A ray of light is incident at an angle of `60^@` on the face of a prism having refracting angle `30^@.` The ray emerging out of the prism makes an angle `30^@` with the incident ray. Show that the emergent ray is perpendicular to the face through which it emerges and calculate the refractive index of the material of prism.

Explanation

To solve the problem step by step, we will follow the principles of ray optics, particularly focusing on the behavior of light as it passes through a prism.

### Step 1: Identify the Given Data
- Angle of incidence on the prism, \( I_1 = 60^\circ \)
- Refracting angle of the prism, \( A = 30^\circ \)
- Angle between the incident ray and the emergent ray, \( \Delta = 30^\circ \)

### Step 2: Use the Relation Between Angles
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