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In Young's experiment fifth bright fring...

In Young's experiment fifth bright fringe produced by light of `4000Å` superposes on the fourth bright fringe of an unknown wavelength. Find the unknown wavelength.

Text Solution

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Here, `lamda_(1)=4000Å,n_(1)=5,n_(2)=4`
Distance between two consecutive fringes for wavelength `lamda_(1)` is `beta_(1)` and that for wavelength `lamda_(2)` it is `beta_(2)`.
Here distance of `n_(1)^(th)` fringe from central maximum=distance of `n_(2)^(th)` fringe from central maximum.
`:.n_(1)beta_(1)=n_(2)beta_(2)`
`:.n_(1)(lamda_(1)D)/(d)=n_(2)(lamda_(2)D)/(d)" "[:.beta=(lamdaD)/(d)]`
`:.n_(1)lamda_(1)=n_(2)lamda_(2)`
`:.lamda_(2)=(n_(1)lamda_(1))/(n_(2))`
`:.lamda_(2)=(n_(1)lamda_(1))/(n_(2))`
`:.lamda_(2)=(5xx4000)/(4)`
`:.lamda_(2)=5000Å`
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