Question

(30 marks (c) The irradiance , of the Fraunhofer diffraction pattem from an aperture of circular diameter D, is described by the first-order Bessel function J of the first kind written as: 2J,() where lo is the maximum intensity and y=kDsin6, k being the propagation constant and e is the andle of view relative to the optical axis. The Bessel function is represented by the curve in Figure 2 The diameter of the aperture is 0.5 mm and the wavelength is 546 nm. K= 3.832 10.173 7.016 13.324 T ring 3.8 Figure 2 2nd ang () Calculate the angle 0 at which the first and second dark ring of the diffraction pattem occurs. Show your workings ciearly. (20 marks) What is the linear diameter of the Airy disc formed 4 m away? (10 marks) () If the circular aperture is replaced by a single slit of width 0.5 mm, determine the width of the central maximum at 4 m away. Compare this value to that in part i) above. (20 marks) 7/12

Answer 1

Axat donk ng Y3.83 at 2 Ko.SX16Amo 2 (516 x10) 3.832 www. iua Yx 3.4t6 x1 X ist dosk 3.832 x 3.46 A1 sin 8 -.332xo 1. 332X(O vel dosk ang Mindにチ616×3.476 x1oy 2 439 x16 さ2.439 X( diameter oai dia ia 24tamt 4tan lb) maall tau o d 332x3-10.6s6x 8x1.33 MAina de Alit ENit widt uauelength 092x10 546lo .516 8.736メ103 wicta 86 Page No.