Question

Figure $\left(\right.i\left.\right)$ shows the refraction of light from air to glass and figure $\left(\right.ii\left.\right)$ shows refraction of light from air to water. The value of the angle $\theta $ in figure $\left(\right.iii\left.\right)$ 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 $(i i),{ }^a \mu_w=\frac{\sin 60^{\circ}}{\sin 41^{\circ}}$
From $(i i i),{ }^w \mu_g=\frac{\sin 41^{\circ}}{\sin \theta}$
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} $
$\Rightarrow \theta=35^{\circ}$