Question

A point source of light is kept below the surface of water $(n_w = \frac{4}{3})$ at a depth of $\sqrt{7}$ m. The radius of the circular bright patch of light noticed on the surface of water is

• A. $\frac{3} {\sqrt {7}} m$
• B. $3\,m$
• C. $\frac{\sqrt {7}} {3} \,m$
• D. ${\sqrt {7}}\, m$

Answer 1

Answer: (B)

$3\,m$

Answer 2

When the ray of light is incident from water-air interface at critical angle $\left(\theta_{c}\right)$, the refracted ray becomes parallel to the interface.

Hence, the radius of the circular bright patch of light noticed on the surface of water is given by
$R=h \,\tan \,\theta_{c}$ (see figure)
$=\sqrt{7} \frac{\sin \theta_{c}}{\cos \theta_{c}}=\sqrt{7}$
$\frac{1 / \mu}{\sqrt{1-\frac{1}{\mu^{2}}}}$
$=\frac{\sqrt{7}}{\sqrt{\mu^{2}-1}}$
$=3\, m$