Question

A prism of apex angle $A=60°$ has the refractive index $\mu =\sqrt{2}$. The angle of incidence for minimum deviation is

• A. $30°$
• B. $45°$
• C. $60°$
• D. None of these

Answer 1

The correct option is B

$45°$

Step 1: Given data

Apex angle, $A=60°$

Refractive index, $\mu =\sqrt{2}$

Step 2: Determine the value of $r$

The condition for minimum deviation is, $r=\frac{A}{2}$

(where r is the angle of reflection and i is the angle of incidence)

$$\begin{gathered} \Rightarrow r=\frac{60}{2} \\ =30° \end{gathered}$$

Step 3: Determine the value of $i$

Using the formula for the refractive index of a prism,

$$\begin{gathered} \mu =\frac{\sin i}{\sin r} \\ \sqrt{2}=\frac{\sin i}{\sin 30} \\ \sin i=\sqrt{2}\times \frac{1}{2} \\ =\sqrt{2} \\ \Rightarrow i={\sin }^{-1}\left(\sqrt{2}\right) \\ i=45° \end{gathered}$$

(where i is the angle of incidence)

Hence, option B is the correct answer.