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Resolving Power of an Optical Instrument
The resolving power of an instrument is a measure of how well it can distinguish between two (apparently) very close sources of light.
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 are very far away.
In practice, the image is not a point because the light from the star is diffracted as it enters the telescope.
 
In the following diagrams (which exaggerate the effect), the ideal image is on the left and what you actually see, on the right.
 
If two stars are far from each other, it is still obvious that we are looking at two separate light sources.
 
 
However if, from our point of view*, they appear to be close together, the diffraction causes their images to overlap.
 
 
Are we now looking at two separate light sources or one weirdly shaped source?
 
Rayleigh (Lord Rayleigh, John William Strutt) 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 above.
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* θ, given by
where λ is the wavelength of the light and b is the diameter of the object lens of the telescope.
 
 
*Note that, two stars which are actually very far apart, can appear to be close together when viewed from a given point, as shown here.
This is why the Rayleigh criterion is stated in terms of the angular separation of the light sources.
 
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