Resolving Power: The Rayleigh’s Criterion

The resolving power of an optical instrument is its ability to resolve (or separate) the images of two point objects lying close to each other. Rayleigh suggested that two images can be seen as distinct when the first minimum of the diffraction pattern due to one object falls on the central maximum of the other. This is called Rayleigh’s criterion.

Resolving Power of Telescope

The resolving power of a telescope is its ability to form separate images of two distant point objects situated close to each other. It is measured in terms of the angle subtended at its objective by two close but distinct objects whose images are just seen in the telescope as separate. This angle is called the limit of resolution of the telescope. If the angle subtended by two distinct objects is less than this angle, the images of the objects can not be resolved by the telescope. The smaller the value of this angle, higher will be the resolving power of the telescope. Thus, the reciprocal of the limit of resolution gives the resolving power of the telescope.

If λ is the wavelength of light, D the diameter of the telescope objective, and θ the angle subtended by the point object at the objective, the limit of resolution of the telescope is given by (Rayleigh’s criterion)

θ = 1.22λ/D

Hence, the resolving power of the telescope,

(R.P)_T = 1/θ = D/1.22λ

To get a high resolving power, a telescope with large aperture objective or light of lower wavelength has to be used.

Resolving Power of Microscope

The resolving power of a microscope represents its ability to form separate images of two objects situated very close to each other. The resolving power of a microscope is measured in terms of the smallest linear separation between the two objects which can just be seen through the microscope as separate. This smallest linear separation between two objects is called the limit of resolution of the microscope. 

The smaller the value of linear separation, the higher will be the resolving power of the microscope. Thus, the reciprocal of the limit of resolution gives the resolving power of the microscope.

If λ is the wavelength of light used to illuminate the object, θ is the half angle of the cone of light from the point object at the eye and n is the refractive index of the medium between the object and the objective, the limit of resolution of the microscope is given by

d = λ/(2n sin θ)

Thus, the resolving power of microscope is

(R.P)_m = (2n sin θ)/λ

The expression (2n sin θ) is called numerical aperture (N.A). The highest value of N.A of the objective obtainable in practice is 1.6, and for the eye, N.A is 0.004.

The resolving power of a microscope can be increased by increasing the numerical aperture and decreasing the wavelength of the light used to illuminate the object.