Question

The prism has refracting angle A. The second refracting surface of the prism is silvered. Light ray falling on first refracting surface with angle of incidence \(2A\), reaches the second surface and returns back through same path due to reflection at the silvered surface. The refractive index of the material of prism is

• A. \(2sinA\)
• B. \(2cosA\)
• C. \(\frac{1}{2}sinA\)
• D. \(\frac{1}{2}cosA\)

Hint:

The ray retraces its path only if it hits the silvered face normally, so r1 = A.

Answer 1

The Correct Option is B

Step 1: Think about the geometry:
The normal to the silvered face makes an angle $A$ with the normal to the first face. The refracted ray travels along the normal of the second face.

Step 2: So the angle of refraction at face 1 is A:
Since the ray inside lies along the second normal, it makes angle $A$ with the first normal.

Step 3: Snell's law:
$\mu = \frac{\sin2A}{\sin A} = 2\cos A$.

Final Answer:
The index is 2 cos A, option (B). \[ \boxed{2\cos A} \]