Physics quiz question: double slit interference

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

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

A double slit is illuminated with monochromatic light of wavelength 540 nm. The m = 0 and m = 1 bright fringes are separated by 3.2 mm on a distant screen 4.0 m from the slits. (Consider the small-angle approximation to be valid.) The path difference between the light from each slit that reaches the m = 1 bright fringe is:
(A) 0.
(B) 270 nm.
(C) 540 nm.
(D) 1.6 mm.
(E) 3.2 mm.

Correct answer: (C)

For monochromatic light passing through double slits, the path length difference to the constructive interference bright fringes must be an integer number of wavelengths. The m = 0 bright fringe will have a path length difference of 0, while the m = 1 bright fringe will have a path length difference of one whole wavelength, or 540 nm.

Section 30882
Exam code: quiz03gR7L
(A) : 1 student
(B) : 3 students
(C) : 10 students
(D) : 5 students
(E) : 8 students

Success level: 37%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.86