REFLECTION OF LIGHT: MIRRORS

chapter

Section 25.1 Wave Fronts and Rays Section 25.2 The Reflection of Light Section 25.3 The Formation of Images by a Plane Mirror

1. Which one of the following phrases most accurately describes the term wave front? (a) the surface of a plane mirror (b) the surface of a convex mirror (c) a surface upon which a wave is incident (d) a surface of constant phase within a wave (e) a surface that is parallel to the direction of wave propagation

2. Which one of the following statements concerning rays is false? (a) Rays point in the direction of the wave velocity. (b) Rays point outward from the wave source. (c) Rays are parallel to the wave front. (d) Rays are radial lines that originate from a point source of waves. (e) Rays for a plane wave are parallel to each other.

3. Which one of the following statements is not a characteristic of a plane mirror? (a) The image is real. (b) The magnification is +1. (c) The image is always upright. (d) The image is reversed right to left. (e) The image and object distances are equal in magnitude.

4. An object is placed near two perpendicular plane mirrors as shown in the figure. How many images will be formed?

(a) 1 (b) 2 (c) 3 (d) 4 (e) 5

object

5. Daniel walks directly toward a plane mirror at a speed of 0.25 m/s. Determine the speed of the image relative to him.

(a) 0.13 m/s (c) 0.50 m/s (e) 1.0 m/s (b) 0.25 m/s (d) 0.75 m/s

6. Five balls labeled A, B, C, D, and E are placed in front of a plane mirror as shown in the figure. Which ball(s) will the observer see reflected in the mirror?

(a) A only (b) C only (c) A and B (d) A, B, D and E (e) A, B, C, D and E

Plane mirror

A B C

D E

256 Chapter 25 Reflection of Light: Mirrors

7. The view in the figure is from above a plane mirror

suspended by a thread connected to the center of the mirror at point C. A scale is located 0.65 m (the distance from point C to point A) to the right of the center of the mirror. Initially, the plane of the mirror is parallel to the side of the scale; and the angle of incidence of a light ray which is directed at the center of the mirror is 30°. A small torque applied to the thread causes the mirror to turn 12° away from its initial position. The reflected ray then intersects the scale at point B. What is the distance from point A to point B on the scale?

(a) 0.37 m (d) 0.89 m (b) 0.58 m (e) 1.0 m (c) 0.76 m

8. A ray of light is reflected from two plane mirror surfaces as shown in the figure. What are the correct values of α and β?

Value of α Value of β (a) 26° 26°

(b) 26° 64°

(c) 38° 52° (d) 52° 26° (e) 64° 26°

9. In the figure, Joel is using a device known as a periscope to observe an object, represented by an upright arrow. The periscope contains two plane mirrors tilted at an angle of 45° relative to Joel’s line of sight. Which one of the following pairs of characteristics of the final image is correct relative to those of the object?

(a) inverted, real (d) inverted, same size (b) upright, enlarged (e) upright, virtual (c) inverted, smaller

10. Two plane mirrors are connected perpendicular to each other, as shown in the figure. If a person looks into the corner at the image straight ahead of him and closes his left eye as shown, which one of the following statements is true?

(a) The left eye of the image is closed. (b) The right eye of the image is closed. (c) Both eyes of the image are open. (d) Both eyes of the image are closed. (e) There is no image straight ahead of him, so this question is meaningless.

11. An object is placed 1 m in front of a plane mirror. An observer stands 3 m behind the object. For what distance must the observer focus his eyes in order to see the image of the object?

(a) 1 m (c) 3 m (e) 5 m (b) 2 m (d) 4 m

12. Two mirrors are arranged as shown in the drawing. Light is incident on the first mirror at an angle of 40.0°. The light reflects toward a second mirror. Determine the angle θ.

(a) 20.0° (c) 15.0° (e) 10.0° (b) 25.0° (d) 30.0°

A

B

30° 0.65 m

12° Initial position of the mirror

Normal to the mirror in its initial position

26o

α

β

90o

45°

45°

Only the left eye is closed.

Physics, 7e TEST BANK 257

Section 25.4 Spherical Mirrors Section 25.5 The Formation of Images by Spherical Mirrors

13. The focal length of a spherical concave mirror is 20 cm. What is its radius of curvature? (a) 5 cm (c) 20 cm (e) 50 cm (b) 10 cm (d) 40 cm

14. The radius of curvature of a spherical convex mirror is 52 cm. What is its focal length? (a) +26 cm (c) +52 cm (e) +104 cm (b) –26 cm (d) –52 cm

15. Which one of the following statements concerning a convex mirror is true? (a) A convex mirror can form a real image. (b) A convex mirror must be spherical in shape. (c) The image produced by a convex mirror will always be inverted relative to the object. (d) A convex mirror produces a larger image than a plane mirror does for the same object

distance. (e) The image a convex mirror produces is closer to the mirror than it would be in a plane

mirror for the same object distance.

16. A concave mirror has a radius of curvature of 30.0 cm. How close to the mirror should an object be placed so that the rays travel parallel to each other after reflection?

(a) 10.0 cm (c) 30.0 cm (e) 60.0 cm (b) 15.0 cm (d) 45.0 cm

17. Which one of the following phrases most accurately describes paraxial rays? (a) rays that pass through the principal focus (b) any rays that are parallel to the principal axis (c) rays that come to a focus on the principal axis (d) rays close to the principal axis and parallel to it (e) rays close to the principal axis, but not necessarily parallel to it

18. Which one of the following statements concerning the image formed by a concave spherical mirror is true?

(a) When the object distance is less than the focal length, the image is virtual. (b) When the object distance is larger than the focal length, the image is virtual. (c) When the object is at the center of curvature, the image is formed at infinity. (d) When the object distance is less than the focal length, the image is inverted relative to the object. (e) When the object distance is larger than the focal length, the image is upright relative to the object.

19. Santa Claus looks at his reflection in a spherical Christmas tree ornament. Which one of the following statements concerning Santa’s image is true?

(a) The image must be real. (b) The image is farther from the ornament than Santa is. (c) The image is larger than Santa. (d) The image must be inverted. (e) The image must be smaller than Santa.

258 Chapter 25 Reflection of Light: Mirrors

Questions 20 through 22 pertain to the system described below: An object is placed in front of a concave

spherical mirror as shown below. The three rays 1, 2, and 3, leave the top of the object and, after reflection, converge at a point on the top of the image. Ray 1 is parallel to the principal axis, ray 2 passes through F, and ray 3 passes through C.

20. Which ray(s) will pass through F after reflection? (a) 1 only (c) 3 only (e) 1, 2, and 3 (b) 2 only (d) both 1 and 2

21. Which ray(s) will reflect back on itself (themselves)? (a) 1 only (c) 3 only (e) 1, 2, and 3 (b) 2 only (d) both 1 and 2

22. Which one of the following groups of terms best describes the image? (a) real, upright, enlarged (d) real, inverted, enlarged (b) real, inverted, reduced (e) virtual, inverted, reduced (c) virtual, upright, enlarged

Section 25.6 The Mirror Equation and the Magnification Equation

23. A concave mirror in an amusement park has a radius of curvature of 4.0 m. A child stands in front of the mirror so that she appears 2.5 times taller than her actual height. If the image is upright, how far is she standing from the mirror?

(a) 1.2 m (c) 2.8 m (e) 7.0 m (b) 3.5 m (d) 4.0 m

24. A convex mirror in an amusement park has a radius of curvature of 3.00 m. A man stands in front of the mirror so that his image is half as tall as his actual height. At what distance must the man focus his eyes in order to see his image?

(a) 2.25 m (c) 4.50 m (e) 6.75 m (b) 3.00 m (d) 5.00 m

25. A woman stands 2.0 m in front of a convex mirror and notices that her image height is 1/4 of her actual height. Determine the radius of curvature of the mirror.

(a) 0.67 m (c) 2.0 m (e) 6.0 m (b) 1.3 m (d) 4.0 m

26. A concave mirror has a radius of curvature of 20 cm. For which one of the following object distances will the image be real, inverted and smaller than the object?

(a) 5 cm (c) 15 cm (e) 25 cm (b) 10 cm (d) 18 cm

27. An object is 1.0 m in front of a mirror. A virtual image is formed 10.0 m behind the mirror. What is the radius of curvature of the mirror?

(a) 0.56 m (c) 2.2 m (e) 10 m (b) 1.1 m (d) 4.4 m

12

3C F

Physics, 7e TEST BANK 259

28. The table below lists object and image distances for five objects in front of mirrors. For which one of the following cases is the image formed by a convex spherical mirror?

Object distance Image distance (a) 7.10 cm 18.0 cm (b) 25.0 cm 16.7 cm (c) 5.0 cm –10.0 cm (d) 20.0 cm –5.71 cm (e) 40.0 cm –80.0 cm

29. An object is placed 30 cm in front of a concave spherical mirror that has a radius of curvature 40 cm. Which one of the following phrases best describes the image?

(a) virtual and located at infinity (d) virtual and located 60 cm from the mirror (b) real and located 60 cm from the mirror (e) virtual and located 120 cm from the mirror (c) real and located 120 cm from the mirror

30. An object is placed 30.0 cm from a convex spherical mirror with radius of curvature 40.0 cm. Which one of the following phrases best describes the image?

(a) virtual and located at infinity (d) virtual and located 12 cm from the mirror (b) real and located 12 cm from the mirror (e) virtual and located 17 cm from the mirror (c) real and located 17 cm from the mirror

31. A spherical concave mirror has a radius of curvature of 6.0 cm. At what distance from the mirror should a 6.0-cm object be placed to obtain an image that is 48 cm tall?

(a) 1.3 cm (c) 4.2 cm (e) 6.8 cm (b) 3.6 cm (d) 5.3 cm

32. A convex mirror has a radius of curvature of 0.50 m. Where must an object be placed in front of the mirror such that the image is formed 0.15 m behind the mirror?

(a) 0.38 m (c) 0.77 m (e) 0.57 m (b) 0.19 m (d) 0.093 m

33. A concave mirror is found to focus parallel rays at a distance of 9.0 cm. Where is the image formed when an object is placed 6.0 cm in front of the mirror?

(a) 11 cm in front of the mirror (d) 5.6 cm behind the mirror (b) 18 cm behind the mirror (e) 9.2 cm in front of the mirror (c) 3.6 cm in front of the mirror

34. A rubber ball is held 4.0 m above a concave spherical mirror with a radius of curvature of 1.5 m. At time equals zero, the ball is dropped from rest and falls along the principal axis of the mirror. How much time elapses before the ball and its image are at the same location?

(a) 0.30 s (c) 0.63 s (e) 0.90 s (b) 0.55 s (d) 0.71 s

35. A 0.127-m pencil is oriented perpendicular to the principal axis of a concave spherical mirror that has a radius of curvature of 0.300 m. What are the image distance and the image height if the pencil is 0.250 m from the mirror?

Image Distance Image Height (a) 0.150 m −0.076 m (b) 0.225 m −0.114 m (c) 0.250 m −0.127 m (d) 0.300 m −0.152 m (e) 0.375 m −0.191 m

260 Chapter 25 Reflection of Light: Mirrors

36. A dime is placed in front of a concave mirror that has a radius of curvature R = 0.15 m. The image of

the dime is inverted and three times the size of the dime. Determine the distance between the dime and the mirror.

(a) 0.23 m (c) 0.10 m (e) 0.038 m (b) 0.15 m (d) 0.075 m

37. The inverted image of a light bulb is formed on a screen located 9.00 m from a spherical mirror. The image is 4.00 times larger than the light bulb. Determine the object distance and the type of mirror used.

(a) +0.444 m, concave (d) +0.0278 m, convex (b) +2.25 m, concave (e) +36.0 m, convex (c) +36.0 m. concave

38. A convex mirror with a focal length of 58 cm is used to form an image that is 29 cm behind the mirror. What is the object distance?

(a) +22 cm (c) +69 cm (e) +58 cm (b) +15 cm (d) +28 cm

Additional Problems

39. A 6.0-ft tall football player stands in front of a plane mirror. How tall must the mirror be so that the football player can see his full-sized image?

(a) 2.0 ft (c) 3.0 ft (e) 6.0 ft (b) 2.5 ft (d) 3.5 ft

40. Which one of the following statements concerning a virtual image produced by a mirror is true? (a) A virtual image is always larger than the object. (b) A virtual image is always smaller than the object. (c) A virtual image is always upright relative to the object. (d) A virtual image is always inverted relative to the object. (e) A virtual image can be photographed or projected onto a screen.

41. A plane mirror is 8 ft tall. What is its focal length? (a) zero feet (c) 8 ft (e) infinity (b) 4 ft (d) 16 ft

Questions 42 and 43 pertain to the situation described below: A 3.0-cm object is placed 8.0 cm in front of a mirror. The virtual image is 4.0 cm further from

the mirror when the mirror is concave than when it is planar.

42. Determine the focal length of the concave mirror. (a) 6.0 cm (c) 24 cm (e) 96 cm (b) 12 cm (d) 48 cm

43. Determine the image height in the concave mirror. (a) 0.5 (c) 2.0 (e) 4.5 (b) 1.5 (d) 3.0