Question

At what angle, a ray of light will incident on one face of an equilateral prism, so that the emergent ray may graze the second surface of the prism $(\mu =1.5)$?

• A. $ 38^{\circ} $
• B. $82^{\circ}$
• C. $ 28^{\circ}$
• D. $48^{\circ}$

Answer 1

Answer: (C)

Maximum deviation occurs when there is grazing incidence.
Since, the prism is an equilateral one, its angles are $60^{\circ}$ each. Maximum deviation occurs when there is grazing incidence, that is, angle of incidence is $90^{\circ}$.

From Snell's law
$\mu =\frac{\sin i}{\sin r}$
$\Rightarrow 1.5=\frac{\sin 90^{\circ}}{\sin r}$
$\Rightarrow \sin r =\frac{1}{1.5}=0.67$
$\Rightarrow r =\sin ^{-1}(0.67)=42^{\circ}$
Also, $r+ r'=A=60^{\circ}$
$\Rightarrow r'=60^{\circ}-r$
$\Rightarrow =60^{\circ}-42^{\circ}=18^{\circ}$
Let the angle of emergence be $i'$. Then
$\frac{\sin i'}{\sin r'}=\mu=1.5$
$\sin i'=1.5 \sin 18^{\circ}=1.5 \times 0.31=0.465$
$\therefore i'=\sin ^{-1}(0.465)=28^{\circ}$