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(C) When a ray of light is incident from the water-air interface at the critical angle $(	heta_{c})$,the refracted ray becomes parallel to the interf

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$3 \ m$

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(C) When a ray of light is incident from the water-air interface at the critical angle $(	heta_{c})$,the refracted ray becomes parallel to the interface.Given depth $h = \sqrt{7} \ m$ and refractive index $\mu = 4/3$.The radius $R$ of the circular bright patch is given by $R = h 	an 	heta_{c}$.Since $\sin 	heta_{c} = 1/\mu$,we have $	an 	heta_{c} = \frac{1}{\sqrt{\mu^{2}-1}}$.Substituting the values:$R = \sqrt{7} 	imes \frac{1}{\sqrt{(4/3)^{2}-1}} = \sqrt{7} 	imes \frac{1}{\sqrt{16/9-1}} = \sqrt{7} 	imes \frac{1}{\sqrt{7/9}} = \sqrt{7} 	imes \frac{3}{\sqrt{7}} = 3 \ m$.

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

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