Question

The critical angle of a prism is $30^{\circ }$. The velocity of light in the medium is :

• A. $1.5\times 10^{8}m/s$
• B. $3\times 10^{8}m/s$
• C. $4.5\times 10^{8}m/s$
• D. none of these

Answer 1

Answer: (A)

The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is $90^{\circ }$.
$\therefore \mu =\frac{\sin 90^{\circ }}{\sin C}=\frac{1}{\sin C}$ ... (i)
Also, $\mu =\frac{v_0}{v}$...(ii)
where $v_0$ is speed of light in vacuum and $v$ is speed in medium.
From Eqs. (i) and (ii), we get
$v=v_0\sin C=3\times 10^8\times \frac{1}{2}$
$=1.5\times 10^{8}m/s$