A point source is located at a depth h beneath the surface of water...

Light from the point source escapes the water surface only if the angle of incidence is less than or equal to the critical angle $\theta_c$.

The circular area is formed by the rays that strike the surface at an angle of incidence equal to the critical angle.

The angle subtended by the radius of this circular area at the source is exactly the critical angle $\theta_c$.

Using Snell's law for the critical angle, we have $\mu \sin \theta_c = 1 \times \sin 90^{{}^{{}^{\circ}}}$.

$\sin \theta_c = \dfrac{1}{\mu}$

\theta_c = \sin^{-1} \left(\dfrac{1}{\mu}\right)