Question

The total deviation of the incident ray when it emerges out of the prism is.

• A. ${30}^o$
• B. ${60}^o$
• C. ${90}^o$
• D. ${45}^o$

Answer 1

The correct option is C ${90}^o$

In figure (a), the incident ray $P$ hits the point Q, R and S and then emerges as $T$. The overall scenario is seen in figure (b) which represents the deviation as $\delta$ .

$\therefore$ Deviation $\delta =90-{\theta }_2+{\theta }_1$ .............(1)

In the prism $DAC$, prism angle $={30}^o$

Using prism angle formula $A=r_2+r^{\prime }$, $\therefore$ ${30}^0=r_1+0^o⟹r_2={30}^o$

Given: Refractive index of the prism $n=2sin{\theta }_1$

Using Snell's law at point $S$, $1\times sin{\theta }_2=n\times sin{r}_2$

$\therefore$ $sin{\theta }_2=2sin{\theta }_1\times sin30$

$sin{\theta }_2=sin{\theta }_1$ $⟹$ ${\theta }_1={\theta }_2$

$\therefore$ From equation (1), deviation of the ray $\delta ={90}^o$