Question

Figure $(i)$ shows the refraction of light from air to glass and figure $(ii)$ shows refraction of light from air to water. The value of the angle $\theta$ in figure $(iii)$ will be:

• A. $30^{\circ }$
• B. $35^{\circ }$
• C. $60^{\circ }$
• D. $41^{\circ }$

Answer 1

Answer: (B)

Applying Snell's law,
From $(i),{}^a{\mu }_g=\frac{\sin 60^{\circ }}{\sin 35^{\circ }}$
From $(ii),{}^a{\mu }_w=\frac{\sin 60^{\circ }}{\sin 41^{\circ }}$
From $(iii),{}^w{\mu }_g=\frac{\sin 41^{\circ }}{\sin \theta }$
Therefore, ${}^a{\mu }_w\times {}^w{\mu }_g={}^a{\mu }_g$
$\Rightarrow \frac{\sin 60^{\circ }}{\sin 41^{\circ }}\times \frac{\sin 41^{\circ }}{\sin {\theta }^{\circ }}=\frac{\sin 60^{\circ }}{\sin 35^{\circ }}\Rightarrow \sin \theta =\sin 35^{\circ }$
$\Rightarrow \theta =35^{\circ }$