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Chapter 36 Geometric Optics Multiple Choice 1. A clown 2 m tall looks at himself in a full-length mirror (floor-to-ceiling). Where in the mirror must he look to see his feet? a. 1 m from the floor b. 50 cm from the floor c. 25 cm from the floor d. at the bottom of the mirror e. 1.5 m from the floor 2. A concave mirror has a focal length of 20 cm. What is the position (in cm) of the resulting image if the image is inverted and four times smaller than the object? a. 15 b. 25 c. 50 d. 100 e. –15 3. A convex mirror has a focal length of –20 cm. What is the position of the resulting image (in cm) if the image is upright and four times smaller than the object? a. –100 b. –25 c. –50 d. –15 e. –10 4. A concave mirror has a focal length of 20 cm. What is the position (in cm) of the object if the image is upright and is two times larger than the object? a. 30 b. 20 c. 10 d. 40 e. 60 5. A concave mirror has a focal length of 20 cm. What is the magnification if the object’s distance is 100 cm? a. 1/2 b. 1/4 c. –2 d. 4 e. –1/4 261

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Chapter 36

Geometric Optics

Multiple Choice

1. A clown 2 m tall looks at himself in a full-length mirror (floor-to-ceiling). Where in the mirror must he look to see his feet?

a. 1 m from the floor b. 50 cm from the floor c. 25 cm from the floor d. at the bottom of the mirror e. 1.5 m from the floor

2. A concave mirror has a focal length of 20 cm. What is the position (in cm) of the resulting image if the image is inverted and four times smaller than the object?

a. 15 b. 25 c. 50 d. 100 e. –15

3. A convex mirror has a focal length of –20 cm. What is the position of the resulting image (in cm) if the image is upright and four times smaller than the object?

a. –100 b. –25 c. –50 d. –15 e. –10

4. A concave mirror has a focal length of 20 cm. What is the position (in cm) of the object if the image is upright and is two times larger than the object?

a. 30 b. 20 c. 10 d. 40 e. 60

5. A concave mirror has a focal length of 20 cm. What is the magnification if the object’s distance is 100 cm?

a. 1/2 b. 1/4 c. –2 d. 4 e. –1/4

261

262 CHAPTER 36

6. A convex mirror has a focal length of –20 cm. What is the object distance if the image distance is –10 cm?

a. 10 cm b. 40 cm c. 60 cm d. 20 cm e. 30 cm

7. A concave mirror has a focal length of 20 cm. What is the magnification if the object and image distances are 10 cm and –20 cm respectively?

a. 1 b. 2 c. 1/2 d. 1/4 e. –1/2

8. A concave mirror has a radius of curvature of 1.0 m. An object is placed 2.0 m in front of the mirror. Determine the location of the image (in cm).

a. 127 b. 83 c. 67 d. 150 e. 200

9. An object 4 cm high is placed 15 cm in front of a convex mirror with a focal length of –10 cm. What is the image position (in cm)?

a. –8 b. –4 c. –2 d. –6 e. 30

10. An object 15 cm high is placed 15 cm in front of a convex mirror with a focal length of –10 cm. What is the image height (in cm)?

a. 2 b. 4 c. 6 d. 8 e. 30

11. An object is placed 10 cm in front of a concave mirror with a 20-cm focal length. Determine the image location (in cm).

a. –20 b. –15 c. –10 d. –5 e. 6.7

Geometric Optics 263

12. An object is placed 15 cm in front of a concave mirror with a focal length of 30 cm. What is the magnification?

a. 1 b. 2 c. 1/2 d. 1/4 e. –2

13. A dentist uses a concave mirror (focal length 2 cm) to examine some teeth. If the distance from the object to the mirror is 1 cm, what is the magnification of the tooth?

a. 6 b. 1 c. 4 d. 2 e. 1.5

14. The actual depth of a shallow pool 1.0 m deep is not the same as the apparent depth seen when you look straight down at the pool from above. How deep (in cm) will it appear to be? (nwater = 1.33.)

a. 133 b. 75 c. 90 d. 117 e. 100

15. Bottles of perfume sometimes have thick glass (n = 1.5) walls which give the impression the volume is larger than it is. Assume a cylindrical bottle has an inner radius of 1 cm and an outer radius of 2 cm. How thick (in cm) would the wall appear if you could see a mark on the inside surface?

a. 0.80 b. 0.51 c. 0.72 d. 80 e. 12

16. Bottles of perfume sometimes have thick glass (n = 1.5) walls which give the impression the volume is larger than it really is. Assume a cylindrical bottle with an inner radius of 1 cm and an outer radius of 2 cm. What percentage of the apparent volume is the real volume?

a. 95% b. 60% c. 80% d. 69% e. 75%

264 CHAPTER 36

17. A plane convex lens is made of glass (n = 1.5) with one flat surface and the other having a radius of 20 cm. What is the focal length (in cm) of the lens?

a. 20 b. 30 c. 40 d. 10 e. 50

18. An object 20-cm high is placed 50 cm in front of a lens whose focal length is 5.0 cm. Where will the image be located (in cm)?

a. 5.13 b. 5.56 c. 5.72 d. 5.93 e. 4.55

19. An object 50-cm high is placed 1 m in front of a converging lens whose focal length is 1.5 m. Determine the image height (in cm).

a. 77 b. 150 c. 52 d. 17 e. 83

20. An object is placed 15 cm in front of a diverging lens whose focal length is 12 cm. Where will the image be located (in cm)?

a. –6.7 b. –7.2 c. –0.15 d. –60 e. –5.0

21. A camera has a converging lens with a focal length of 56 mm. If the f-number is 2.8, what is the diameter of the lens (in mm)?

a. 10 b. 31 c. 0.5 d. 20 e. 50

22. The purpose of prescription glasses for a near-sighted person is to bring distant objects

a. to the far point of the eye b. to the near point of the eye c. to the retina of the eye d. none of the above

Geometric Optics 265

23. A far-sighted student has a near point of 1.0 m. Calculate the focal length (in cm) of the glasses needed so the near point will be normal (25 cm).

a. 72 b. 25 c. 33 d. 100 e. –33

24. A 10-cm focal length converging lens is used to magnify small newspaper print 2.0 mm high. Calculate the height of the image (in mm) for the maximum magnification for a normal eye.

a. 3.5 b. 7.0 c. 9.2 d. 12 e. 2.5

25. A compound microscope is made with an objective lens (f0 = 0.90 cm) and an eyepiece (f0 = 1.1 cm). The lenses are separated by a distance of 10 cm. If an object is 1.0 cm in front of the objective lens, where will the final image of the eyepiece be located?

a. –30 b. –15 c. –23 d. –11 e. –9

26. A compound microscope is made with an objective lens (f0 = 0.900 cm) and an eyepiece (fe = 1.10 cm). The lenses are separated by a distance of 10.0 cm. What is the angular magnification? (Assume the near point is 25.0 cm.)

a. –253 b. –450 c. –770 d. –980 e. –635

27. A telescope is constructed with two lenses separated by a distance of 25 cm. The focal length of the objective is 20 cm. The focal length of the eyepiece is 5 cm. Calculate the angular magnification of the telescope.

a. 6 b. 4 c. 8 d. 10 e. 5

266 CHAPTER 36

28. If you stand closer to a concave mirror than a distance of one focal length, the image you see is

a. real and inverted. b. real and upright. c. virtual and inverted. d. virtual and upright. e. none of the above because you do not get an image.

29. When you stand in front of a convex mirror, the image you see is

a. real and inverted. b. real and upright. c. virtual and inverted. d. virtual and upright. e. real and inverted if your distance from the mirror is greater than two focal

lengths.

30. The image of an object beneath the surface of a medium of refractive index n > 1 is seen in air by a person looking down on the surface. This image, formed by light rays leaving the flat refractive surface, is

a. real and closer to the viewer than the object. b. virtual and closer to the viewer than the object. c. real and farther from the viewer than the object. d. virtual and farther from the viewer than the object. e. virtual and the same distance from the viewer as the object.

31. A magician can make a candle look as if it is burning under water by focusing light from a candle flame burning in air directly on top of an underwater candle. To do this you want to use a

a. concave mirror farther than one focal length from the burning candle. b. a convex mirror farther than one focal length from the burning candle. c. a biconcave lens farther than one focal length from the burning candle. d. a concave mirror closer than one focal length to the burning candle. e. a convex lens closer than one focal length to the burning candle.

32. If a convex lens were made out of very thin clear plastic filled with air, and were then placed underwater where n = 1.33 and where the lens would have an effective index of refraction n = 1, the lens would act in the same way

a. as a concave mirror in air. b. as a concave lens in air. c. as a convex lens in air. d. as a flat refracting surface between water and air as seen from the water

side. e. as the glasses worn by a farsighted person.

