Explain Rayleigh criterion of resolving power of optical instrument.
What is resolving power? Find the resolving power of telescope.
Resolving Power of Optical Instruments
“The resolving power of an instrument is a measure of how well it can distinguish between two (apparently) very close sources of light”. A quantity that characterizes the ability of optical instruments to produce separate images of two points of an object that are close to each other. The smallest linear or angular distance between the two points at which their images begin to merge is called the linear or angular limit of resolution. The inverse quantity usually serves as a quantitative measure of the resolving power.
The resolving power of a telescope is defined as the reciprocal of the smallest angular separation’s θ’ between the two distant objects whose images are just seen in the telescope as separate. This angle dθ is given by
dθ = (1.22 λ) / D
λ is the wavelength of the light used and D is the diameter of the aperture of the objective of the telescope and d θ is the angle which the two point objects subtend at the objective. Thus the resolving is given by
Resolving power = 1 / (dθ) = D / (1.22 λ).
Resolving limit or power of a lens
To illustrate this we will consider an astronomical telescope.
Even when using a telescope of high magnification, the image of a star should be a very small point of light. This is because even the closest stars ware very far away. In practice, the image is not a point because the light from the star is diffracted as it enters the telescope. The effect is exaggerated in the following diagrams.
If two stars are far from each other, it is still obvious that they are two separate light sources.
However, if they are (apparently) close together, the diffraction causes their images to overlap.
Rayleigh suggested that the images should be considered as just resolved if the central maximum of one image coincides with the first minimum of the other image, as shown in the next diagram.
This idea is now called the Rayleigh criterion and (for a circular aperture)… it can be shown that it corresponds to the light sources having an angular separation* , given by
θ = 1.22 λ/b
λ = the wavelength of the light.
b = the diameter of the object lens of the telescope.
*The two stars in the diagram below have an angular separation of q from the point of view of the observer. Notice that they are not, in fact, very close to each other.