# Resolving Power of Optical Instruments

When two objects are very class to each other, it may not be possible for our eye to see them separately. If we wish to see them separately, then we will have to make use of some optical instruments like microscope, telescope, grating, prism etc. The ability of an optical instrument

to form distinctly separate images of two objects, very close to each other is called the resolving

power of instrument. A lens system like microscope and telescope gives us a geometrical

resolution while a grating or a prism gives a spectral resolution. In fact the image of a point

object or line is not simply a point or line but what we get is a diffraction pattern of decreasing

intensity. For a two point system two diffraction patterns are obtained which may and may

not overlap depending upon their separation. The minimum separation between two objects

that can be resolved by an optical instrument is called resolving limit of that instrument. The

resolving power is inversely proportional to the resolving limit.

5.9.1 Rayleigh Criterion of Resolution

According to Lord Rayleigh’s arbitrary criterion two nearby images are said to be resolved if (i) the position of central maximum of one coincides with the first minima of the other or vice versa.

Figure 5.10 Rayleigh criterian

To illustrate this let us consider the diffraction patterns due to two wavelengths A.1 and

2 There may be three possibilities. First let the difference (λ12) is sufficiently large so that

central maximum are quite separate, this situation is called well resolved.

Secondly consider that (λ) is such that central maximum due to one falls on the first minima of the other. The resultant intensity curve shows a distinct dip in the middle of two central maxima. This situation is called just resolved as the intensity of the dip can be resolved by our eyes.

ldip = 0.81  Imax                                                                                                    … (1)

Thirdly let the (λ12) is very small such that they come still closes as shown in Figure 5.10. The intensity curves have sufficient overlapping and two images cannot be distinguished separately. The resultant curve almost appears as one maxima. This case is known as unsolved.  Thus the minimum limit of resolution is that when two patterns are just resolved.