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In a Young's double slit experiment using red and blue lights of wavelengths 600 \mathrm{~nm} and 480 \mathrm{~nm} respectively, the value of \mathrm{n} for which the \mathrm{nth} red fringe coincides with (\mathrm{n}+1) th blue fringe is:

Option: 1

5


Option: 2

4


Option: 3

3


Option: 4

2


Answers (1)

best_answer

Let nth red coincides with mth blue, then

\mathrm{\begin{aligned} & \frac{\mathrm{n} \lambda_{\mathrm{R}} \mathrm{D}}{\mathrm{d}}=\frac{\mathrm{m} \lambda_{\mathrm{B}} \mathrm{D}}{\mathrm{d}} \\ & \therefore \frac{\mathrm{n}}{\mathrm{m}}=\frac{\lambda_{\mathrm{B}}}{\lambda_{\mathrm{R}}}=\frac{480}{600}=\frac{4}{5} \end{aligned}}

i.e., \mathrm{ 4^{\text {th }}} red coincides with \mathrm{ 5^{\text {th }}} blue. Next \mathrm{ 8^{\text {th }}} red will coincide with \mathrm{10^{\text {th }}} blue and so on. Thus,\mathrm{ n=4} and \mathrm{ \quad m=n+1=5}

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manish

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