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
$\operatorname{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)$
$\sin \dot{i}_{ c }=\frac{\mu_{ R }}{\mu_{ D }}=\frac{ u _{ D }}{ u _{ R }}$
$i _{ c }=\sin ^{-1}\left(\frac{3}{4}\right)$