In a Young's double slit experiment, the line-width of a bright fringe is occasionally defined as the distance between the points on either side of the central line at which the intensity drops to half of its maximum value. Determine this line-width in terms of , d , and D , assuming these symbols carry their standard meanings.

Step-by-step solution

The intensity of light in Young's double slit experiment is given by I = I_ max ^2 ( 2 ) , where is the phase difference. For the intensity to drop to half of its maximum value, I = I_ max 2 . ^2 ( 2 ) = 1 2 ( 2 ) = 1 2 2 = 4 = 2 The phase difference is related to the path difference x by = 2 x . 2 x = 2 x = 4 In YDSE, the path difference is x = y d D , where y is the distance from the central maximum. y d D = 4 y = D 4d The line-width is the distance between these two points on either side of the central maximum: