Final answer:
The optical resolution formula r = 1.22λ/2n sin θ reflects the Rayleigh criterion's diffraction limit, with the constant 1.22 derived from the Bessel function for a circular aperture. The Numerical Aperture (NA) relates to the resolving power, where a higher NA enables finer detail resolution.
Step-by-step explanation:
The optical resolution formula r = 1.22λ/2n sin θ is derived from the Rayleigh criterion, which is a determination of the diffraction limit for optical systems. The number 1.22 is a constant that comes from the first zero of the Bessel function, which describes the diffraction pattern generated by the circular aperture of an optical system. By definition, a lens's Numerical Aperture (NA) is NA = n sin α, where n is the index of refraction, and α is half the vertex angle of the maximum cone of light that can enter or exit the lens. A comparison of two diffraction patterns shows the minimum angular separation, corresponding to this first zero, as θ = 1.22 λ/D. This value correlates to the smallest angle at which two point light sources can be distinguished as separate entities. A lens with a higher Numerical Aperture can resolve finer details as it can gather more light from a smaller area, yielding better resolution.