Coherent sources and their importance in interference

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Question

In YDSE, find the thickness $(in μm)$ of a glass slab $(μ = 1 .5)$ which should be placed before the upper slit S₁ so that the central maximum now lies at a point where 5th bright fringe was lying earlier (before inserting the slab). Wavelength of light used is $5000 Å$ .

Moderate

Solution

According to the question, shift = 5 (fringe width)
$\begin{array}{l} ∴ \frac{(μ - 1) tD}{d} = \frac{5 λD}{d} \\ ∴ t = \frac{5 λ}{μ - 1} = \frac{25000}{1 .5 - 1} = 50, 000 Å = 5 \times 10^{- 6} m \end{array}$

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