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`

Answer

A, B

Explanation

Due to TIR, light will be reflected back into be the
water if `igttheta_C.` So, only that portion of incident light will
escape which passes through the cone of angle `theta=2 theta_C.`
So, the fraction of light escaping
`f=("area ACB")/("Total area of sphere") =(2piR^2(1-cos theta_C))/(4piR^2)=(1-cos theta_C)/2`
Now, as f depends on `theta_C` and which depends only on `mu,` it is
independent of h.
Further
`cos theta_C=sqrt(mu^2-1)/mu=sqrt(1-1//mu^2) rArr f=(1-sqrt(1-1)//mu^2)/2`