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