Thread: elliptical footprint of a round beam

Hi,

I have some problems with a basic geometric problem (it is a long time ago I had some mathematics)
How do I calculate the surface area of a elliptical footprint of a beam that falls into the surface under a 45 degree angle? I only have the diameter D of the incident beam.
I got:
sqrt(2) pi (D/2)^2

is this correct?

thanks,
Ilindema

Originally Posted by ilindema

Hi,

I have some problems with a basic geometric problem (it is a long time ago I had some mathematics)
How do I calculate the surface area of a elliptical footprint of a beam that falls into the surface under a 45 degree angle? I only have the diameter D of the incident beam.
I got:
sqrt(2) pi (D/2)^2

is this correct?

thanks,
Ilindema

Start by drawing an isosceles right triangle The hypotenuse is the image of the beam and one of the legs is a diameter of the beam. That is, so c, the major axis of the ellipse, is . The minor axis is, of course, the diameter of the beam, D.

The area of an ellipse with major and minor semi-axes a and b is so, yes, the area of this ellipse is , exactly what you have.

thanks a lot! Now I have some peace