In an interference experiment, the $\mathrm{n}^{\text {th }}$ bright fringe for light of wavelength…

In an interference experiment, the $\mathrm{n}^{\text {th }}$ bright fringe for light of wavelength $\lambda_1(n=0,1,2,3 \ldots)$ coincides with the $\mathrm{m}^{\text {th }}$ dark fringe for light of wavelength $\lambda_2(m=1,2,3 \ldots)$. The ratio $\frac{\lambda_1}{\lambda_2}$ is
  1. $\frac{m-1}{n}$
  2. $\frac{2 \mathrm{~m}-1}{\mathrm{n}}$
  3. $\frac{2 \mathrm{~m}-1}{2 \mathrm{n}}$
  4. $\frac{2 \mathrm{~m}+1}{2 \mathrm{n}}$

Solution

As $\mathrm{n}^{\text {th }}$ bright fringe coincides with $\mathrm{m}^{\text {th }}$ dark fringe $\begin{array}{ll} \therefore & \frac{\mathrm{n} \lambda_1 \mathrm{D}}{\mathrm{~d}}=\frac{(2 \mathrm{~m}-1) \lambda_2 \mathrm{D}}{2 \mathrm{~d}} \\ \therefore & \frac{\lambda_1}{\lambda_2}=\frac{(2 \mathrm{~m}-1)}{2 \mathrm{n}} \end{array}$ /

Asked in: MHT CET 2024 (03 May Shift 1)

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