1. b. The antinodal lines seen in Figure 33.4b are diverging.

2. Smaller. Shorter-wavelength light doesn’t spread as rapidly as longer-wavelength light. The fringe spacing $\text{Δ}y$ is directly proportional to the wavelength $\text{λ}$.

3. d. Larger wavelengths have larger diffraction angles. Red light has a larger wavelength than violet light, so red light is diffracted farther from the center.

4. b or c. The width of the central maximum, which is proportional to $\text{λ}/a$, has increased. This could occur either because the wavelength has increased or because the slit width has decreased.

5. d. Moving $\text{M}{}_1$ in by $\text{λ}$ decreases $r_1$ by $2\text{λ}$. Moving $\text{M}{}_2$ out by $\text{λ}$ increases $r_2$ by $2\text{λ}$. These two actions together change the path length by $\text{Δ}r=4\text{λ}$.

1. 470 nm

3. 3.2 cm

5. 1.3 m

7. $0.286\text{°}$

9. 167 cm

11. 530

13. $43.2\text{°}$

15. 14.5 cm

17. 500 nm

19. 0.20 mm

21. 4.0 mm

23. 633 nm

25. $2.9\text{°}$

27. 1.3 m

29. 9

31. 1.6

33. $0.015\text{ rad}\text{,}0.87\text{°}$

35. 78 cm

37. 30,467

39.

1. Double slit

2. 0.16 mm

41. 0.40 mm

43. 6.0 GHz

45. 667.8 nm

47. 1.3 m

49. 43 cm

51.

1. $L\text{λ}/d$

2. $(L/d)\text{Δ}\text{λ}$

3. 0.250 nm

53. $16\text{°}$

55. $1.8\mu \text{m}$

57. ${\displaystyle \frac{\sqrt{2}}{2}}d$

59. b. $50\mu \text{m}$

61. 0.88 mm

63.

1. 550 nm

2. 0.40 nm

65. 50 cm

67.

1. 3.0 mm

2. $\frac{1}{4}T$

3. $\frac{1}{2}\pi \text{rad}$

4. 0.75 mm toward slit with glass

69.

1. Dark

2. 1.597

71. 3

73.

1. $\text{Δ}y={\displaystyle \frac{\text{Δ}\text{λ}L}{d}}$

2. $\text{Δ}{y}_{\text{min}}={\displaystyle \frac{\text{λ}}{N}}$

3. 3646 lines

75.

1. 0.52 mm

2. $0.074\text{°}$

3. 1.3 m