(a) A pinhole camera is essentially a rectangular box with a tiny pinhole in front. An inversted image of the object is formed on the rear of the box. Consider a parallel beam of light incident normally on the pinhole. If we neglect diffraction effects then the diameter of the image will increase linearly with the diameter of the pinhole. On the other hand, if we assume Fraunhofer diffraction, then the diameter of the first dark ring will go on increasing as we reduce the diameter of the pinhole. Find the pinhole diameter for which the diameter of the geometrical image is approximately equal to the diameter of the first dark ring in the Airy pattern. Assume λ = 6000 Å and a separation of 15 cm between the pinhole and the rear of the box.
[Ans. (a) 0.47mm]
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