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Cesium
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Homework Statement
A point source of light is at depth h below the surface of a large and deep lake. Show that the fraction, f, of the light energy that escapes directly form the water surface is independent of h and is given by
[tex]f=0.5(1-\sqrt{1-1/n^2}[/tex])
where n is the index of refraction of the water. Absorption within the water and reflection at the surface (except where it is total) have been neglected.
Homework Equations
n1sin(theta1) = n2sin(theta2)
E=hv?
The Attempt at a Solution
First step would be to find the critical angle:
nsin(theta1)=sin(90) (n2=1 for air)
theta1 = arcsin(1/n)
So anything with an incident angle greater than theta1, will be totally reflected. The problem seems to assume that all of the light with angle less than theta1 will be refracted (even though in reality some will be reflected, too).
So here's where I am going wrong: I tried to assume that all of the light would be equally split up between all angles of radiation. So out of 180 degrees, arcsin(1/n) would escape.
So my fraction and answer would be arcsin(1/n)/180, but that's obviously wrong.
I am having trouble relating energy to this. Thanks in advance.