Obtain the expression for shift in fringes when a thin transparent sheet is introduced in the path of one of the waves in a double slit interference experiment.

In a double-slit interference experiment, when a thin transparent sheet is introduced in the path of one of the waves, it creates a phase difference between the two interfering waves, resulting in a shift in the fringes observed on the screen. This phenomenon is known as the phase shift or path difference, and it can be derived using principles of wave optics.

Let's consider a typical setup for a double-slit interference experiment. We have a coherent light source emitting monochromatic light, which passes through two narrow slits (S1 and S2) and then onto a screen where interference fringes are observed. The light waves emanating from the two slits are coherent, meaning they have a constant phase relationship.

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