Question

Light travelling in air falls at an incidence angle of $2^o$ on one refracting surface of a prism of refractive index 1.5 and angle of refraction $4^o$. The medium on the other side is water $(n=4/3)$. Find the deviation produced by the prism.

• A. $1^o$
• B. $2^o$
• C. $3^o$
• D. $4^o$

Answer 1

The correct option is A $1^o$

$\begin{array}{c}\text{we know, for a thin prism}\\ \sin \theta \approx \theta \end{array}$

$\begin{array}{c}\text{at point}A:\\ {\mu }_1\sin 2^{\circ }={\mu }_2\sin r_1\end{array}$

$1\times \left(\frac{2\times \pi }{180}\right)=1.5r_1$

$\frac{\pi }{90\times 1.5}=r_1\Rightarrow r_1=\frac{\pi }{135}\text{rad}-\left(i\right)$

$\begin{array}{c}\text{we know,}\\ A=r_1+r_2\&i+e=\delta +A\end{array}$

$\text{A}=r_1+r_2$

$\frac{4\pi }{180}=\frac{\pi }{135}+\frac{4e}{4\cdot 5}$

$e=(\frac{4\pi }{180}-\frac{\pi }{135})\times \frac{4.5}{4}=0.052rad-\left(iii\right)$

$\begin{array}{c}\text{also,}i+e=\delta +A\\ \frac{2\cdot \pi }{180}+0.052=\delta +\frac{4\pi }{180}\end{array}$

$\begin{array}{cc}0.04+0.05& =\delta +0.07\\ \delta & =0.02\text{rad}\\ & =0.02\times {180}^{\circ }={1.15}^{\circ }\\ & \approx 1^{\circ }\end{array}$