1.

Light consisting of a plane waves of wavelength, lamda_(1)=8xx10^(-5)cmandlamda_(2)=6xx10^(-5)cm generates an interference pattern in Young's double slit experiment. If n_(1) denotes the n_(1) th dark fringe due to light of wavelength lamda_(1) which coincides with n_(2) th bright fringe due to light of wavelength lamda_(2), then

Answer»

`n_(1)=3,n_(2)=1`
`n_(1)=4,n_(2)=5`
`n_(1)=1,n_(2)=2`
`n_(1)=3,n_(2)=2`

Solution :Given, `lamda_(1)=8xx10^(-5)cmandlamda_(2)=6xx10^(-5)cm` Position `n^(th)` DARK FRINGE (due to light of wavelength `lamda_(1)`) is given by,
`x_(n_(1))=(2n_(1)XX1)(Dlamda_(1))/(2d)`
Position of `n_(2)^(th)` bright fringe due to light of wavelength `lamda_(2)` is given by
`x_(n_(2))=-(n_(2)Dlamda_(2))/(d)`
Since both the fringes are coincide to each other. Hence,
`(2n_(1)+1)(Deltalamda_(1))/(2d)=(n_(2)Dlamda_(2))/(d)`
`(2n_(1)+1)/(n_(2))=(2lamda_(2))/(lamda_(1))=(2xx6xx10^(-5))/(8xx10^(-5))`
`(2n_(1)+1)/(n_(2))=(3)/(2)`
`4n_(1)+2=3n_(2)`
`4n_(1)-3n_(2)=-2`
`4n_(1)-3n_(2)=-2""......(i)`
when `n_(1)=1andn_(2)=2`, then Eq. (i) is SATISFIED.
Hence, for `n_(1)=1andn_(2)=2` given fringes coincide to each other.


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