Question

A light ray falls on a square glass slab as shown in the figure. The index of refraction of the glass, if total internal reflection is occur at vertical face, is equal to

• A. \( \sqrt{\frac{2}{5}} \)
• B. \( \sqrt{\frac{5}{2}} \)
• C. \( \frac{3}{2} \sqrt{\frac{3}{2}} \)
• D. \( \sqrt{\frac{3}{2}} \)

Hint:

For total internal reflection, use the critical angle and the refractive index formula to find the refractive index of the medium.

Answer 1

The Correct Option is D

Total internal reflection occurs when the angle of incidence exceeds the critical angle. The critical angle \( \theta_c \) is given by:

\[ \sin \theta_c = \frac{1}{n} \] where \( n \) is the refractive index of the medium. The critical angle is the angle of incidence at which the refracted ray travels along the boundary of the two media, and beyond this angle, total internal reflection occurs, meaning no light escapes the medium. In this case, the refractive index \( n \) is calculated as \( \sqrt{\frac{3}{2}} \), which gives the condition for total internal reflection to occur.

Thus, the correct answer is (d).