Physics quiz question: moving screen away from single slit

Physics 205B Quiz 3, spring semester 2012
Cuesta College, San Luis Obispo, CA

Light from a red laser illuminates single slit to form a diffraction pattern on a distant screen. If the distance from the slit to the screen is increased, the width of the central maximum on the screen would:
(A) increase.
(B) remain the same.
(C) decrease.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

From the first minima equation (which uses the angle that measures one-half of the width of the central maximum on the screen), where W is the width of the slit:

W·sinθ = (1)·λ,

such that the "spread angle" is given by:

θ = sin^–1(λ/W).

Since the wavelength λ and the slit width W remain constant, the "spread angle" θ is unchanged if the distance from the slit to the screen in increased.

However, from trigonometry, the relation between the angle θ and the adjacent leg L (distance from the single slit to the screen) and the opposite leg y (one-half of the width of the central maximum on the screen) is given by:

tanθ = y/L,

where:

θ = tan^–1(y/L),

and since the distance L from the slit to the screen is increased, while the "spread angle" θ remains constant (as λ and W are constant), then y, which is one-half of the width of the central maximum on the screen must increase, and correspondingly the width of the entire central maximum on the screen would increase as well.

Section 30822
Exam code: quiz03gR7L
(A) : 21 students
(B) : 3 students
(C) : 3 students
(D) : 0 students

Success level: 78%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.71