Q. 32

# The line-width of a bright fringe is sometimes defined as the separation between the points on the two sides of the central line where the intensity falls to half the maximum. Find the line-width of a bright fringe in a Young’s double slit experiment in terms of λ. d and D where the symbols have their usual meanings.

Answer :

Given, separation between the slits

The distance between the screen and the slit,

Wavelength of light, .

Let the maximum intensity be and the intensity at y be .

Given,

therefore, path difference,

But the fringe extends to both sides of the maximum. Hence, the line width is

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Consider the arrangement shown in figure (17-E7). By some mechanism, the separation between the slits S_{3} and S_{4} can be changed. The intensity is measured at the point P which is at the common perpendicular bisector of S_{1}S_{2} and S_{3}S_{4}. When , the intensity measured at P is I. Find this intensity when z is equal to

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