Physics quiz question: interference maxima angle

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

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Multiple-Choice Question 25.7

Tracks on a DVD (digital videodisc) are spaced 740 nm apart[*], and are illuminated by a yellow laser[**] of unknown wavelength, producing an m = 1 interference maxima at an angle of 53° on a screen 5.0 m away. If the screen is brought closer to the DVD, the m = 1 interference maxima angle will:
(A) decrease.
(B) increase.
(C) remain the same.
(D) (Not enough information is given.)

[*] en.wikipedia.org/wiki/File:Comparison_CD_DVD_HDDVD_BD.svg.
[**] crystalaser.com/new/yellowlaser.html.

Correct answer (highlight to unhide): (C)

The first maxima angle θ for double-slit (and grating) interference is given by relation:

d·sinθ = m·λ,

where m = 1, such that:

θ = sin–1(λ/d).

Note that if the screen is brought closer to the DVD (or farther away), this angle will not change, as d, m, and λ all remain constant. (The spacing of the maxima and minima interference pattern on the screen will change, however.)

Sections 30882, 30883
Exam code: quiz03cDvD
(A) : 17 students
(B) : 12 students
(C) : 11 students
(D) : 0 students

Success level: 28%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.38

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