Geometric Optics
Practice Problems
Ray Tracing - Draw at least two principle rays and show the image created by the lens or mirror.
1.
2.
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10.
Practice Problems - Mirrors
Classwork
11. A candle is placed at a distance of 12 cm from of a concave mirror with a focal length of 8 cm. The
candle is 5 cm tall.
a. Where is the image located?
b. What is the height of the image?
12. A candle is placed at a distance of 14 cm from of a concave mirror with a focal length of 6 cm. The
candle is 7 cm tall.
a. Where is the image located?
b. What is the height of the image?
13. A candle is placed at a distance of 5 cm from of a concave mirror with a focal length of 10 cm. The
candle is 6 cm tall.
a. Where is the image located?
b. What is the height of the image?
14. An object is placed at a distance of 6 cm from a concave mirror and an image is produced at a distance
of 14 cm from the mirror. What is the focal length?
Homework
15. A candle is placed at a distance of 18 cm from of a concave mirror with a focal length of 12 cm. The
candle is 9 cm tall.
a. Where is the image located?
b. What is the height of the image?
16. A candle is placed at a distance of 15 cm from of a concave mirror with a focal length of 5 cm. The
candle is 8 cm tall.
a. Where is the image located?
b. What is the height of the image?
17. A candle is placed at a distance of 4 cm from of a concave mirror with a focal length of 12 cm. The
candle is 10 cm tall.
a. Where is the image located?
b. What is the height of the image?
18. An object is placed at a distance of 12 cm from a concave mirror and an image is produced at a
distance of 8 cm from the mirror. What is the focal length?
Practice Problems - Lenses
Classwork
19. An object is placed at a distance of 60 cm from a converging lens with a focal length of 20 cm.
a. Where is the image located?
b. What is the magnification of the lens?
20. An object is placed at a distance of 20 cm from a converging lens with a focal length of 30 cm.
a. Where is the image located?
b. What is the magnification of the lens?
21. An object is placed at a distance of 60 cm from a converging lens with a focal length of 40 cm.
a. Where is the image located?
b. What is the magnification of the lens?
Homework
22. An object is placed at a distance of 40 cm from a converging lens with a focal length of 15 cm.
a. Where is the image located?
b. What is the magnification of the lens?
23. An object is placed at a distance of 15 cm from a converging lens with a focal length of 20 cm.
a. Where is the image located?
b. What is the magnification of the lens?
24. An object is placed at a distance of 50 cm from a converging lens with a focal length of 30 cm.
a. Where is the image located?
b. What is the magnification of the lens?
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?
3. An object is placed at a distance of 45 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?
Answers
5.
1.
6.
2.
7.
3.
8.
4.
11. a) 24 cm b) 10 cm
12. a) 10.5 cm b) 6.1 cm
13. a) -10 cm b) 12 cm
14. 4.2 cm
9.
15. a) 36 cm b) 18 cm
16. a) 7.5 cm b) 4 cm
17. a) -6 cm b) 15 cm
18. 4.8 cm
19. a) 30 cm b) 0.5
20. a) -60 cm b) 3
10.
21. a) 120 cm b) 2
22. a) 24 cm b) 0.6
23. a) -60 cm b) 4
24. a) 75 cm b) 1.5
Free Response Answers
1. a. see answer for problem #1
b. di = 30 cm; It is real
c. hi = 8 cm; It is inverted
d. see answer for problem #4
2.
a. see answer for problem #6
b. di = 30 cm; It is real
c. hi = 5 cm; It is inverted
3. a. see answer for problem #5
b. di = 90 cm; It is real
c. hi = 16 cm