Physics quiz question: diffraction through single slits of different widths

Physics 205B Quiz 3, spring semester 2014
Cuesta College, San Luis Obispo, CA

Light from a green laser pointer (wavelength 532 nm) illuminates a single slit. If the slit is made narrower than __________, the first diffraction minima will not be visible anywhere on a screen.
(A) 266 nm.
(B) 532 nm.
(C) 797 nm.
(D) 1,064 nm.

Correct answer (highlight to unhide): (B)

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 both responses (C) and (D) have slit openings greater than 532 nm, they will produce a first minimum fringe at θ = 41.9° and 30°, respectively.

Response (B) has a slit opening that is equal to the 532 nm wavelength, such that θ = 90°, which is the boundary case where an opening slightly larger than 532 nm that would result in a spread angle slightly less than 90° (and thus be visible on a screen), and an opening slightly smaller than 532 nm would result in an undefined spread angle, as the inverse sine function would operate on a value greater than 1, so there would be no first minimum fringe at any angle (or on a screen) if the slit opening W is less than 532 nm.

Response (A) is already too narrow to produce a first diffraction minima, as it is already smaller than 532 nm.

Sections 30822, 30883
Exam code: quiz03cDvD
(A) : 11 students
(B) : 28 students
(C) : 0 students
(D) : 1 student

Success level: 70%
Discrimination index (Aubrecht & Aubrecht, 1983): –0.05