In a Young's double-slit experiment,the slits | vedclass

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(D) Let the $n^{th}$ bright fringe of the first wavelength coincide with the $m^{th}$ bright fringe of the second wavelength.For bright fringes,the po

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$4.5$

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(D) Let the $n^{th}$ bright fringe of the first wavelength coincide with the $m^{th}$ bright fringe of the second wavelength.For bright fringes,the position $y$ is given by $y = \frac{n \lambda_1 D}{d} = \frac{m \lambda_2 D}{d}$.Thus,$\frac{n}{m} = \frac{\lambda_2}{\lambda_1} = \frac{9000 \, \mathring{A}}{7500 \, \mathring{A}} = \frac{6}{5}$.The first point of coincidence occurs at $n = 6$ and $m = 5$.The distance $y$ from the central maximum is $y = \frac{n \lambda_1 D}{d} = \frac{6 	imes 7500 	imes 10^{-10} \, m 	imes 2 \, m}{2 	imes 10^{-3} \, m}$.$y = 6 	imes 7500 	imes 10^{-7} \, m = 45000 	imes 10^{-7} \, m = 4.5 	imes 10^{-3} \, m = 4.5 \, mm$.

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