Physics quiz question: index of refraction of NaCl

Physics 205B Quiz 1, spring semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 22.18

Light of wavelength 550 nm in air (index of refraction 1.000) with an incident angle of 45.0° is transmitted at an angle of 27.3° into sodium chloride (NaCl). (Drawing is not to scale.) The index of refraction of sodium chloride is:
(A) 1.38.
(B) 1.54.
(C) 1.65.
(D) 1.93.

Correct answer (highlight to unhide): (B)

From Snell's law, where air is medium 1 and NaCl is medium 2:

n₁·sinθ₁ = n₂·sinθ₂,

and solving for n₂:

n₂ = n₁·sinθ₁/sinθ₂ = (1.000)·sin(45.0°)/sin(27.3°) = 1.54171474555,

or to three significant figures, the index of refraction n₂ of NaCl is 1.54.

(Response (A) is 3·sin(27.3°); response (C) is (45.0°)/(27.3°); response (D) is 1/tan(27.3°).)

Section 30882
Exam code: quiz01b3Es
(A) : 2 students
(B) : 30 students
(C) : 2 students
(D) : 1 student

Success level: 86%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.27