What is the critical angle of diamond?

• A. 60 degrees
• B. 42 degrees
• C. 24.5 degrees
• D. 15 degrees

Answer: (C)

The critical angle is the angle of incidence inside a denser medium (diamond) at which light hitting a boundary with a less dense medium (air) refracts at 90 degrees or, beyond that, reflects back entirely. It satisfies sin(theta_c) = n2 / n1, where n1 is the refractive index of the denser medium and n2 is that of the lighter medium.

For diamond in visible light, n1 is about 2.42 and air is about 1.00. So sin(theta_c) ≈ 1.00 / 2.42 ≈ 0.413. Taking the arcsin gives theta_c ≈ 24.4 degrees, which rounds to about 24.5 degrees.

That relatively small critical angle explains why diamonds exhibit strong internal reflections: light inside the diamond can only escape at specific angles, contributing to their characteristic brilliance.