The two slits are 1 mm apart from each other and illuminated with a light of wavelength `5xx10^(-7)` m. If the distance of the screen is 1 m from the slits, then the distance between third dark fringe and fifth bright fringe is

Options

A. `1.5` mm
B. `0.75` mm
C. `1.25` mm
D. `0.625` mm

Answer

C

Explanation

Given : `lambda=5xx10^(-7) m, D=1 m, d=1 mm`
where `n=1, 2, 3,` …
-Distance of `n^(th)` bright fringe from the center `=(nDlambda)/(d)`
So the distance of `5^(th)` bright fringe `=(5Dlambda)/(d)`
Distance of `n^(th)` dark fringe from the center `=(n+(1)/(2))(Dlambda)/(d)`
where `n=1, 2, 3, 4,` .......
`3^(rd) "dark fringe" =(3-(1)/(2))(Dlamda)/(d)=(5)/(2)(Dlamda)/(d)`
Distance between them `=(5-(5)/(2))(Dlamda)/(d)=(5)/(2)(Dlambda)/(d)`
`=(5xx1xx5xx10^(-7))/(2xx1xx10^(-3))=12.5xx10^(-4) m =1.25 mm`