Question

A light ray is incident at an angle ${30}^o$ on a transparent surface separating two media. If the angle of refraction is ${60}^o$ then critical angle is

• A. ${\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
• B. ${\sin }^{-1}\left(\sqrt{3}\right)$
• C. ${\sin }^{-1}\left(\frac{2}{3}\right)$
• D. ${45}^o$

Answer 1

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

Snell's law gives ${\mu }_1\sin {30}^o={\mu }_2\sin {60}^o$ but critical angle

${\theta }_c={\sin }^{-1}\left(\frac{{\mu }_2}{{\mu }_1}\right)={\sin }^{-1}\left(\frac{\sin {30}^o}{\sin {60}^o}\right)={\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$