question_answer

A point source of light is placed at depth h below the surface of a lake. Fraction of light energy that escapes from the lake depends on

A) \[h\]                             

B) \[{{h}^{2}}\]

C) \[{{h}^{-\,2}}\]                       

D)        \[{{h}^{0}}\]

Correct Answer: D

Solution :

Let P luminous intensity of source, then amount of light diverging from source in 1 s is \[4\pi P.\]

Light escapes in air through a cone of semi-vertical angle \[{{i}_{c}},\]

So, fraction of light that escapes in the air is

\[f=\frac{2\pi P(1-\cos {{i}_{c}})}{4\pi P}=\frac{1}{2}(1-\cos {{i}_{c}})\]

\[=\frac{1}{2}(1-\sqrt{1-{{\sin }^{2}}{{i}_{c}})}\]

This fraction is independent of depth h, of sources below the surface.