A fringe width of a certain interference pattern is `beta=0.002` cm. What is the distance of `5^(th)` dark fringe from centre ?

Options

A. `1.1xx10^(-2)`cm
B. `1xx10^(-2)` cm
C. `3.28xx10^(6)` cm
D. `11xx10^(-2)` cm

Explanation

Here,
Fringe width, `beta=0.002cm=2xx10^(-3)cm`
Distance of `n^(th)` dark fringe from centre
`x_(n)=(n-1/2) (lambdaD)/(d)` where `n=1, 2, 3, ..`
As `beta=(lambdaD)/(d)`
`:.x_(n)=(n-1/2)beta`
For `5^(th)` dark fringe, `n=5`
`:.x_(5)=(5-1/2)beta=9/2 beta= 9/2 xx 2xx10^(-3)` cm
`= 9 xx10^(-3)`cm
`**` None of the given options is correct.