Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Question 23.7
Light in crown glass and light in flint glass are each transmitted out into air. (Drawing is not to scale.) __________ has a greater index of refraction.
(A) Crown glass.
(B) Flint glass.
(C) (There is a tie.)
(D) (Not enough information is given.)
Correct answer (highlight to unhide): (B)
Snell's law relates the indices of refraction with the incident and transmitted angles:
ncrown glass·sin(θcrown glass) = nair·sin(θair),
nflint glass·sin(θflint glass) = nair·sin(θair),
where the given (or assumed to be known) quantities, unknown quantities, and quantities to be explicitly solved for (or compared) are denoted.
Since the terms nair·sin(θair) appear in both Snell's law equations, we can then eliminate those two terms and set the following quantities equal to each other, in order to directly compare the indices of refraction for crown glass and flint glass:
nair·sin(θair) = nair·sin(θair),
ncrown glass·sin(θcrown glass) = nflint glass·sin(θflint glass),
ncrown glass·sin(41.3°) = nflint glass·sin(39.6°),
and because sin(41.3°) is greater than sin(39.6°), then ncrown glass must be less than nflint glass, such that flint glass has the higher index of refraction. More specifically:
(sin(41.3°)/sin(39.6°))·ncrown glass = nflint glass,
(0.6600016679/0.6374239897)·ncrown glass = nflint glass,
1.035420189·ncrown glass = nflint glass,
where to three significant figures, the index of refraction of flint glass is 1.04× that of crown glass (or 4% greater than that of crown glass).
Student responses
Sections 30882, 30883
Exam code: quiz01c0Co
(A) : 12 students
(B) : 35 students
(C) : 1 student
(D) : 0 students
Success level: 73%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.48
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