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)

${}_g{\mu }_a=\frac{\sin i}{\sin r}$
$\Rightarrow \frac{1}{{}_a{\mu }_g}=\frac{\sin i}{\sin 2i}$
$\frac{1}{16}=\frac{\sin i}{2\sin i\cos i}$ 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 $i={\sin }^{-1}\left(\frac{3}{5}\right)$