Rayleigh’s Criterion
The minimum distances between images must be such that the central maximum of the first image lies on the first minimum of the second and vice versa. Such an image viewed from an optical device is calculated using Rayleigh’s criterion.
When two objects placed at a distance from each other are separated by an angular separation θ, the diffraction patterns of the two objects will overlap each other. They would appear as one when the two central maxima overlap. This defines Rayleigh’s resolution criterion. It can be shown that, for a circular aperture of a given diameter, the first minimum in the diffraction pattern occurs at,
θ = 1.22(λ/D)
Where,
θ: the angular separation measured in radians
λ: the wavelength of light
D: the diameter of the aperture
Resolving Power of a Microscope and Telescope
Wave optics, also known as Physical optics, deals with the study of various phenomena such as diffraction, polarization, interference, resolution, and other occurrences. Wave optics is the segment of optics that focuses on the study and behavior of light and its wave characteristics. Wave optics particularly describes the connection between waves and rays of light. According to the wave theory of light, light is a form of energy, it travels through a medium in the form of transverse wave motion. The speed of light traveling through a medium depends upon the nature of the medium.
Here, the approximation is carried out by using ray optics for the estimation of the field on a surface. Integrating ray-estimated field over a mirror, lens, or aperture for the calculation of the scattered or transmitted field also gets involved later on. Wave optics stands as a witness to the scientific study of understanding the nature of light. One is the particle nature of light and the other is the wave nature of light.