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631.


Problem 45.10 (RHK)


A thin flake of mica is used to cover one slit of a double-slit arrangement. The central point on the screen is occupied by what used to be the seventh bright fringe. If , we have to find the thickness of the mica.


Solution:           Click For PDF Version

In the absence of the mica sheet the position of the seventh bright fringe is given by the condition that

.

Let the thickness of the mica sheet be . The refractive index of mica is

.

When the mica sheet is inserted as shown in the figure, the optical path corresponding to ray gets changed to

.

It is given that after the mica sheet has been inserted, the central point on the screen is occupied by what used to be the seventh bright fringe. Therefore, we have