Question

The refractive index of the material of a glass prism is \( 3 \). The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

• A. 50°
• B. 60°
• C. 58°
• D. 48°

Hint:

For prisms, when the angle of minimum deviation equals the angle of the prism, use the relation involving the refractive index to calculate the angle of the prism.

Answer 1

The Correct Option is B

For a prism, the angle of minimum deviation \( D_{\text{min}} \) is related to the refractive index \( n \) and the angle of the prism \( A \) by the following equation: \[ n = \frac{\sin\left( \frac{A + D_{\text{min}}}{2} \right)}{\sin\left( \frac{A}{2} \right)}. \] Given that the angle of minimum deviation is equal to the angle of the prism, i.e., \( D_{\text{min}} = A \), we can simplify the equation: \[ n = \frac{\sin\left( \frac{A + A}{2} \right)}{\sin\left( \frac{A}{2} \right)} = \frac{\sin(A)}{\sin\left( \frac{A}{2} \right)}. \] Substitute \( n = 3 \): \[ 3 = \frac{\sin(A)}{\sin\left( \frac{A}{2} \right)}. \] Solving for \( A \), we find that the angle of the prism is \( A = 60^\circ \).