Question

An object is located at a distance of $5\text{cm}$ from a thin prism. The referactive index of the prism is $\mu =1.5$. When the object is viewed from the opposite side of the thin prism, then the vertical shift produced by the thin prism is recorded as $\frac{\pi }{36}\text{cm}$. Calculate the angle of the thin prism.

• A. $2^{\circ }$
• B. $5^{\circ }$
• C. ${3.5}^{\circ }$
• D. $4^{\circ }$

Answer 1

The correct option is A $2^{\circ }$

Given,
Distance of the object from the prism $\left(a\right)=5\text{cm}$
Refractive index of the prism $\left(\mu \right)=1.5$
Shift produced by the thin prism $\left(S\right)=\frac{\pi }{36}\text{cm}$

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.
$\Rightarrow \frac{\pi }{36}=5\times (1.5-1)\times A$

$\Rightarrow A=\frac{\pi }{5\times 18}\text{radian}$

Or, $A=2^{\circ }$

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