Question

A ray of light passes from glass having a refractive index of $1.6$, to air. The angle of incidence for which the angle of refraction is twice the angle of incidence is

• A. $\sin ^{-1}\left(\frac{4}{5}\right)$
• B. $\sin ^{-1}\left(\frac{3}{5}\right)$
• C. $\sin ^{-1}\left(\frac{5}{8}\right)$
• D. $\sin ^{-1}\left(\frac{2}{5}\right)$

Answer 1

Answer: (B)

$_g\mu_{a}=\frac{\sin i}{\sin r}$
$\Rightarrow \frac{1}{{ }_{a} \mu_{g}}=\frac{\sin i}{\sin 2 i}$
$\frac{1}{16}=\frac{\sin i}{2 \sin i \cos i}$ or $\frac{1}{\cos i} \frac{1}{10}=\frac{5}{8}$
or $\frac{1}{\cos i}=\frac{5}{4}$ or $\cos i=\frac{4}{5}$
Now, $\sin i=\sqrt{1-\cos ^{2}} i$
or $\sin r=\sqrt{1-\frac{16}{25}}=\sqrt{\frac{9}{265}}=\frac{3}{5}$
or $i=\sin ^{-1}\left(\frac{3}{5}\right)$