A point source of light is placed at a distance h below the surface of a large and deep lake. Show that the fraction f of light that escape directly from water surface is independent of h and is given by
`f=[[1-sqrt(1-1//mu^2)])/2`

Explanation

At water-air surface:
When `igtC`, T.I.R. takes place, hence only those rays escape from the surface, which lie within a cone of semi-angle C.
Therefore, fraction of light escaping
`f=("Surface area of cap outside water")/("Area of full spherical surface")`
`=(2piRy)/(4piR^2)=(y)/(2R)`
`y=R-h`
`f=(R-h)/(2R)=1/2[1-h/R]=1/2[1-cosC]`
`=1/2[1-sqrt(1-sin^2C)]=1/2[1-sqrt(1-1//mu^2)]`