Light of wavelength `lambda` is incident on slit of width d. The resulting diffraction pattern is observed on a screen placed at distance D. The linear width of central maximum is equal to width of the slit then D = .......

Options

A. `(d^(2))/(2lambda)`
B. `(d)/(lambda)`
C. `(2lambda^(2))/(d)`
D. `(2lambda)/(d)`

Answer

A

Explanation

For first order diffraction,
`d sin theta= lambda`
For small angle,
`d (theta)=lambda`
For first order diffraction on both side of Q,
`d(2 theta)=2lambda`
but `theta=(x)/(D)`
`:.d((2x)/(D))=2lambda`
`:.(d(d))/(D)=2lambda( :.2x=d` given )
`:.(d^(2))/(D)=2 lambda`
`:.D=(d^(2))/(2lambda)`