Diamond has an index of refraction of 2.419 and air 1.00. What is the critical angle for a diamond to air surface?
A11.9 degrees
B24.4 degrees
C45.0 degrees
D65.6 degrees
Answer & Solution
Correct answer: B. 24.4 degrees
1. Light starting inside the diamond gives n1 = 2.419, and the air outside gives n2 = 1.00.
2. The critical angle is theta_c = inverse sine of (n2 divided by n1) = inverse sine of (1.00 divided by 2.419).
3. The bracket is 0.413, so theta_c = inverse sine of 0.413 = 24.4 degrees.
4. That is a very small critical angle, which is why light struggles to escape once it is inside a diamond.
5. The 11.9 degrees option is the refraction angle for a 30.0 degree ray entering diamond, a different quantity altogether.
_Source: OpenStax College Physics (CC BY 4.0), Ch 25 "Geometric Optics", section 25.4 Total Internal Reflection_
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