1. Given Data

• Refracting Angle of Prism (A): 60°
• Refractive Index (n): 1.524
• Condition: The ray just suffers total internal reflection (TIR) at the second face.

2. Calculating Critical Angle (C)

For the ray to just suffer total internal reflection at the second face, the angle of incidence at that face (r₂) must be equal to the critical angle (C).

sin(C) = 1 / n

sin(C) = 1 / 1.524

sin(C) = 0.6562

Now, finding the angle:

C = sin^-1(0.6562)

C ≈ 41°

Therefore, r₂ = 41°

3. Calculating Angle of Refraction (r₁)

For a prism, the refracting angle A is related to the internal angles by:

A = r₁ + r₂

Substituting the values:

60° = r₁ + 41°

r₁ = 60° - 41°

r₁ = 19°

4. Calculating Angle of Incidence (i)

Using Snell's Law at the first interface:

sin(i) = n × sin(r₁)

Substituting the values:

• sin(i) = 1.524 × sin(19°)
• sin(i) = 1.524 × 0.3256
• sin(i) = 0.4962

Now, finding the angle i:

i = sin^-1(0.4962)

i ≈ 29.75°