geometric optics - center for teaching &...

Geometric Optics

PSI AP Physics 2 Name________________________________

Multiple-Choice

1. When an object is placed in front of a plane mirror the image is:

(A) Upright, magnified and real

(B) Upright, the same size and virtual

(C) Inverted, demagnified and real

(D) Inverted, magnified and virtual

2. A point object is placed in front of a plane mirror. Which is the correct location of the image

produced by the mirror?

(A)A (B) B (C) C (D) D

3. A narrow beam of light is incident on the surface of a plane mirror. The initial angle between the

incident ray and reflected ray is 2α. If the mirror is turned around point A by the angle Θ what is

the change of the angle between two rays?

(A) Θ (B) 2Θ (C) 4Θ (D) Θ/2

4. A candle is placed in front of a concave mirror.

The image produced by the mirror is:

(A) Real, inverted and magnified

(B) Real, inverted and demagnified

(C) Virtual, upright and magnified

(D) Virtual, upright and demagnified

5. A candle is placed in front of a concave

mirror. The image produced by the mirror is:





6. A candle is placed in front of a concave mirror.






7. A candle is placed in front of a convex mirror.






8. A very narrow light ray AB strikes the surface of a concave mirror as shown on the diagram.

Which of the following diagrams represents the reflected ray?

(A) (B)

(C) (D)

9. A very narrow light ray AB strikes the surface of a concave mirror as shown on the diagram.


(A) (B)

(C) (D)

10. A very narrow light ray AB strikes the surface of a convex mirror as shown on the diagram.


(A) (B)

(C) (D)

11. An object is located far away from a concave mirror. The image is located at:

(A) The distance d>R

(B) The distance d<F

(C) The distance F<d<R

(D) The focal point

12. An object is placed at the focal point in front of a concave mirror. The image is located:

(A) The distance d>R


(C) The focal point

(D) No image is formed

13. An object is placed at the center of the curvature in front of a concave mirror. The image is

located:

(A) The distance d=R


(C) The distance F<d<R

(D) The focal point

14. A light ray AB is incident obliquely on the surface of a glass block. Which of the following

diagrams represents the refracted ray?

(A) (B)

(C) (D)

15. A light ray AB passes from glass into air at an angle less than the critical angle. Which of the

following diagrams represents the refracted ray?

(A) (B)

(C) (D)

16. A light ray AB passes from glass into air at the critical angle. Which of the following diagrams

represents the refracted ray?

(A) (B)

(C) (D)

17. A boy is trying to catch a fish from a lake. Which of the following diagrams represents the image

of the fish observed the boy?

(A) (B)

(C) (D)

18. Which of the lens or lenses is the converging lens?

(A) I and V (B) II, III and IV (C) II and III (D) III and IV

19. Which of the lens or lenses is the diverging lens?

(A) I and V (B) II, III and IV (C) II and III (D) III and IV

20. An object is placed in front of a converging lens at a distance greater than 2F. The image

produced by the lens is:

(A)Real, inverted and demagnified

(B)Real, inverted and magnified



21. An object is placed in front of a converging lens at a distance between F and 2F. The image






22. An object is placed in front of a converging lens at a distance less than F. The image produced by

the lens is:





23. An object is placed in front of a diverging lens at a distance between F and 2F. The image






24. A light ray is incident on a glass prism with one angle of 90 ̊and the

other angle θ. If θ is greater than the critical angle for glass-air

boundary, which of the following is correct for the emerging ray from

the opposite face of the prism?

(A) (B) (C)

(D)

25. A light ray is incident on a glass prism with one angle of 90 ̊and the

other angle θ. If θ is less than the critical angle for glass-air boundary,

which of the following is correct for the emerging ray from the

opposite face of the prism?

(A) (B) (C)

(D)

Multi Correct Questions

26. An object is placed in front of a concave mirror. Which of the following are possible images that

can be formed by this placement? Select two answers.

(A) A real image that is magnified and upright

(B) A real image that is demagnified and inverted.

(C) A virtual image that is magnified and upright

(D) A virtual image that is demagnified and inverted.

27. A group of students collect data using a lens.

They varied the distance of the object and

measured the the distance of the image. The

graph to the right represents their data. Which of

the following can be determined from their data?

Select two answers.

(A) The focal length of the lens.

(B) The magnification when the object is placed at

any given distance.

(C) The height if the object and image.

(D) The index of refraction of the glass.

28. A real, inverted, and magnified image is formed. Which of the following could have created this

image? Select two answers.

(A) An object placed in passed the focal length of a converging lens.

(B) An object placed within the focal length of a concave mirror.

(C) An object placed passed the focal length of a diverging lens.

(D) An object placed passed the focal length of a concave mirror.

29. As a ray of light passes from glass into air, which if the following happen? Select two answers.

(A) A reflected ray’s angle is larger than the incident ray’s angle.

(B) A refracted ray bends towards the normal line.

(C) A reflected ray’s angle is equal to the incident ray’s angle.

(D) A refracted ray bends away from the normal line.

Free Response Problems

1. A candle is placed at a distance of 15 cm from of a concave mirror with a focal length of 10 cm.

The candle is 4 cm tall.

a. On the diagram below use ray-tracing to show the image produced by the

mirror.

b. Find the image distance. Is the image real or virtual?

c. Find the size of the image. Is the image upright or inverted?

d. The concave mirror is replaced by a convex mirror. On the diagram below use

ray-tracing to show the new image formed by the convex mirror

2. An object is placed at a distance of 60 cm from a converging lens with a focal length of 20 cm.

a. On the diagram below use ray-tracing to show the image formed by the lens.

b. Calculate the image distance. Is the image virtual or real?

c. If the object is 10 cm tall, what is the size of the image?

d. An identical converging lens is placed behind the first lens at the focal point. On

the diagram below use ray-tracing to show the image formed by two lenses.

