Learning Goal: To use the formulas for the locations of the dark bands and under

Question

Learning Goal: To use the formulas for the locations of the dark bands and understand Rayleigh's criterion of resolvability.

An important diffraction pattern in many situations is diffraction from a circular aperture. A circular aperture is relatively easy to make: all that you need is a pin and something opaque to poke the pin through. The figure shows a typical pattern. It consists of a bright central disk, called the Airy disk, surrounded by concentric rings of dark and light.

While the mathematics required to derive the equations for circular-aperture diffraction is quite complex, the derived equations are relatively easy to use. One set of equations gives the angular radii of the dark rings, while the other gives the angular radii of the light rings. The equations are the following:

Diffraction due to a circular aperture is important in astronomy. Since a telescope has a circular aperture of finite size, stars are not imaged as points, but rather as diffraction patterns. Two distinct points are said to be just resolved (i.e., have the smallest separation for which you can confidently tell that there are two points instead of just one) when the center of one point's diffraction pattern is found in the first dark ring of the other point's diffraction pattern. This is called Rayleigh's criterion for resolvability.

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Explanation / Answer

Given that wave length is =632.8 x 10-9 m diameter D=0.465 x 10-3 m if is the angle at which first dark ring is observed then sin=1.22/D       =(1.22)(632.8 x 10-9)/(0.465 x 10-3)     =9.51 x 10-2 Deg

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