Question

In the figure, a ray of light is perpendicular to the face $AB$ of a glass prism $(\mu =1.52)$. Find the value of $\theta$ so that the ray is totally reflected at face $AC$, if the prism is immersed in water $(\mu =1.33)$. Given $\sin 61^{\circ }=0.875$

• A. $45^{\circ }$
• B. $30^{\circ }$
• C. $15^{\circ }$
• D. None of these

Answer 1

Answer: (B)

Given, ${\mu }_g=1.52,{\mu }_w=1.33,\theta =?$
Apply Snell's law at point D,
${\mu }_g\sin i_C=\mu w\sin 90^{\circ }$
$\Rightarrow \sin i_c=\frac{{\mu }_w}{{\mu }_g}=\frac{1.33}{1.52}$
$\Rightarrow i_c={\sin }^{-1}\left(\frac{1.33}{1.52}\right)=61^{\circ }$
From figure, $\theta +i_c=90^{\circ }$
$\Rightarrow \theta =90^{\circ }-61^{\circ }=29^{\circ }\approx 30^{\circ }$