Question

A light ray incidents on an equilateral prism made of material of refractive index $\sqrt{3}$. Inside the prism, if the light ray moves parallel to the base of the prism, then the angle of incidence of the light ray is:

• A. $30^\circ$
• B. $45^\circ$
• C. $75^\circ$
• D. $60^\circ$

Hint:

When a ray travels parallel to the base of an equilateral prism, the angle of refraction is half the prism angle. Use Snell’s law accordingly.

Answer 1

The Correct Option is D

Step 1: Understand the geometry of the prism The prism is equilateral, so each angle of the prism is \( A = 60^\circ \). Given that the light travels parallel to the base inside the prism, it implies the angle of refraction \( r \) at the first face is \( 30^\circ \). 
Step 2: Use Snell's Law at the first surface \[ \mu = \frac{\sin i}{\sin r} \] Given: \( \mu = \sqrt{3}, r = 30^\circ \) 
Step 3: Solve for angle of incidence \( i \) \[ \sqrt{3} = \frac{\sin i}{\sin 30^\circ} = \frac{\sin i}{1/2} \Rightarrow \sin i = \sqrt{3} \cdot \frac{1}{2} = \frac{\sqrt{3}}{2} \] \[ \Rightarrow i = 60^\circ \]