Question

Consider a light ray travelling from a denser medium to air. The refractive index of the medium is $\sqrt{3}$. Calculate the angle of incidence, such that if it is further increased, total internal reflection will occur at the denser medium.

• A. $si{n}^{-1}\left(\frac{1}{\sqrt{3}}\right)$
• B. $si{n}^{-1}\left(\frac{1}{\sqrt{2}}\right)$
• C. $si{n}^{-1}\left(\frac{1}{\sqrt{5}}\right)$
• D. None of the above

Answer 1

The correct option is A

$si{n}^{-1}\left(\frac{1}{\sqrt{3}}\right)$

For total internal reflection to occur, the light ray should be incident at an angle greater than the critical angle.
From Snell's law, critical angle is:
$\frac{sin{\theta }_c}{sin\left({90}^{\circ }\right)}=\frac{1}{\sqrt{3}}$
$\therefore {\theta }_c=si{n}^{-1}\left(\frac{1}{\sqrt{3}}\right)$