Question

The total internal reflection in diamond makes it shine, because the critical angle of diamond is

• A. very high
• B. very low
• C. exactly 45°
• D. None of these

Answer 1

The Correct Option is B

Step 1: Understand total internal reflection and its relation to the critical angle.

Total internal reflection occurs when light traveling through a denser medium (e.g., diamond) strikes the boundary with a less dense medium (e.g., air) at an angle greater than the critical angle. The critical angle (\( \theta_c \)) depends on the refractive indices of the two media:

\[ \sin \theta_c = \frac{n_{\text{air}}}{n_{\text{diamond}}}. \]

Diamond has a very high refractive index (\( n_{\text{diamond}} \approx 2.42 \)), which results in a very low critical angle (\( \theta_c \approx 24^\circ \)). This low critical angle allows light to undergo multiple internal reflections within the diamond, making it shine brightly.

Step 2: Analyze the options.

• (1) Very high: The critical angle of diamond is not very high; it is very low. This option is incorrect.
• (2) Very low: This is correct because the high refractive index of diamond results in a very low critical angle.
• (3) Exactly 45°: The critical angle of diamond is much lower than \( 45^\circ \). This option is incorrect.
• (4) None of these: This option is incorrect because the critical angle is indeed very low.

Final Answer: The critical angle of diamond is \( \mathbf{\text{very low}} \), which corresponds to option \( \mathbf{(2)} \).