Resolving Power Of Grating And Other Image Forming System

Resolving Power of Grating and other Image forming system: 

Resolution of image forming system An optical system is used to form the image of objects. These objects may be situated at very large distances (like stars in galaxy) or very fine in size (microscopic size) The quality of image depends upon the quality of lenses used (Abberations). Even if we have perfect lens systems, the quality of image (sharpness) is limited by the diffraction at the aperture (entrance slit of the optical instruments). It means that if there are more than two light sources (illuminated objects) nearby, whether the images of these two sources (intensity distribution on screen) is separate or overlaps on each other will depend upon intensity distribution due to either sources on screen.

Till now we discuss the cases where monochromatic light was coming from a distant source (so that when it reaches the slit the wave front is plane). We discussed the intensity distribution on screen after the light passes through a slit or a system of slits. Clearly, the intensity distribution will change, if light is coming from some other source also(at some angle of incidence not equal to 0⁰) or having more than one wavelength. Resolution or resolving power an optical instrument is the ability to separate the image pattern arising due to two nearby sources or due to two closely spaced wavelengths.

Let us consider the diffraction pattern for monochromatic light coming from two distant sources, whose angular separation from slit is

(Fig.A.).

The parallel wave front reaching the slit will be inclined at an angle with respect to each other and the central maxima for these two set of rays will also be separated by .

The resultant diffraction pattern on the screen will be superposition of the patterns from these two sources as shown in

(Fig.B).

From figure, we can see that if the angular separation between the two central maxima is large, the diffraction pattern is well separated. However, if the angular separation is very small, the diffraction patterns overlap and we can not separate the two images. The two patterns are just resolved if the central maxima of one falls on first minima of other. This is known as Rayleigh criterion of resolution. In this case (first order minima of one pattern), where d is slit width.

For small , the angular separation between the two principal maxima, when these are just resolved will be . If a lens of focal length f is used to form the image at the screen and the lens is placed close to the slit then the linear separation between the two maxima will be y , such that   or