Problems

Note to Instructors: Most of the homework problems in this chapter are available for assignment via an online homework management program such as WileyPLUS or WebAssign, and those marked with the icon are presented in a guided tutorial format that provides enhanced interactivity. See Preface for additional details.
ssm Solution is in the Student Solutions Manual.
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Section 25.2 The Reflection of Light,
Section 25.3 The Formation of Images by a Plane Mirror

| 1 | ssm www Two diverging light rays, originating from the same point, have an angle of 10° between them. After the rays reflect from a plane mirror, what is the angle between them? Construct one possible ray diagram that supports your answer.

| 2 | 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?

| 3 | Review Conceptual Example 2. Suppose that in Figure 25-9b the two perpendicular plane mirrors are represented by the − x and − y axes of an x, y coordinate system. An object is in front of these mirrors at a point whose coordinates are and . Find the coordinates that locate each of the three images.

| 4 | 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°. The beam emerges from the laser at a point that is 1.10 m from the mirror and 1.80 m above the floor. After reflection, how far from the base of the mirror does the beam strike the floor?

| 5 | ssm Two plane mirrors are separated by 120°, as the drawing illustrates. If a ray strikes mirror M1 at a 65° angle of incidence, at what angle does it leave mirror M2?

| 6 | 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.

* | 7 | The drawing shows a top view of a square room. One wall is missing, and the other three are each mirrors. From point P in the center of the open side, a laser is fired, with the intent of hitting a small target located at the center of one wall. Identify six directions in which the laser can be fired and score a hit, assuming that the light does not strike any mirror more than once. Draw the rays to confirm your choices.

* | 8 | 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?

** | 9 | In the drawing for problem 7, a laser is fired from point P in the center of the open side of the square room. The laser is pointed at the mirrored wall on the right. 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?
Section 25.4 Spherical Mirrors,
Section 25.5 The Formation of Images by Spherical Mirrors

| 10 | Concept Simulation 25.2 at illustrates the concepts pertinent to this problem. 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.

| 11 | A concave mirror has a focal length of 20.0 cm. A 2.0-cm-high object is located 12.0 cm in front of this mirror. 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.

| 12 | 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.

| 13 | ssm The radius of curvature of a convex mirror is . An object that is 10.0 cm high is placed 25.0 cm in front of this mirror. 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.

| 14 | Concept Simulation 25.3 at illustrates the concepts pertinent to this problem. 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.

* | 15 | A plane mirror and a concave mirror () are facing each other and are separated by a distance of 20.0 cm. An object is placed 10.0 cm in front of the plane 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.
Section 25.6 The Mirror Equation and the Magnification Equation

| 16 | 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?

| 17 | ssm 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.

| 18 | 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?

| 19 | Refer to Interactive Solution 25.19 at for help with problems like this one. A concave mirror () 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 25-19a. (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?

| 20 | 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.

| 21 | ssm www A small postage stamp is placed in front of a concave mirror (radius = R), such 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.

| 22 | A concave mirror () 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.

| 23 | ssm www 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?

* | 24 | 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?

* | 25 | Consult Interactive Solution 25.25 at for insight into this problem. 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 of the object distance to the focal length of the mirror?

* | 26 | The same object is located at the same distance from two spherical mirrors, A and B. The magnifications produced by the mirrors are and . Find the ratio of the focal lengths of the mirrors.

* | 27 | ssm www An image formed by a convex mirror () has a magnification of 0.150. Which way and by how much should the object be moved to double the size of the image?

** | 28 | 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 within the focal point.

** | 29 | Using the mirror equation and the magnification equation, show that for a convex mirror the image is always (a) virtual (i.e., di is always negative) and (b) upright and smaller, relative to the object (i.e., m is positive and less than one).

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