Two sources of light of wavelengths 2500 ,mat | vedclass

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(B) In Young's double slit experiment,the position of the $n^{th}$ bright fringe for a wavelength $\lambda$ is given by $y_n = \frac{n \lambda D}{d}$.

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$7^{th}$ order of $1^{st}$ source and $5^{th}$ of the $2^{nd}$

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(B) In Young's double slit experiment,the position of the $n^{th}$ bright fringe for a wavelength $\lambda$ is given by $y_n = \frac{n \lambda D}{d}$.For two wavelengths $\lambda_1 = 2500 \,\mathring{A}$ and $\lambda_2 = 3500 \,\mathring{A}$ to coincide at the same position $y$,we have:$n_1 \lambda_1 = n_2 \lambda_2$Substituting the given values:$n_1 	imes 2500 = n_2 	imes 3500$$\frac{n_1}{n_2} = \frac{3500}{2500} = \frac{7}{5}$This implies that the $7^{th}$ order fringe of the $1^{st}$ source $(\lambda_1 = 2500 \,\mathring{A})$ coincides with the $5^{th}$ order fringe of the $2^{nd}$ source $(\lambda_2 = 3500 \,\mathring{A})$.

Two sources of light of wavelengths $2500 \,\mathring{A}$ and $3500 \,\mathring{A}$ are used in Young's double slit experiment simultaneously. Which orders of fringes of the two wavelength patterns coincide?

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