Question

Two transparent media $1$ and $2$ are separated by a plane boundary. The speed of light in medium $1$ is $2.0\times {10}^8{\text{ms}}^{-1}$ and in medium $2$ is $2.5\times {10}^8{\text{ms}}^{-1}$. The critical angle for which a ray of light going from $1$ to $2$ is totally internally reflected is

• A. ${\sin }^{-1}\left(\frac{1}{2}\right)$
• B. ${\sin }^{-1}\left(\frac{2}{5}\right)$
• C. ${\sin }^{-1}\left(\frac{4}{5}\right)$
• D. ${\sin }^{-1}\left(\frac{1}{3}\right)$

Answer 1

The correct option is C ${\sin }^{-1}\left(\frac{4}{5}\right)$

We know,
${\mu }_{21}=\frac{{\mu }_2}{{\mu }_1}=\frac{v_1}{v_2}=\frac{2.0\times {10}^8}{2.5\times {10}^8}=\frac{4}{5}$

Now, critical angle,
$i_c={\sin }^{-1}\left(\frac{{\mu }_2}{{\mu }_1}\right)={\sin }^{-1}\left(\frac{4}{5}\right)$