Question

The minimum deviation produced by a glass prism having an angle of ${60}^o$ is ${30}^o$. If the velocity of light in vacuum is $3\times {10}^{10}cm/sec$, then its velocity in glass will be

• A. $2.12\times {10}^{10}cm.s^{-1}$
• B. $2.52\times {10}^{10}cm.s^{-1}$
• C. $2.21\times {10}^{10}cm.s^{-1}$
• D. $2.82\times {10}^{10}cm.s^{-1}$

Answer 1

The correct option is A $2.12\times {10}^{10}cm.s^{-1}$

$\mu =\frac{sin\left(\frac{A+{\delta }_m}{2}\right)}{sinA/2}$
$=\frac{sin\left[\right(\frac{60+30}{2}\left)\right]}{sin\left(60/2\right)}=\frac{sin{45}^o}{sin{30}^o}$
$=\frac{1\sqrt{2}}{1/2}=\sqrt{2}$
$=1.414$
Velocity of glass $=\frac{Velocityinvacuum}{\mu }$
$=\frac{3\times {10}^{10}}{1.414}$
$=2.12\times {10}^{10}cm/sec$