A major advantage of film or a photoelectric detector over the eye is its ability to collect light for a long time. In the eye, 'exposures' are fixed at about 1/20 s. With modern detectors, exposures of several hours are possible. Therefore, the limiting magnitude for direct visual observing is not as faint as for photography or photoelectric detectors.
We now look at resolving power. Resolution is the ability to separate the images of stars that are close together. It also allows us to discern the details in an extended object.
One phenomenon that affects resolution is diffraction. Diffraction is the bending or spreading of waves when they strike a barrier or pass through an aperture. As they spread out, waves from different parts of the aperture or barrier interfere with one another, producing maxima and minima, as shown in Fig. 4.1. As the aperture size, relative to the wavelength, increases, there are more waves to interfere, so the pattern is less spread out. Most of the power is in the central maximum, whose angular width AO (in radians) is related to the wavelength of the wave A and the diameter of the aperture, D, by
Diffraction results in the images of stars being smeared out by this angle. That means that if two stars are closer than AO, their images will blend together. We consider the images of two stars to just be resolved when the maximum of one diffraction pattern falls on the first minimum of the other. This condition is called the Rayleigh criterion. While equation (4.1a) is an approximation good for all shapes of aperture, the actual size of the diffraction pattern depends on the shape of the aperture. You may remember that, for circular apertures, the resolution is given by
Example 4.2 Angular resolution
Estimate the angular resolution of the eye for light of wavelength 550 nm.
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