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The refractive index of air is 1.0003 and the refractive index of crystalline quartz is 1.544. What is the critical angle for a ray going from quartz into air?
A0.7048 rad
B49.61 degrees
C20.19 degrees
D0.6479 rad
Answer & Solution
Correct answer: A. 0.7048 rad
1. Since light travels from quartz into air, n1 = 1.544 (quartz) and n2 = 1.0003 (air), because n1 must be the larger index.
2. The critical angle formula gives sin(theta_c) = n2 / n1 = 1.0003 / 1.544 = 0.6480.
3. Taking the inverse sine of 0.6480 gives theta_c = 40.39 degrees.
4. Converting to radians: 40.39 degrees x (pi / 180) = 0.7048 rad.
5. 49.61 degrees and 20.19 degrees do not match this computed angle.
6. 0.6479 rad converts to about 37.1 degrees, which is the sine value itself mistaken for the angle in radians, not the actual critical angle.
_Source: OpenStax Physics (CC BY 4.0), Ch 16 "Mirrors and Lenses", section 16.2 Refraction_
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