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(a) Describe briefly how a dffraction pattern is obtained on a screen due to a single narrow slit illuminated by a monochromatic source of light. Hence obtain the conditions for the angular width of secondary maxima and secondary minima. (b) Two wavelengths of sodium light of 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture 2 xx 10^(-6) m. The distance between the slit and the screen is 1.5 m. Calculate the separation between the positions of first maxima of the diffraction pattern obtained in the two cases. |
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Answer» SOLUTION :`lambda_1 = 590 nm = 590 xx 10^(-9) m` `lambda_2 = 596 nm = 596 xx 10^(-9) m` `D = 1.5 m , a = 2 xxx 10^(-6) m` x is DISTANCE of first secondary maxima for CENTRE of SCREEN `x = 3/2 (LAMBDA D)/a` For two wavelengths `lambda_1 and lambda_2` we have `x_1 = 3/2 (lambda_1D)/a, x_2 = 3/2 (lambda_2D)/(a)` `x_2 - x_1 = 3/2 D/a (lambda_2 - lambda_1)` `= 3/2 xx (1.5)/(2 xx 10^(-6)) xx 6 xx 10^(-9)` `= 6.75 xx 10^(-3) m`. |
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