Dear Student,

The limit of resolution (or resolving power) is a measure of the ability of the objective lens to separate in the image adjacent details that are present in the object . It is defined as the inverse of the distance or angular separation between two objects which can be just resolved when viewed through the optical instrument.

The resolving power of an optical system is ultimately limited by diffraction by the aperture. Thus an optical system cannot form a perfect image of a point.

Resolving Power of Telescope :

In telescopes, very close objects such as binary stars or individual stars of galaxies subtend very small angles on the telescope. To resolve them we need very large apertures. We can use Rayleigh’s to determine the resolving power. The angular separation between two objects must be

θ = 1.22 λ/d  and Resolving power = 1/θ = d/1.22 λ

Thus, the higher the diameter d, the better the resolution. The best astronomical optical telescopes have mirror diameters as large as 10 m to achieve the best resolution. Also, larger wavelengths reduce the resolving power, and consequently, radio and microwave telescopes need larger mirrors.

Resolving Power of Microscope :

For microscopes, the resolving power is the inverse of the distance between two objects that can be just resolved.

d = λ/2 n sin θ

Resolving power = 1/ d = 2n sin θ/ λ

Where n is the refractive index of the medium separating object and aperture. Note that to achieve high-resolution n sin θ must be large. This is known as the Numerical aperture.

Happy Learning!