General equation for light intensity entering half circle

1. Jul 19, 2013

tylerscott

Hello,

I am currently working on a problem to calculate the light that makes it through a half circle. For example, say I put a cylinder out in the sun, where the intensity is known to be 1030 W/m^2. I would like to compute the intensity/energy/power that makes it into this. Now, given the curvature of this half circle, I know this will somehow need to incorporate an integration over the sphere based upon the angle, but I'm thinking I'm missing some fundamental physics equation in the process.

See attached picture for the idea I have in my mind.

2. Jul 19, 2013

tiny-tim

hello tylerscott!

doesn't the intensity of the light falling on a body simply depend on how wide it is?

3. Jul 19, 2013

tylerscott

The intensity falling on it will be constant, yes. But the angle at which the light hits will determine how much is transmitted through the material. This is what I'm trying to figure out.

4. Jul 20, 2013

tiny-tim

your diagram shows the light coming "from infinity" (like sunlight) and falling perpendicularly on the cylinder

what angle do you mean?

the amount of sunlight hitting a body is the measured precisely by the size of its shadow

5. Jul 20, 2013

frogguy

Hi guys!
I guess you ask that in terms of transmitted and reflected light?
In that case you should compute the fresnel's equations over the sphere surface.

6. Jul 20, 2013

tylerscott

Ah! That's what I was looking for. So, how do you suggest integrating these over the surface?

7. Jul 20, 2013

frogguy

Numerically with respect to the sphere tangent over small areas, i think