In Young's double slit experiment with monochromatic light, fringes are obtained on a screen placed at some…

In Young's double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by $5 \times 10^{-2} \mathrm{~m}$ towards the slits, the change in fringe width is $3 \times 10^{-5} \mathrm{~m}$. If the separation between the slits is $10^{-3} \mathrm{~m}$, the wavelength of light used is
  1. $6000 Å$
  2. $5000 Å$
  3. $45000 Å$
  4. $3000 Å$

Solution

$\begin{aligned} & \omega=\frac{\lambda D}{d} \\ & \Rightarrow \Delta \omega=\frac{\lambda(\Delta D)}{d} \\ & \therefore \lambda=\frac{(d)(\Delta \omega)}{\Delta D}=\frac{\left(\left(10^{-3}\right)\left(3 \times 10^{-5}\right)\right)}{5 \times 10^{-2}}=0.6 \times 10^{-6} \mathrm{~m}=6000 Å\end{aligned}$

Asked in: MHT CET 2022 (08 Aug Shift 1)

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