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In a double slit pattern (lambda = 6000Å...

In a double slit pattern `(lambda = 6000Å)`, the first order and tenth order maxima fall at 12.50 mm and 14.55mm from a particular reference point. If `lambda` is changed to 5500Å, find the position of zero order and tenth order fringes, other arrangements remaining the same.

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Distance between 10 fringes is
`9beta = (14.75-12.50)mm=2.25mm`
`:.` Fringe width `beta=0.25mm`
As fringe width `prop lambda`
When the wavelength is changed from `6000Å` to `5500Å` then the new fringe width will become
`beta'=((5500)/(6000))beta=((5500)/(6000))(0.25)`
`beta'=0.23mm`
The produce of central for zero order maxima will remain unchanged Earlier it was at a position
`y_(0)=y_(1)=beta`
`=12.50-0.25=12.25mm`
The new position of tength order maxima will be
`y_(10)=y_(0)+10beta'`
`=12.25+(10)(0.23)=14.55mm`
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