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Bichromatic light is used in YDSE having...

Bichromatic light is used in YDSE having wavelengths `lambda_(1)=400nm` and `lambda_(2)=700nm` Find minimum order of `lambda_(1)` which overlaps with `lambda_(2)`

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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_(1)D)/d=(n_(2)lambda_(2)D)/d`

or `n_(1)/n_(2)=lambda_(2)/lamda_(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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