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How can we determine maximum number of fringes displayed in screen How can we determine maximum number of fringes displayed in screen
Path difference = n*lambda = d*sin(theta)where n Is some positive real number, d is the inter-slit distance, theta is the angle is subtended by the fringe at the point lying midway the two slits and lambda is the wavelength of light.For the very last fringe (bright) on the distant screen, the angle theta = 90 degrees. So the above formula becomes n*lambda = d*sin(90) = d*1 = dTherefore, n*lambda = d which implies n = d/lambdaHowever, because the number of fringes has to be a whole number, it becomes necessary to introduce a floor function (aka greatest integer function). That is,floor(n) = [n] = number of fringes on one half of the screenHence, total number of fringes = number of fringes on both halves of the screen plus the lone central maxima at the center of the screenThat is, total number of fringes = 2[n]+ 1 = 2[d/lambda]+1This is the method of calculating total number of fringes based on the conventional analysis of Young’s Double Slit ExperimentHope it helpsThanks and regardsArun
Path difference = n*lambda = d*sin(theta)
where n Is some positive real number, d is the inter-slit distance, theta is the angle is subtended by the fringe at the point lying midway the two slits and lambda is the wavelength of light.
For the very last fringe (bright) on the distant screen, the angle theta = 90 degrees. So the above formula becomes n*lambda = d*sin(90) = d*1 = d
Therefore, n*lambda = d which implies n = d/lambda
However, because the number of fringes has to be a whole number, it becomes necessary to introduce a floor function (aka greatest integer function). That is,
floor(n) = [n] = number of fringes on one half of the screen
Hence, total number of fringes = number of fringes on both halves of the screen plus the lone central maxima at the center of the screen
That is, total number of fringes = 2[n]+ 1 = 2[d/lambda]+1
This is the method of calculating total number of fringes based on the conventional analysis of Young’s Double Slit Experiment
Hope it helps
Thanks and regards
Arun
Dear student For more informaton please refer this https://www.askiitians.com/forums/Wave-Motion/how-can-we-determine-maximum-no-of-fringes-displa_258196.htmGood Luck
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