Geometric Optics 267

33. The inhabitants of a planet in another galaxy have their eyes at the exact center of their 4.0-m long bodies. How long must a plane mirror be for such a creature to be able to see all of its body in the mirror?

a. 1.0 m b. 2.0 m c. 2.5 m d. 4.0 m e. 8.0 m

34. Of the possible statements that parallel rays are brought to a focus by a

1) concave mirror, 2) convex mirror, 3) converging lens, 4) diverging lens,

a. 1 and 2. b. 3 and 4. c. 1 and 3. d. 2 and 3. e. 2 and 4.

35. The object in a ray diagram is perpendicular to the principal axis but does not have one end lying on the principal axis. The minimum number of rays that must be drawn in this ray diagram in order to determine the position of the image is

a. 1. b. 2. c. 3. d. 4. e. 5.

268 CHAPTER 36

36. Which ray diagrams are correct? The three rays in each diagram are distinguished by different types of lines.

A

O

I

B

O

I

C

O

I

D

O

I

E

O

I

a. B and C b. C and D c. D and E d. C and E e. C, D and E

Geometric Optics 269

37. Which ray diagram is correct? The three rays in each diagram are distinguished by different types of lines.

A

O

B

O I

C

O

I

E

O

I

D

OI

a. A b. B c. C d. D e. E

38. Ilona and Olivia observe a virtual image formed by an object placed a distance

f2

in front of a convex lens of focal length f. They argue about where to place a concave lens of focal length − f to have a virtual image at the same location relative to the lens that they had with the convex lens. Ilona says that the object

should also be placed a distance

f2

in front of the concave lens. Olivia says that

this won’t work. Which one, if either, is correct, and why?

a. Ilona, because concave and convex lenses produce virtual images at equal image distances when the object distances are equal.

b. Ilona, because both p and q are negative for a concave lens. c. Olivia, because both p and q are positive for a concave lens.

d. Olivia, because if q = −

2f

, then p was p = ∞ .

e. Olivia, because if q = − = ∞ . f , then p was p

270 CHAPTER 36

39. An object is placed a distance y0 = −2 f in front of a convex lens of focal length f

that is located at y = 0 . An identical object is placed a distance ′y0 = −2 f in front of a concave lens of focal length − f that is located at ′y = 0 . The difference between the two image positions, yi − ′iy , is

a.

f2

.

b. f.

c.

43

f .

d. 2 f .

e.

83

f .

40. An object is placed a distance y0 = −2 f in front of a concave mirror of focal

length f that is located at y = 0 . An identical object is placed a distance ′y0 = −2 f in front of a convex mirror of focal length − f that is located at ′y = 0 . The difference between the two image positions, yi i− ′y , is

fa.

2.

b. f. 4

c. 3

f .

d. 2 f .

83

f . e.

41. A girl is sitting on the edge of a pier with her legs dangling over the water. Her soles are 80.0 cm above the surface of the water. A boy in the water looks up at her feet and wants to touch them with a reed. ( n =water 1.333 .) He will see her soles as being

a. right at the water surface. b. 53.3 cm above the water surface. c. exactly 80.0 cm above the water surface. d. 107 cm above the water surface. e. an infinite distance above the water surface.

Geometric Optics 271

Open-Ended Problems

42. A magnifying glass has a convex lens of focal length 15 cm. At what distance from a postage stamp should you hold this lens to get a magnification of +2?

43. A contact lens is made of plastic with an index of refraction of 1.50. The lens has an outer radius of curvature of +2.0 cm and an inner radius of curvature of +2.5 cm. What are the focal length and the power of the lens?

44. A concave mirror with a radius of curvature of 1 m is illuminated by a candle located on the symmetry axis 3 m from the mirror. Where is the image of the candle?

45. Suppose an object is placed 6 cm in front of a lens that has a focal length of 4 cm. Where is the image located? What are the magnification and the character of the image?

272 CHAPTER 36

Geometric Optics 273

Chapter 36

Geometric Optics

1. a

2. b

3. d

4. c

5. e

6. d

7. b

8. c

9. d

10. c

11. a

12. b

13. d

14. b

15. a

16. d

17. c

18. b

19. b

20. a

21. d

22. a

23. c

24. b

25. d

26. a

27. b

28. d

29. d

30. b

31. a

32. b

33. b

34. c

35. c

36. e

37. d

38. e

39. e

40. e

41. d

42. 7.5 cm

43. +20 cm, +5 diopters

44. 60 cm in front of the mirror

45. 12 cm beyond the 4 cm lens, M = –2, the image is real and inverted

274 CHAPTER 36