Question

A ray is incident at an angle of incidence $i$ on one surface of a prism $($with angle of prism $A={90}^{\circ })$ and emerges parallel to the opposite surface. If the refractive index of the material of the prism is$\frac{2}{\sqrt{3}},$ then the angle of incidence is equal to

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$

Answer 1

The correct option is D ${\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$

$\sin i_c=\frac{1}{\mu }=\frac{\sqrt{3}}{2}$



$i_c={60}^{\circ }$

$r_2=i_c={60}^{\circ }$$($as grazing refraction$)$

$r_1+r_2=A\Rightarrow r_1={30}^{\circ }$

From Snell's law
$\Rightarrow \sin i=\mu \sin {30}^{\circ }\Rightarrow i={\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$