A diver at a depth of 1.2 m in clear water \( \left(n = \displaystyle\frac{4}{3}\right) \) sees the sky in a cone of semi-vertical angle:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \sin^{-1}\displaystyle\frac{3}{4} \)
Light from the sky enters the water at every angle of incidence up to \( 90^\circ \). A ray that grazes the surface (incidence \( 90^\circ \)) is refracted at the critical angle \( C \), so all the light from the sky reaches the diver inside a cone of semi-vertical angle \( C \).
By Snell's law for the grazing ray:
\( \displaystyle 1 \times \sin 90^\circ = n\sin C \;\Rightarrow\; \sin C = \frac{1}{n} = \frac{3}{4} \)
\( \displaystyle C = \sin^{-1}\frac{3}{4} \)
The depth of the diver does not change the angle; it only sets the radius of the bright circle on the surface, \( r = h\tan C \).