Rays from a point source of light situated at height h below the liquid surface having refractive index , forms a circular patch of light of radius r on the surface. The area of the patch is

Step-by-step solution

Consider the figure as shown below: Area of the light patch = r^2 We know the patch forms due to total internal reflection. Light rays from source S are incident at the edge of the circular path at critical angle _ C (as shown at points P and Q ), the refracted ray exits at angle 2 w.r.t. the normal. Using Snell's Law aligned & ( _C )=1 ( ( 2 ) ) & _C= 1 = r h^2+r^2 & r^2= (h^2+r^2 ) ^2 & r^2= h^2 ( ^2-1 ) aligned Area of the patch = ( h^2 ^2-1 )