Q34 of 79 Page 380

Consider the arrangement shown in figure (17-E7). By some mechanism, the separation between the slits S3 and S4 can be changed. The intensity is measured at the point P which is at the common perpendicular bisector of S1S2 and S3S4. When , the intensity measured at P is I. Find this intensity when z is equal to


Let the intensity of slits and be . For and , The distance from the central maximum is .

So the path difference is


Given,



And the corresponding phase difference is



Now, intensity at each slit is given by



Here, P is also central maxima. So the intensity is



(a)For ,


and



Therefore, intensity at each slit is


.


This means that both slits and would be dark. Thus intensity at P would be zero.


(b)For ,


and



Therefore, intensity at each slit is


.


Hence intensity at P is


(c)For ,


and



Therefore, intensity at each slit is


.


Hence intensity at P is

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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.

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Consider the situation shown in figure (17-E6). The two slits S1 and S2 placed symmetrically around the central line are illuminated by a monochromatic light of wavelength λ. The separation between the slits is d. The light transmitted by the slits falls on a screen ∑1 placed at a distance D from the slits. The slit S3 is at the central line and the slit S4 is at a distance z from S3. Another screen ∑2 is placed a further distance D away from ∑1. Find the ratio of the maximum to minimum intensity observed on ∑2 if z is equal to

(a)


(b)


(c)



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