Question

A ray of laser of a wavelength 630 nm is incident at an angle of $30^\circ$ at the diamond-air interface. It is going from diamond to air. The refractive index of diamond is 2.42 and that of air is 1. Choose the correct option.

• A. angle of refraction is $24.41^\circ$
• B. angle of refraction is $30^\circ$
• C. angle of refraction is $53.4^\circ$
• D. refraction is not possible

Hint:

Always check the critical angle when light moves from a denser medium (higher \(\mu\)) to a rarer medium (lower \(\mu\)).
For diamond, the critical angle is very small (\(\approx 24.4^\circ\)), which is why it sparkles and often causes TIR.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
When light travels from a denser medium to a rarer medium, it may undergo Total Internal Reflection (TIR) if the angle of incidence is greater than the critical angle.
Step 2: Key Formula or Approach:
Critical angle (\(C\)) is given by: \[\sin C = \frac{\mu_{\text{rarer}}}{\mu_{\text{denser}}}\]
If incidence angle \(i>C\), TIR occurs and no refraction happens.
Step 3: Detailed Explanation:
Given:
\(\mu_{\text{diamond}} = 2.42\), \(\mu_{\text{air}} = 1\), \(i = 30^\circ\).
Calculate the critical angle:
\[ \sin C = \frac{1}{2.42} \approx 0.4132 \]
Now calculate \(\sin i\):
\[ \sin 30^\circ = 0.5 \]
Since \(0.5>0.4132\), it follows that \(\sin i>\sin C\), which means \(i>C\).
Because the angle of incidence is greater than the critical angle, the ray undergoes total internal reflection back into the diamond.
No ray enters the air, so refraction is not possible.
Step 4: Final Answer:
Refraction is not possible due to Total Internal Reflection.