Question about optics (diffraction)

[Gza]

I was working out a practice test on optics and was a little confused about how to tackle this problem:


If you illuminate a hole and project the resulting pattern on a screen- as you decrease the hole size, the screen pattern gets smaller initially and then ultimately begins to grow larger. Why is this? Derive a formula for the screen pattern diameter as a function of the hole size, distance between screen and hole and the wavelength.


I know the effect is diffraction, but deriving the mentioned relation is giving me trouble. I was thinking of using the kirchhoff integral theorem, and then perhaps carrying out an integral over a rectangular aperature; but maybe that is overkill. Is their an easier way to start thinking about this?

 

[Galileo]

If you illuminate a hole and project the resulting pattern on a screen- as you decrease the hole size, the screen pattern gets smaller initially and then ultimately begins to grow larger. Why is this? Derive a formula for the screen pattern diameter as a function of the hole size, distance between screen and hole and the wavelength.

Is this considered introductory physics nowadays? I must be getting old.

Maybe this will help a bit:
http://en.wikipedia.org/wiki/Diffraction

 

[Gza]

Lol, yeah this was probably a mispost; i got a chance to check the other posts in this section and realized it at that point. Thanks for the reference though galileo.