First slide

In YDSE one of the slits is covered with a thin transparent sheet

Question

In Young’s double slit experiment, the fringes are displaced by a distance $x$ when a glass plate of refractive index 1.5 is introduced in the path of one of the beams. When this plate is replaced by another plate of the same thickness, the shift of fringes is $(3 / 2) x$ . The refractive index of the second plate is

Moderate

Solution

The fringe shift with first plate is given by $x = \frac{(μ_{1} - 1) t β}{λ} ...... (1)$
For second plate the shift is given by $\frac{3}{2} x = \frac{(μ_{2} - 1) t β}{λ} ....... (2)$
Divide (2) by (1)
$\begin{array}{l} \frac{3}{2} = \frac{μ_{2} - 1}{1.5 - 1} \\ ∴ μ_{2} = 1.75 \end{array}$

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