Question

When a ray of light is incident normally on one refracting surface of an equilateral prism of refractive index \(1.5\), the emerging ray \([\sin^{-1}(1/1.5)=41.8^\circ]\)

• A. just grazes the second refracting surface.
• B. is deviated by \(20^\circ\).
• C. is deviated by \(30^\circ\).
• D. undergoes total internal reflection at second refracting surface.

Hint:

If the angle of incidence inside a denser medium exceeds the critical angle, total internal reflection always occurs.

Answer 1

The Correct Option is D

Step 1: Understand prism geometry.
For an equilateral prism, the prism angle \(A = 60^\circ\). When light is incident normally on the first surface, it enters the prism without deviation.

Step 2: Angle of incidence at second surface.
Inside the prism, the ray travels parallel to the base. Hence, the angle of incidence at the second refracting surface equals the prism angle:
\[ i = 60^\circ \]
Step 3: Calculate the critical angle.
The critical angle \(C\) for the prism material is given as:
\[ C = \sin^{-1}\left(\frac{1}{1.5}\right) = 41.8^\circ \]
Step 4: Compare angles.
Since the angle of incidence at the second surface (\(60^\circ\)) is greater than the critical angle (\(41.8^\circ\)), total internal reflection occurs.

Step 5: Conclusion.
The ray undergoes total internal reflection at the second refracting surface.