Question

(a) If a single slit produces a first minimum at 14.5º, at what angle is the second-order minimum?

(b) What is the angle of the third-order minimum?
(c) Is there a fourth-order minimum?
(d) Use your answers to illustrate how the angular width of the central maximum is about twice the angular width of the next maximum (which is the angle between the first and second minima).
a) (a) 29.0º, (b) 43.5º, (c) Yes
b) (a) 21.0º, (b) 36.9º, (c) No
c) (a) 36.9º, (b) 50.0º, (c) Yes
d) (a) 43.5º, (b) 58.1º, (c) No

Answer 1

The second-order minimum is at 29.0°, the third-order minimum is at 43.5°, there is no fourth-order minimum, and the angular width of the central maximum is about twice the angular width of the next maximum.

Step-by-step explanation:

(a) The first minimum occurs at an angle of 14.5°. The second-order minimum occurs at an angle that is twice the angle of the first minimum. Therefore, the angle of the second-order minimum is 14.5° x 2 = 29.0°.

(b) Similarly, the angle of the third-order minimum will be three times the angle of the first minimum. Therefore, the angle of the third-order minimum is 14.5° x 3 = 43.5°.

(c) Since the angle of the fourth-order minimum would be four times the angle of the first minimum (14.5° x 4 = 58.0°), and the angle of the third-order minimum is 43.5°, there is no fourth-order minimum.

(d) The angular width of the central maximum is approximately twice the angular width between the first and second minima. In this case, the angular width between the first and second minima is 14.5° (29.0° - 14.5° = 14.5°). Therefore, the angular width of the central maximum is approximately 2 x 14.5° = 29.0°.