Question

The prism shown in the figure has a refractive index of $1.60$ and angle $A$ as ${30}^{\circ }$. Two parallel light rays $P$ and $Q$ enter the prism. The angle between the light rays, when they emerge is:
$[$Given: ${\sin }^{-1}\left(0.8\right)={53}^{\circ }]$

• A. ${46}^{\circ }$
• B. ${54}^{\circ }$
• C. ${60}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is A ${46}^{\circ }$

Since the two angles $A$ are equal, the incident rays will show symmetrical refraction pattern.


From geometry, we can see that, $i_1=i_2=A={30}^{\circ }$

On applying Snell's law,

${\mu }_d\sin i_1={\mu }_a\sin r$

$\Rightarrow 1.60\times \sin {30}^{\circ }=1\times \sin r$

$\Rightarrow \sin r=0.8$

$\Rightarrow r={53}^{\circ }$

Now, $\delta =r-i_1={53}^{\circ }-{30}^{\circ }={23}^{\circ }$

So, the angle between the emerging rays,

$=2\delta ={46}^{\circ }$

Why this question? It tests your ability to pick up the symmetry involved during refraction, because the rays & the two angles lie on the opposite side of the line of symmetry.