Physics quiz question: CD illuminated by DVD drive laser

Physics 205B Quiz 3, spring semester 2013
Cuesta College, San Luis Obispo, CA

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

Tracks on a CD (compact disc) are spaced 1.6 µm apart, illuminated by a 780 nm wavelength laser in a CD player[*]. The CD is then placed in a DVD (digital videodisc) drive with a 650 nm wavelength laser, which will produce a first maximum angle that is __________ the first maximum angle produced by the 780 nm wavelength laser.
(A) smaller than.
(B) the same as.
(C) larger than (but less than 90°).
(D) (There is no defined first maximum produced by the 780 nm wavelength laser.)

[*] wki.pe/Comparison_of_high_definition_optical_disc_formats.

Correct answer (highlight to unhide): (A)

The first maximum 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).

The first maxima angle produced by the (infrared) CD 780 nm laser is:

θ = sin^–1(780×10^–9 m/1.6×10^–6 m) = sin^–1(0.49) = 29°,

while the first maxima angle produced by the DVD 650 nm laser is:

θ = sin^–1(650×10^–9 m/1.6×10^–6 m) = sin^–1(0.41) = 24°.

Section 30882
Exam code: quiz03rD1o
(A) : 21 students
(B) : 1 student
(C) : 10 students
(D) : 0 students

Success level: 65%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.28