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Bichromatic light is used in YDSE having...

Bichromatic light is used in YDSE having wavelengths
` lambda_1 = 400 nm and lambda_2= 700nm`. Find minimum order of bright fringe of `lambda_1`
which overlaps with bright fringe of `lambda_2` .

Text Solution

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Let `n_1` bright fringe of `lambda_1` overlaps with `n_2` bright fringe of `lambda_2`. Then,
`(n_1 lambda_1D)/d = (n_2 lambda_2)/d)/d` or `n_1/n_2 = lambda_2/lambda_1 = 700/400 = 7/4`

the ratio `n_1/n_2 = 7/4` implies that 7th bright fringe of `lambda_1` will overlap with 4th bright fringe of `lambda_2`.
Similarly, 14th of `lambda_1` will overlap with 8th of `lambda_2` and so on.
So, the minimum order of `lambda_1` which overlaps with `lambda_2` is 7.
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