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Transcript

DIFFRACTION Diffraction is the penetration of light wave towards the geometrical shadow region around a sharp obstacle such as the edge of a slit, sharp aperture etc. (a) In Fresnel class of diffraction, the source and/or screen are at a finite distance from the aperture. The wave front is either spherical or cylindrical in shape (b) In Fraunhoffer class of diffraction, the source and screen are at infinite distance from the diffracting aperture. The wave front is plane. Single slit Fraunhoffer diffraction P A slit of width ‘a’ is divided into N parallel strips of width x. Each strip acts as a radiator of Huygens’s wavelets and produces a characteristic wave disturbance at P, whose position on the screen for a particular arrangement of apparatus can be described by the angle . a If the strips are narrow enough – which we assume – all points on a given strip have essentially the same optical path length to P, and therefore all the light from the strip will have the same phase when it arrives at P. The amplitudes E0 of the wave disturbances at P from the various strips may be taken as equal if is not too large. The wave disturbances from adjacent strips have a constant phase difference between them at P, given by phase difference path difference 2 2 x sin Thus at P, N vectors with the same amplitude E0, the same frequency and the same phase difference DF between adjacent members combine to produce a result disturbance. In the R limiting case (N → ∞), → 0 R From geometry E E 2R sin , m R 2 E E m .sin /2 2 sin , where Or E E m . 2 En Em As 2 a sin sin As I E I I m In brief sin E E m ; a sin 2 2 sin I I m ; a sin 2 2 Single slit diffraction formula Minima occur when, a = np n – 1, 2, 3……. a sin x sin x n . If q is small, min Condition for minima a For n 3, it can be assumed that the nth secondary maximum is midway between the adjacent minima. If we know the shape of front at t = 0 then from Huygens principle allows us to determine the shape of wave front at any time t. Let us consider a diverging wave originating from point 0. f1 f2 represent a portion of the spherical wave front at t = 0 Now according to Huygens principle, each point of the wave front is the source of a secondary disturbance and the wavelets emanating from these points spread out in all dandies with the speed of the wave. These wavelets emanating from the wave front are usually referred to as secondary wavelets and if we draw a common tangent to all these spheres we obtain the new position of the wave front at dater time. Thus if we wish to determine the shape of the wave front at t = we draw the sphere of radius v from each point on the spherical wave front. The common tangent draw to all these spheres gives the new position of the wave front C1 C2 with center at O. we also have a back wave which is shown as 1 2. According to Huygens the amplitude of the secondary wavelength in forward direction and zero in the backward direction Sandeep tiwari