20101006

Physics quiz question: double slit interference maxima spacing on screen

Physics 205B Quiz 3, fall semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 25.31

Light incident on a pair of slits produces an interference pattern on a screen 5.00 m from the slits. The slit separation is 0.0120 cm and the spacing between adjacent bright fringes on the screen is 2.30 cm. The wavelength of the light is:
(A) 479 nm.
(B) 522 nm.
(C) 552 nm.
(D) 690 nm.

Correct answer (highlight to unhide): (C)

Maxima angles (bright fringes) are given by d·sinθ = m·λ. The angle for the m = 0 bright fringe is θ = 0°, while the angle θ for the m = 1 bright fringe can be found from:

d·sinθ = (1)λ.

From trigonometry, tanθ = y/L, where y is the distance along the screen (here, the space between adjacent bright fringes such as m = 0 and m = 1), and L is the distance from the slits to the screen. Thus setting m = 1, and solving for λ:

d·sinθ = m·λ

λ = d·sinθ/m,

λ = (d/m)·sin(tan–1(y/L)),

λ = ((0.0120×10–2 m)/(1))·sin(tan–1((2.30×10–2 m)/(5.00 m)) = 5.51994159933×10–7 m,

which is 552 nm.

(Response (A) is L·y/(2·d); response (B) is 2·L·d/y; response (D) is L·d·y/2.)

Student responses
Section 70856
(A) : 3 students
(B) : 1 student
(C) : 7 students
(D) : 0 students

Success level: 63%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.67

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