3. An object is placed at a distance of 80 cm from a converging lens with a focal length of 30 cm.

a. On the diagram below use ray-tracing to show the image formed by the lens.

b. Calculate the image distance. Is the image virtual or real?

c. If the object is 8 cm tall, what is the size of the image?

d. A diverging lens with the same focal length is placed behind the first lens at the

point 3F. On the diagram below use ray-tracing to show the image formed by two

lenses.

4. A light ray strikes a flat piece of glass at an angle of incidence 60 ̊. The thickness of the glass is 2

cm and the index of refraction of the glass is 1.5.

a. On the diagram below use ray-tracing to show the refracted ray from both faces

of the glass.

b. The light ray partially reflects from the surface of the glass. Find the angle of

reflection.

c. Find the angle at which the ray emerges from the glass.

d. Find the linear displacement between the emerging ray and the incident ray.

5. A light ray travels from glass to air at an angle of incidence θ1 = 35 .̊ The ray partially reflected

from the glass-air boundary at the angle θ2 and partially refracted at the angle θ3. The index of

refraction of the glass is 1.6.

a. What is the speed of light in glass?

b. What is the angle of reflection θ2?

c. What is the angle of refraction θ3?

d. What is the minimum value of θ1 at which light doesn’t emerge from the top

face of the glass?

6. A narrow beam of white light is incident normally on the surface of a triangular silicate flint glass

prism with one angle of 90 .̊ The index of refraction for violet light is 1.66 and for red light is

1.61. The angle θ in the prism is less than the critical angle for this type of glass.

a. On the diagram below show an approximate sketch for the refracted light from

the opposite face of the prism.

b. Find the critical angle of the glass for both violet and red light.

c. If the angle θ is 30 ̊, calculate the angular width of the dispersion spectrum.

d. The situation has changed to opposite; now a beam of white light travels in a

huge glass block and strikes the surface of an air bubble in a shape of triangular

prism. On the diagram below show an approximate sketch for the refracted light

from the opposite face of the prism.

7. A student needs to perform an experiment to determine the index of refraction of a transparent

block. The student shines a laser from air (n = 1) into the block at an angle θi and measures the

angle of refraction θr as shown in the figure below, left. Measurements are taken of the angles

of incidence and refractions and are listed in the table below, middle.

a. In the blank table above, list values this student should use to create a graph that can be

used to find the index of refraction.

b. Graph the values you chose so that the index of refraction can be calculated using the slope

of your graph.

c. Calculate the index of refraction.

θi (°) θr (°)

20 15

35 25

45 32

60 40

75 46

8. The figure below shows two transparent blocks, the first with an index of refraction of 1.25 and

the second with an index of refraction of 1.6. A laser is positioned such that it passes into the

top block head on without refracting and hits point P. A piece of paper is placed on top of block

1 so that two bright spots are projected on it as shown below. The spot closer to Q will be called

point A and the spot further from Q will be called spot B.

a. In a paragraph-length answer, explain how the two bright spots A and B are formed and

why B is further away from Q than A.

b. On the figure above, draw a ray diagram that shows the formation of the spots A and B.

c. Now the angle is increased such that one of the spots becomes brighter due to total

internal reflection. Explain which spot becomes brighter and why.

d. Again the angle is increased such that one of the spots disappears. Explain which spot

disappears and why.

Multiple Choice Answers

1. B

2. D

3. B

4. B

5. A

6. C

7. D

8. B

9. A

10. C

11. C

12. D

13. A

14. A

15. C

16. D

17. C

18. B

19. A

20. A

21. B

22. C

23. D

24. A

25. C

26. B, C

27. A, B

28. A, D

29. C, D

Free Response Answers

1. a.

b. di = 30 cm; It is real

c. hi = 8 cm; It is inverted

d.

2. a.


c. hi = 5 cm; It is inverted

d.

3. a.


c. hi = 4.8 cm

d.

4. a.

b. 60O

c. 60O

d. Δx = 0.42 cm

5. a. v = 1.9 x 108 m/s

b. ϴ = 35O

c. ϴ = 66.6O

d. ϴ =38.7O

6. a.

b. ϴCR = 38.4O; ϴCV = 37O

c. Δϴ = 2.5O

d.

7. a.

Sin θi Sin θr

0.34 0.26

0.57 0.42

0.71 0.53

0.87 0.64

0.97 0.72

b. c. The slope and index of refraction should be approximately 1.37.

8.

a. When the ray hits point P it is both reflected and refracted. The reflected ray forms the bright

spot at point A. The refracted ray hits the surface between block 2 and air and is both reflected

and refracted. That refracted ray then hits the surface between block 2 and block 1 and is

reflected and refracted. This refracted ray forms the bright spot at point B.

b. c. Spot B gets brighter because the ray is no longer refracted at the boundary between block 2 and

the air. It is only reflected so that the reflected ray gets brighter.

d. Spot B disappears because the ray is no longer refracted as it passes through the boundary from

block 2 to block 1. It is only reflected back into block 2.

geometric optics - center for teaching &...

Documents