Question

An isosceles prism of angle $120^{\circ }$ has a refractive index of $1.44$. Two parallel monochromatic rays enter the prism parallel to each other in air as shown. The rays emerging from the opposite faces

• A. Are parallel to each other
• B. Are diverging
• C. Make an angle $2{\sin }^{-1}(0.72)$ with each other
• D. Make an angle $2\left\{{\sin }^{-1}(0.72)-30^{\circ }\right\}$ with each other

Answer 1

Answer: (D)

At point $A.\frac{\sin 30^{\circ }}{\sin r}=\frac{1}{1.44}$

$\Rightarrow r={\sin }^{-1}(0.72)$ also $\angle BAD=180^{\circ }-\angle r$
In rectangle $ABCD,\angle A+\angle B+\angle C+\angle D=360^{\circ }$
$\Rightarrow \left(180^{\circ }-r\right)+60^{\circ }+\left(180^{\circ }-r\right)+\theta =360^{\circ }$
$\Rightarrow \theta =2\left[{\sin }^{-1}(0.72)-30^{\circ }\right]$