One face of a prism with a refrective angle of `30^@` is coated with silver. A ray of light incident on another face at an angle of `45^@` is refracted and reflected from the silver coated face and retraces its path. What is the refractive index of the prism?

Explanation

To find the refractive index of the prism, we can follow these steps:

### Step 1: Understand the Geometry of the Prism
We have a prism with a refractive angle \( A = 30^\circ \). A ray of light is incident on one face of the prism at an angle \( i_1 = 45^\circ \).

### Step 2: Identify the Angles
When the ray of light enters the prism, it is refracted. Since the ray retraces its path after reflecting off the silvered face, we can conclude that the angle of refraction \( r_2 = 0^\circ \) (the ray reflects back along the same path).

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