Question

A prism of prism angle $\frac{\pi }{4}$ gives a deviation of $\frac{\pi }{4}$. If the velocity of light in vacuum is $3\times 10^{8}m{s}^{-1}$, then find the velocity of light in material of the prism.

• A. $1.25\times 10^{8}m{s}^{-1}$
• B. $1.33\times 10^{8}m{s}^{-1}$
• C. $2.4\times 10^{8}m{s}^{-1}$
• D. $1.62\times 10^{8}m{s}^{-1}$

Answer 1

Answer: (D)

Using $\mu =\frac{\sin \left(A+{\delta }_m\right)/2}{\sin \frac{A}{2}}$
Here, $A=\frac{\pi }{4}=45^{\circ },\sin =\frac{\pi }{4}=45^{\circ }$
$c=3\times 10^{8}m{s}^{-1}$
$\mu =\frac{\sin (45+45)/2}{\sin \frac{45}{2}}$
$\Rightarrow \mu =\frac{0.707}{0.3826}=1.85$
Therefore, $v=\frac{c}{\mu }=\frac{3\times 10^8}{1.85}$
$\Rightarrow v=1.62\times 10^{8}m{s}^{-1}$