Question

An isosceles prism of angle ${120}^{\circ }$ has a refractive index $1.44$. 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 $2\left[{\sin }^{-1}\right(0.72)-{30}^{\circ }]$
• D. Make an angle $2{\sin }^{-1}\left(0.72\right)$

Answer 1

The correct option is C Make an angle $2\left[{\sin }^{-1}\right(0.72)-{30}^{\circ }]$

Applying Snell's law at $P,\mu =\frac{\sin r}{\sin {30}^{\circ }}sinr=\frac{1.44}{2}=0.72$
$\therefore \delta =r-{30}^{\circ }={\sin }^{-1}\left(0.72\right)-{30}^{\circ }$
Therefore, the rays make an angle of $2\delta =2\left[{\sin }^{-1}\right(0.72)-30]$ with each other.
c is the correct option.