Question

Two transparent media $A$ and $B$ are separated by a plane boundary. The speed of light in those media are $1.5\times 10^{8}m/s$ and $2.0\times 10^{8}m/s$, respectively The critical angle for a ray of light for these two media is :

• A. ${\tan }^{-1}(0.750)$
• B. ${\sin }^{-1}(0.500)$
• C. ${\sin }^{-1}(0.750)$
• D. ${\tan }^{-1}(0.500)$

Answer 1

Answer: (C)

$\mu =\frac{C}{u}\Rightarrow u\propto \frac{1}{\mu }$
Critical angle
${\mathrm{Sini}}_c=\frac{{\mu }_R}{{\mu }_D}=\frac{u_D}{u_R}=\frac{1.5}{2}=\frac{3}{4}$
$i_c={\sin }^{-1}\left(\frac{3}{4}\right)$
$\sin {\dot{i}}_c=\frac{{\mu }_R}{{\mu }_D}=\frac{u_D}{u_R}$
$i_c={\sin }^{-1}\left(\frac{3}{4}\right)$