Question

A ray of light travelling in air is incident on a denser surface at an angle of ${60}^o$. If the velocity of light in the denser medium is $2\times {10}^8{ms}^{-1}$, the angle of refraction inside the denser medium is :

• A. ${30}^o$
• B. ${\sin }^{-1}\left(0.75\right)$
• C. ${\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
• D. ${\sin }^{-1}\left(0.6666\right)$

Answer 1

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

Since the speed of light in the denser medium is $2\times {10}^{8}m/s$, the refractive index of the medium is

$\mu =\frac{c}{v}=\frac{3\times {10}^8}{2\times {10}^8}=\frac{3}{2}$

From Snell's law,

$sini=\mu sinr$

$⟹sin{60}^{\circ }=\frac{3}{2}sinr$

$⟹r=si{n}^{-1}\frac{1}{\sqrt{3}}$