Diffraction through a ring aparture

[avisha03]

Homework Statement

1.compute the diffraction pattern through a ring aparture, internal radius a, external radius b, wave length lambda. the incoming wave is a monochromatic, plane wave, vertical to the ring plane.
2.how will the diffraction expression change when a->b?
3.near the aparture a narrow lens with f=10 cm' lambda=1micrometer, a=2mm, b=2.05mm.
draw the intensity i the lens focus plane, according to the first computation, and themn according to the second.

Homework Equations

fernahufer diffraction equations.

The Attempt at a Solution

I did article 1 and got an electrical field with 2 bessel functions, one minus the other. I don't really know how to do 2,3.

 

[badphysicist]

Well, your solution to 1 sounds good because the solution to a circular aperture (easily found on the internet) involves a bessel function and you should be able to do a superposition to get a disk. For 2 you should be able to just take a limit of you equation from part 1 as a goes to b. Otherwise you could solve a ring aperture of delta function width.