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Laser light of wavelength 640mm incident...

Laser light of wavelength `640mm` incident on a pair of slits produces an interference pattern in which the bright fringes are separated by `7.2mm`. Calculate the wavelength of another source of light which produces interference fringes separated by `8.1mm` using same arrangement. Also find the minimum value of the order (n) of bright fringe of shorter wavelength which coincides with that of longer wavelength.

Text Solution

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As , fringe width,
`beta=(Dlambda)/(2d)`
`:.7.2mm=(Dxx660nm)/(2d)`….`(i)`
and `8.1mm=(Dxxlambda.)/(2d)`…….`(ii)`
Diving (i) by (ii)
`:.(7.2mm)/(8.1mm)=(640nm)/(lambda.)`
or `lambda.=640xx(8.1)/(7.2)nm=720nm`
Also `y_(n)=n_(1)(Dlambda)/(2d)=n_(2)(Dlambda.)/(2d)`
or `n_(1)lambda=n_(2)lambda.`
`impliesn_(1)xx640=n_(2)xx720`
`:.(n_(1))/(n_(2))=(720)/(640)=(9)/(8)`
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