Two wavelengths ?? and ?? are used in Young's double slit experiment. ?? = 450 nm and ?? = 650 nm. The minimum order of fringe produced by ?? which overlaps with the fringe produced by ?? is n. The value of n is

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Solution

Q.
Two wavelengths $λ_{1}$ and $λ_{2}$ are used in Young's double slit experiment. $λ_{1}$ = 450 nm and $λ_{2}$ = 650 nm. The minimum order of fringe produced by $λ_{2}$ which overlaps with the fringe produced by $λ_{1}$ is $n$ . The value of $n$ is ____. [2024]

Ans.
(9)    $m_{2} λ_{2} = m_{1} λ_{1}$

   $\frac{m_{2}}{m_{1}} = \frac{λ_{1}}{λ_{2}} = \frac{450}{650} = \frac{9}{13}$

$i . e . 9^{th} maxima of λ_{2} overlaps with 13^{th} maxima of λ_{1} .$

   $∴ n = 9$

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