Fraction of light that escapes!

Classical Mechanics Level 4

A point source of light is placed a distance ' h h ' below the surface of water. What is the fraction of light energy that escapes directly from the water surface? Give your answer to 3 decimal places.

Assume μ water = 4 3 \mu_{\text{water}} = \frac{4}{3} and ignore any absorption or scattering of light.


The answer is 0.16928.

Nishant Rai by Nishant Rai , 25, India

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2 solutions

Nishant Rai
May 16, 2015

7 Helpful 0 Interesting 0 Brilliant 0 Confused
Prakhar Bindal
Oct 2, 2016

Directly Use Concept of Solid Angle.

The light source emits light energy in whole 3 dimensional space (as spherical source)

Now the light will be emitted till light energy strikes the lake surface lesser than the critical angle otherwise light will be totally internally reflected back.

sinx = 3/4 where x is critical angle

Solid Angle for complete space = 4pi

Solid angle for our region = 2pi(1-cosx)

Fraction = (1-cosx)/2 = 0.17

2 Helpful 0 Interesting 0 Brilliant 0 Confused

right bro ? @Aniket Sanghi

you solved by this method or any other?

Prakhar Bindal - 4 years, 8 months ago

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Exactly the same method bro! :)

Aniket Sanghi - 4 years, 8 months ago

Same method! But the problem was very nice :P

Swapnil Das - 4 years, 8 months ago

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