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}$