Question

The critical angle of a medium w.r.t. to vacuum is ${30}^{\circ }$, velocity of light in this medium in m/s is :

• A. $3\times {10}^8$
• B. $6\times {10}^8$
• C. $1.5\times {10}^8$
• D. $\sqrt{2}\times {10}^8$

Answer 1

The correct option is C $1.5\times {10}^8$

Critical angle
${\theta }_C={\sin }^{-1}\left(\frac{1}{\mu }\right)$
$\Rightarrow \sin \left({30}^{\circ }\right)=\frac{1}{\mu }$
$\Rightarrow \frac{1}{2}=\frac{1}{\mu }$ $(\because \sin {30}^{\circ }=1/2)$
$\Rightarrow \mu =2$
Speed of light in medium $=\frac{speedoflightinvacuum}{\mu }$

$=\frac{3\times {10}^8}{2}$ m/s

$=1.5\times {10}^8$ m/s