Looking for classes? Ksquare Career Institute, Bengaluru →
Two transparent media A and B are separated by a plane boundary. The speed of light in those media are $1.5\times10^8\ m/s$ and $2.0\times10^8\ m/s$, 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
$\tan^{-1}(0.500)$
Detailed Solution
$\mu = \frac{c}{v} \Rightarrow \mu \propto \frac{1}{v}$
A is the denser medium (lower speed). For critical angle (ray going from A to B):
$\sin i_c = \frac{\mu_B}{\mu_A} = \frac{v_A}{v_B} = \frac{1.5}{2.0} = \frac{3}{4}$
$i_c = \sin^{-1}(0.750)$