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I'm projecting a circular beam of some known divergence and power onto a surface angled relative to the center of the beam. Say holding a flashlight, with a cone of half angle

*θ*, at my waist some height

*h*off the ground, projecting it onto the ground at an incidence angle

*α.*

Assuming the beam has constant intensity across solid angle from the source, I want to determine the irradiance as a function of position across the spot. I can easily calculate the area of the projected ellipse to determine the

*average*irradiance across the spot, but I'm interested in the difference between irradiances at the near and far ends of the spot.

Basically I'm trying to find a function to relate differential solid angle of the beam to differential projected area of the spot, and I'm getting stuck figuring out the proper way to set it up.

Any and all help is much appreciated.