At what angle should a ray of light be incident on the face of a prism of refracting angle `60^(@)` so that it just suffers total internal reflection at the other face ? The refractive index of the prism is 1.524.

Explanation

To solve the problem of finding the angle of incidence \( I \) for a ray of light incident on a prism with a refracting angle of \( 60^\circ \) and a refractive index of \( 1.524 \) such that it just suffers total internal reflection at the other face, we can follow these steps:

### Step 1: Understand the Geometry of the Prism
The prism has a refracting angle \( A = 60^\circ \). When light enters the prism, it refracts at the first face (let's call it face AB) and then reaches the second face (face AC) where it will experience total internal reflection.

### Step 2: Determine the Condition for Total Internal Reflection
For total internal reflection to occur at face AC, the angle of refraction \( r_2 \) at this face must be \( 90^\circ \). This means that the angle of incidence \( I_1 \) at face AB and the angle of refraction \( r_1 \) at face AC must satisfy the prism angle relationship:
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