest mirror in which she can see her entire image? (b) How far above the floor should the bottom edge of the mirror be placed?

Shoukat Ali

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Problem 40

A drop of water on a countertop reflects light from a flower held 3.0 cm directly above it. The flower’s diameter is 2.0 cm, and the diameter of the flower’s image is 0.10 cm. What is the focal length of the water drop, assuming that it may be treated as a convex spherical mirror?

Shoukat Ali

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Problem 41

A small postage stamp is placed in front of a concave mirror (radius R) so that the image distance equals the object distance. (a) In terms of R, what is the object distance? (b) What is the magnification of the mirror? (c) State whether the image is upright or inverted relative to the object. Draw a ray diagram to guide your thinking.

Shoukat Ali

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Problem 42

Identical objects are located at the same distance from two spherical mirrors, A and B. The magnifications produced by the mirrors are $m_{\mathrm{A}}=4.0$ and $m_{\mathrm{B}}=2.0 .$ Find the ratio $f_{\mathrm{A}} / f_{\mathrm{B}}$ of the focal lengths of the mirrors.

Shoukat Ali

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Problem 43

You walk at an angle of $\theta=50.0^{\circ}$ toward a plane mirror, as in the drawing. Your walking velocity has a magnitude of 0.90 $\mathrm{m} / \mathrm{s}$ . What is the velocity of your image relative to you (magnitude and direction)?

Shoukat Ali

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Problem 44

A candle is placed 15.0 cm in front of a convex mirror. When the convex mirror is replaced with a plane mirror, the image moves 7.0 cm farther away from the mirror. Find the focal length of the convex mirror.

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Problem 45

An object is placed in front of a convex mirror, and the size of the image is one-fourth that of the object. What is the ratio $d_{0} / f$ of the object distance to the focal length of the mirror?

Shoukat Ali

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Problem 46

A man holds a double-sided spherical mirror so that he is looking directly into its convex surface, 45 $\mathrm{cm}$ from his face. The magnification of the image of his face is $+0.20 .$ What will be the image distance when he reverses the mirror (looking into its concave surface), maintaining the same distance between the mirror and his face? Be sure to include the algebraic sign $(+\text { or }-\text { ) with your answer. }$

Shoukat Ali

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Problem 47

A lamp is twice as far in front of a plane mirror as a person is. Light from the lamp reaches the person via two paths, reflected and direct. It strikes the mirror at a 30.0 angle of incidence and reflects from it before reaching the person. The total time for the light to travel this path includes the time to travel to the mirror and the time to travel from the mirror to the person. The light also travels directly to the person without reflecting. Find the ratio of the total travel time along the reflected path to the travel time along the direct path.

Shoukat Ali

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