Physics quiz question: laser diffraction through variable-width single slit

Physics 205B Quiz 3, spring semester 2017
Cuesta College, San Luis Obispo, CA

A red laser (wavelength 632 nm) illuminates a single slit with a width that can be closed or opened. No first minimum fringe would be observed if the slit opening is __________ than 632 nm.
(A) narrower.
(B) wider.
(C) (Neither of the above choices.)
(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,

θ = sin^–1(λ/W),

which would give a domain error from the inverse sine function if the quantity (λ/W) is greater than 1, so there would be no first minimum fringe at any angle if the slit opening W is less than the wavelength λ.

Sections 30822, 30883
Exam code: quiz03d3St
(A) : 18 students
(B) : 10 students
(C) : 0 students
(D) : 0 students

Success level: 64%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.26