1. c. The light spreads vertically as it goes through the vertical aperture. The light spreads horizontally due to different points on the horizontal lightbulb.

2. c. There’s one image behind the vertical mirror and a second behind the horizontal mirror. A third image in the corner arises from rays that reflect twice, once off each mirror.

3. a. The ray travels closer to the normal in both media 1 and 3 than in medium 2, so $n_1$ and $n_3$ are both larger than $n_2$. The angle is smaller in medium 3 than in medium 1, so $n_3>n_1\text{.}$

4. e. The rays from the object are diverging. Without a lens, the rays cannot converge to form any kind of image on the screen.

5. a, e, or f. Any of these will increase the angle of refraction ${\theta }_2$.

6. Away from. You need to decrease $s\prime$ to bring the image plane onto the screen. $s\prime$ is decreased by increasing $s$.

7. c. A concave mirror forms a real image in front of the mirror. Because the object distance is $s\approx \infty$, the image distance is $s\prime \approx f$.

1.

1. 3.3 ns

2. 0.75 m, 0.67 m, 0.46 m

3. 5.4 m

5. $30\text{°}$

7. 9.0 cm

9. 433 cm

11. 1.4

13. $23.3\text{°}$

15. $76.7\text{°}$

17. 3.2 cm

19. 1.52

21. Inverted

23. 15 cm in front of lens, upright

25. $-68\text{cm}$

27. 2.0 m

29. 2.0 cm

31. 30 cm, 0.50 cm

33. b. 40 cm, 2.0 cm, agree

35.

1. 47 cm, same side

2. 6.3 cm, inverted

37. b. $-8.6\text{cm,}1.1\text{ cm},\text{ agree}$

39. Inverted

41. Upright

43. 6.4 cm

45. 1.7

47.

1. $2{\text{cos}}^{-1}\left({\displaystyle \frac{n}{2n_{\text{air}}}}\right)$

2. $82.8\text{°}$

49.

1. 87 cm

2. 65 cm

3. 43 cm

51. 4.7 m

53. 1.46

55. $30\text{°}$

57. $35\text{°}$

59. 2.7 m/s

61. 15.1 cm

63. 17 cm

65. 2; 0.50 cm, inverted; 8.0 cm, inverted

67.

1. 5.9 cm

2. 6.0 cm

69. $4f$

71. 16 cm

73. $20\mu \text{m}\text{/}\text{s}$ away from the lens

75. 13 cm

77. 1.2 m

79. 2.8 cm

81.

1. ${\displaystyle \frac{n_1}{c}}\sqrt{x^2+a^2}+{\displaystyle \frac{n_2}{c}}\sqrt{(w-x{)}^2+b^2}$

2. ${\displaystyle \frac{dt}{dx}}=0={\displaystyle \frac{n_{1}x}{c\sqrt{x^2+a^2}}}-{\displaystyle \frac{n_2(w-x)}{c\sqrt{(w-x{)}^2+b^2}}}$