In Young's double slit experiment the separation between the slits is doubled without changing other setting…

In Young's double slit experiment the separation between the slits is doubled without changing other setting of the experiment to obtain same fringe width, the distance ' $\mathrm{D}$ ' of the screen from slit should be made
  1. $\frac{D}{2}$
  2. $\frac{\mathrm{D}}{\sqrt{2}}$
  3. $2 \mathrm{D}$
  4. $4 \mathrm{D}$

Solution

Fringe width, $\mathrm{W}=\frac{\lambda \mathrm{D}}{\mathrm{d}}$ Given: $\mathrm{d}=2 \mathrm{~d}$ $\Rightarrow \mathrm{W}^{\prime}=\frac{\lambda \mathrm{D}^{\prime}}{2 \mathrm{~d}}$ Since given, $\begin{aligned} & \mathrm{W}=\mathrm{W}^{\prime} \\ \therefore & \frac{\lambda \mathrm{D}}{\mathrm{d}}=\frac{\lambda \mathrm{D}^{\prime}}{2 \mathrm{~d}} \\ \therefore & \mathrm{D}^{\prime}=2 \mathrm{D} \end{aligned}$

Asked in: MHT CET 2023 (10 May Shift 1)

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