What is the concept behind the wavelength/2 of the diffraction limit of the resolution of a microscope?

Question

How it is derived? What is the origin of that theory? Any site/link that you can provide?

Answer 1

Check this wiki article about the Airy disc, and the implication it has for optical resolution. After the Young experiment demonstrated the wave property of life, there was a great deal of mathematical development of light diffraction in the early 1800s, and Airy worked out the diffraction pattern for a circular aperture prior to 1831.

The consequence of the diffraction pattern for a circular aperture is that every point-like object has a round, rippled image with an intensity pattern looking something like a Mexican sombero. If two point-like objects are too close together, their Mexican sombero-like patterns merge, and it becomes hard to distinguish between the peaks, and this is what limits image resolution.

For a pictorial graph of the Airy diffraction pattern, check the last link of the wiki article for mathematical details of how it was derived. It has a 3D graph of the pattern, showing the Mexican sombero shape.