Question

The refracting angle of the prism is ${60}^o$ and minimum deviation of ${30}^o$, then the angle of incidence is:-

• A. ${30}^o$
• B. ${45}^o$
• C. ${25}^o$
• D. ${60}^o$

Answer 1

The correct option is B ${45}^o$

$\begin{array}{c}\angle A={60}^{\circ }\\ \angle S_m={30}^{\circ }\end{array}$

$\text{we know,}$

$\mu =\frac{\sin \left(\frac{A+S_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}$

$\begin{array}{cc}\mu & =\sin \left(\frac{60+30}{2}\right)/\sin \left(\frac{60}{2}\right)\\ \mu & =\frac{\sin {45}^{\circ }}{\sin {30}^{\circ }}=\frac{1}{\sqrt{2}}/\frac{1}{2}\end{array}$

$\mu =\sqrt{2}\left(1\right)$

$\begin{array}{c}\text{at min deviation condition,}\\ r_2=r_1=\frac{A}{2}={30}^{\circ }\\ {\mu }_i\sin i={\mu }_r\sin r_1\\ 1\times \sin i=\sqrt{2}\times \sin {30}^{\circ }\\ \sin i=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}\\ i={45}^{\circ }\end{array}$