Physics quiz question: laser diffraction through a single slit

Physics 205B Quiz 3, spring semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 25.49

Light from a green laser of wavelength 550 nm passes through a single slit to form a diffraction pattern on a screen 4.0 m from the slit, where the width of the central maximum on the screen is 14 mm. The width of the slit is:
(A) 2×10^–8 m.
(B) 6×10^–8 m.
(C) 8×10^–5 m.
(D) 3×10^–4 m.

Correct answer (highlight to unhide): (D)

From trigonometry, the relation between the angle θ and the adjacent leg L = 4.0 m (distance from the single slit to the screen") and the opposite leg y = 7 mm (one-half of the "width of the central maximum on the screen):

tanθ = y/L,

θ = tan^–1(y/L).

Then 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,

W = λ/sinθ,

W = λ/(sin(tan^–1(y/L)),

W = (550×10^–9 m)/sin(tan^–1((7×10^–3 m)/(4.0 m))) = 3.14286195535×10^–4 m,

which to one significant figure means the slit is 3×10^–4 m wide.

(Response (A) is L·λ·y; response (B) is 4L·λ·y; response (C) is L·λ/(4y).)

Student responses
Section 30822
Exam code: quiz03F3ld
(A) : 2 students
(B) : 1 student
(C) : 2 students
(D) : 2 students

Success level: 29%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50