How Does Light Intensity Vary with Distance from an Incoherent Extended Source?

[reasonableman]

I'm currently trying to look into the optics of extended sources. Google doesn't seem too helpful.

Anyway, I have just been thinking about it and thought that surely one of the easiest problems would be the intensity at a screen at a particular distance from an incoherent, spatial extended source.

To me it looks pretty much like an electrostatics problem, common as an undergraduate.

I'm envisioning a line of infinitesimal sources, which will each contribute some light to a point. Which assuming a Lambertian emitter will be the intensity of that infinitesimal point but taking into account the 1/r^2 drop off and the cosine of the angle of the point.

I then integrate over the whole source. However when I put this into maxima (can't do it manually) I get some horrendously long expressions.

Am I doing something wrong with my model and can anyone suggest an introductory text for extended sources?

 

[Andy Resnick]

It is covered in many optics courses, but disguised. In fact, what you are asking is the far-field diffraction pattern for an aperture, when the field aperture is not a (coherent) plane wave but an incoherent field, and the aperture is shaped like your source. Try that approach and see what happens.