1. Tardigrade
  2. Question
  3. Physics
  4. In Young's double slit experiment, the slits are 2mm apart and are illuminated by photons of two wavelengths λ1 = 12000 mathring A and λ2 = 10000 mathring A. At what minimum distance from the common central bright fringe on the screen 2m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other ?

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Q. In Young's double slit experiment, the slits are 2mm apart and are illuminated by photons of two wavelengths $\lambda_1 = 12000 \mathring A $ and $\lambda_2 = 10000 \mathring A.$ At what minimum distance from the common central bright fringe on the screen 2m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other ?

NEETNEET 2013Wave Optics

Solution:

According to question $ n_1 \lambda_1 = n_2 \lambda_2$
So $\frac{n_1}{n_2} = \frac{\lambda_2}{\lambda_1} = \frac{10000}{12000} = \frac{5}{6}$
so minimum $n_1$ and $n_2$ are 5 and 6 respectively
$ X_{min} = \frac{n_1 \lambda_1 D}{d} = \frac{5(12000 \times 10^{-10})(2)}{2 \times 10^{-3}}$
$ = 6 \times 10^{-3} m = 6 mm $