Question

A ray of light passing through an equilateral triangular prism gets deviated at least by 30. Then, the refractive index of the material of the prism must be :

• A. $\le \sqrt{2}$
• B. $\ge \sqrt{2}$
• C. $\le \sqrt{3}$
• D. $\ge \sqrt{3}$

Answer 1

The correct option is B $\ge \sqrt{2}$

The refractive index of a prism is calculated from the formula, $\mu =\frac{sin\frac{A+D}{2}}{sin\frac{A}{2}}\mu =\frac{sin\frac{A+D}{2}}{sin\frac{A}{2}}$.

In this case, as it is an equilateral prism, the angle of prism is 60 degrees and the angle of minimum deviation is given as 30 degrees.

So, $\mu =\frac{sin\frac{60+30}{2}}{sin\frac{60}{2}}=\frac{sin45}{sin30}=\ge \sqrt{2}$.

Hence, the refractive index of the material of the prism must be $\ge \sqrt{2}$.