General equation for light intensity entering half circle

[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.

 

[tiny-tim]

hello tylerscott!

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

 

[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.

 

[tiny-tim]

But the angle at which the light hits will determine how much is transmitted through the material.

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

 

[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.

 

[tylerscott]

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

 

[frogguy]

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