Question

Light travels in two media A and B with speeds $1.8\times {10}^{8}m{s}^{-1}$ and $2.4\times {10}^{8}m{s}^{-1}$ respectively. Then the critical angle between them is

• A. ${sin}^{-1}\left(\frac{2}{3}\right)$
• B. ${tan}^{-1}\left(\frac{3}{4}\right)$
• C. ${tan}^{-1}\left(\frac{2}{3}\right)$
• D. ${sin}^{-1}\left(\frac{3}{4}\right)$

Answer 1

The correct option is D ${sin}^{-1}\left(\frac{3}{4}\right)$

The Critical angle for the medium is given by:

$\Rightarrow {\sin }^{-1}\frac{1}{\mu }$

The refractive index of the medium A with respect to medium B is given by:

${}^A{\mu }_{{}_B}=\frac{v_2}{v_1}$

$\mu =\frac{24}{18}=\frac{4}{3}$

Now the critical angle is obtained as:

$={\sin }^{-1}\frac{3}{4}$