In the Young's double slit experiment, the slits are 0.4 cm apart and the screen is 100 cm awayIf the wavelength of light used is 5000 Å then the distance between the fourth dark fringe and central bright will be ......

Options

A. `4.37xx10^(-2) cm`
B. `4.37 cm`
C. `4.37xx10^(-1) cm`
D. `8.74 cm`

Answer

A

Explanation

For `n^(th)` dark fring,
`d sin theta_(n)=(2n-1)(lambda)/(2)`
but `sin theta_(n)=(x_(n))/(D)`
`:.(dx_(n))/(D)=(2n-1) (lambda)/(2)`
`:.x_(n)=((2n-1)lambdaD)/(2d)`, here `n=4, d=0.4 cm`
`lambda=5xx10^(-5)cm, D=100 cm and n=4`
`:.x_(4)=(7lambdaD)/(2d)`
`=(7xx5xx10^(-5)xx100)/(2xx0.4)`
`:.x_(4)=4.37xx10^(-2) cm`