Question

A ray of light is incident on a refracting face of a glass prism of refractive angle ${30}^o$. If the ray emerges normally from the second refracting surface, the angle of incidence is ${[}^a{\mu }_g=1.5]$

• A. ${\sin }^{-1}\left(0.6\right)$
• B. ${\sin }^{-1}\left(0.7\right)$
• C. ${\sin }^{-1}\left(0.75\right)$
• D. ${\sin }^{-1}\left(0.8\right)$

Answer 1

The correct option is C ${\sin }^{-1}\left(0.75\right)$

$i=\theta ;r_1=r;r_2=0^{\circ };e=0^{\circ }$

$\begin{array}{c}\text{at point}A\\ n_1\sin i=n_2\sin r\end{array}$

$\begin{array}{cc}1\times \sin \theta & =1.5\times \sin r\\ \sin r& =\frac{\sin \theta }{1.5}-\left(i\right)\end{array}$

$\begin{array}{c}\text{we know,}A=r_1+r_2\\ \Rightarrow {30}^{\circ }=0^{\circ }+{\sin }^{-1}\left(\frac{\sin \theta }{1.5}\right)\\ \Rightarrow \frac{1}{2}=\frac{\sin \theta }{1.5}\Rightarrow \sin \theta =0.75\\ \Rightarrow \theta ={\sin }^{-1}\left(0.75\right)\end{array}$