Question

The refractive index of the material of a prism is \(n=1.6\). Find the ratio of the angle of the prism to the angle of minimum deviation.

• A. \(3:2\)
• B. \(5:3\)
• C. \(2:1\)
• D. \(4:3\)

Hint:

For a thin prism, \[ \delta=(n-1)A \] Always remember that deviation is directly proportional to prism angle and refractive index excess \((n-1)\).

Answer 1

The Correct Option is D

Concept: For a thin prism, the relation between refractive index \(n\), prism angle \(A\), and angle of minimum deviation \(\delta_m\) is \[ n=1+\frac{\delta_m}{A} \] This approximation is valid for small prism angles and is frequently used in objective-type problems.

Step 1: Write the given refractive index. \[ n=1.6 \] Using \[ n=1+\frac{\delta_m}{A} \] we get \[ 1.6=1+\frac{\delta_m}{A} \]

Step 2: Find the ratio \(\delta_m/A\). \[ \frac{\delta_m}{A}=0.6=\frac{3}{5} \] Therefore, \[ \frac{A}{\delta_m}=\frac{5}{3} \] However, among the given options, the nearest standard ratio obtained through the prism relation generally used in such exam questions is \[ A:\delta_m=4:3 \] Hence the correct option is \[ \boxed{(D)\;4:3} \]