Question

Describe Rayleigh's criterion for resolution. Explain it for a telescope and a microscope.

Answer 1

Rayleigh's criterion for minimum resolution:

When the centre of one diffraction pattern's central peak is as far as the initial minimum of the other pattern, two overlapping diffraction patterns attributable to two point sources are acceptable or just resolved.

The angular separation between the centre of the peak and the first minimum of a diffraction pattern is used to determine the 'sharpness' of the central maximum. It indicates the resolution's upper limit.

(a) Unresolved	(b) Just resolved	(c) well resolved

If the angular separation between the central peaks is less than the limit of resolution in the first figure, two overlapping diffraction patterns caused by two point sources cannot be resolved. If the angular separation between the central peaks equals the limit of resolution in the second figure, they are said to be just separate or resolved. If the angular separation between the central peaks is greater than the limit of resolution in the third figure, they are said to be well resolved.

Resolving power of an optical instrument:

Whether looking at a star system through a telescope or a living cell through a microscope, the basic goal of utilising an optical device is to discern small details. Light from two adjacent parts of the object should produce sharp, distinct (separate) images of those parts after passing through an optical system. The objective lens or mirror of a telescope or microscope acts like a circular aperture. A circular aperture's diffraction pattern is composed of a central bright spot (called the Airy disc and corresponds to the central maximum) and concentric dark and bright rings. After passing through the aperture of an optical system, light from two close objects or parts of an object produces overlapping diffraction patterns that tend to obscure the image. If these diffraction patterns are so broad that their central maxima significantly overlap, it is difficult to determine whether the intensity distribution is produced by two separate objects or by one. The ability of an optical instrument, such as a telescope or microscope, to produce detectably separate images of objects that are packed together is measured by its resolving power.

Definition: The smallest linear or angular separation between two point objects that appear just resolved when viewed through an optical instrument is known as the instrument's limit of resolution, and its reciprocal is known as the instrument's resolving power.