Question

If velocity of light in two media are, respectively, $2\times {10}^{8}m{s}^{-1}$ and $2.82\times {10}^{8}m{s}^{-1}$, then calculate the critical angle between the two media.

• A. $30$
• B. $60$
• C. $45$
• D. $90$

Answer 1

The correct option is C $45$

It is to be remembered that the refractive index of a medium is inversely proportional to the speed of light in that medium.
Hence, $\frac{{\mu }_1}{{\mu }_2}=\frac{speedoflightinmedium2}{speedoflightinmedium1}$
$\frac{{\mu }_1}{{\mu }_2}=\frac{2/{10}^8}{2.8/{10}^8}=\frac{1}{1.4}$
Hence the critical angle will be
$C={\sin }^{-1}\left(\frac{{\mu }_1}{{\mu }_2}\right)={\sin }^{-1}\left(\frac{5}{7}\right)$
$C={45.58}^0$