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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

Verified by Experts

The correct Answer is:
`7^(th)`
Let `n_(1)` bright fringes of `lambda_(1)` overlaps with `n_(2)` bright fringes of `lambda_(2)`. Then,
`(n_(1) lambda_(1) D)/(d) = (n_(2) lambda_(2) D)/(d)`
or `(n_(1))/(n_(2)) = (lambda_(2))/(lambda_(2)) = (700)/(400) = (7)/(4)`
The ratio implies tha 7th bright fringe of `lambda_(1)` will overlap with 4th bright fringe of `lambda_(2)`. Similarly, 14th bright fringe of `lambda_(1)` will overlap with 8th bright fringe of `lambda_(2)` and so on. So, the minimum order of `lambda_(1)` which of overlaps with `lambda_(2)` is 7.
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