Question

An equilateral prism is made of material of refractive index \(\sqrt{3}\). The angle of minimum deviation through the prism is:

• A. \(60\degree\)
• B. \(30\degree\)
• C. \(45\degree\)
• D. \(0\degree\)

Answer 1

The Correct Option is B

\(\text{ The relation between the refractive index } n, \text{ the angle of the prism } A, \text{ and the minimum deviation } D_{\text{min}} \text{ is given by the formula:}\)\[n = \frac{\sin \left( \frac{A + D_{\text{min}}}{2} \right)}{\sin \left( \frac{A}{2} \right)}\]
\(\text{Here, the refractive index } n = \sqrt{3}, \text{ and for an equilateral prism, the angle of the prism } A = 60^\circ.\)
\(\text{ Substituting these values:}\)\[\sqrt{3} = \frac{\sin \left( \frac{60^\circ + D_{\text{min}}}{2} \right)}{\sin(30^\circ)}\]
\(\text{Solving for } D_{\text{min}}, \text{ we find that } D_{\text{min}} = 30^\circ.\)