Question

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

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

Answer 1

Answer: (D)

Using $\mu=\frac{\sin \left(A+\delta_{m}\right) / 2}{\sin \frac{A}{2}}$
Here, $A=\frac{\pi}{4}=45^{\circ}, \sin =\frac{\pi}{4}=45^{\circ}$
$c =3 \times 10^{8} ms ^{-1}$
$\mu =\frac{\sin (45+45) / 2}{\sin \frac{45}{2}}$
$ \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} \,ms ^{-1}$