Question

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

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

Answer 1

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

We know that the speed of light is less in denser medium and more in rarer medium.
Speed of light in medium $A$ (Denser medium), $v_d=2.0\times {10}^8{\text{ms}}^{-1}$
Speed of light in medium $B$ (Rarer medium), $v_r=2.5\times {10}^8{\text{ms}}^{-1}$
From definition of $\mu$,
$\mu =\frac{c}{v}$
So,
$\frac{{\mu }_r}{{\mu }_d}=\frac{v_d}{v_r}$
$\Rightarrow \frac{{\mu }_r}{{\mu }_d}=\frac{2.0\times {10}^8}{2.5\times {10}^8}=\frac{4}{5}$ .............$\left(1\right)$


From formula,
$i_c={\sin }^{-1}\left(\frac{{\mu }_r}{{\mu }_d}\right)$
$\Rightarrow i_c={\sin }^{-1}\left(\frac{4}{5}\right)$
$[$from $\left(1\right)]$