What does the Rayleigh criterion mean and what is image resolution?

[lha08]

Homework Statement

I'm not sure but what exactly does the Rayleigh Criterion mean? Also, what does it mean when they say the "resolution" of the image...?
Thanks.

Homework Equations

The Attempt at a Solution

 

[nickjer]

No matter how good your instrument is there will be diffraction. So your image will be smeared a bit. Well if you have two images fairly close to each other you won't be able to resolve both of them if they lie too close to each other, since they are smeared a bit they will look like one image. The Rayleigh criterion defines how close the images can be together that you can still distinguish between the both of them.