Question

As you can seen from Fig. (i) and (ii) shows refraction of light from air to glass and from air to water. Find out the value of the angle $\theta$ in the case of refraction as shown in figure (iii) will be

• A. $30^{\circ }$
• B. $50^{\circ }$
• C. $40^{\circ }$
• D. $45^{\circ }$

Answer 1

Answer: (C)

${}^a{\mu }_g=\frac{\sin 50^{\circ }}{\sin 40^{\circ }}...(i)$
${}^a{\mu }_w=\frac{\sin 50^{\circ }}{\sin 45^{\circ }}...(ii)$
${}^w{\mu }_g=\frac{\sin 45^{\circ }}{\sin \theta }...(iii)$
${}^a{\mu }_w\times {}^w{\mu }_g={}^a{\mu }_g$
$\frac{\sin 50^{\circ }}{\sin 45^{\circ }}\times \frac{\sin 45^{\circ }}{\sin \theta }=\frac{\sin 50^{\circ }}{\sin 40^{\circ }}$
( Using Eq. (i), (ii) and (iii)
$\sin \theta =\sin 40^{\circ }$
$\theta =40^{\circ }$