Question

An object is located at a distance of $2\text{m}$ from a thin prism. The angle of the prism is $5^{\circ }$ and the refractive index of prism is $\mu =1.5$. When the object is viewed from the opposite side of the thin prism, then the shift produced by the thin prism will be :

• A. $5\text{m}$
• B. $\frac{\pi }{6}\text{m}$
• C. $\frac{\pi }{36}\text{m}$
• D. $0.5\text{m}$

Answer 1

The correct option is C $\frac{\pi }{36}\text{m}$

Given,
Distance of the object from the prism $\left(a\right)=2\text{m}$
Angle of the thin prism $\left(A\right)=5^{\circ }$
Refractive index of the prism $\left(\mu \right)=1.5$

We know that the shift $\left(S\right)$ produced by the thin prism is given by :
$S=a(\mu -1)A$
Putting the values given in the question.
$\Rightarrow S=2\times (1.5-1)\times 5\times \frac{\pi }{180}$
$\Rightarrow S=\frac{\pi }{36}\text{m}$

Hence, option $\left(c\right)$ is the correct answer.