For a parallel beam of monochromatic light wavelength `lambda` diffraction is produced by single slit whose width 'a' is of the order of th wavelength of the light. If 'D' is the distance the screen from the slit, the width of th central maxima will be ......

Options

A. `(2Dlambda)/(a)`
B. `(Dlambda)/(a)`
C. `(Da)/(lambda)`
D. `(2Da)/(lambda)`

Answer

A

Explanation

The width of central maxima means the distance between two first minimum on the screen
`:.` Condition for first minimum.
In `d sin theta= n lambda, d=a, n=1`
`:.sin theta=(lambda)/(a)`
`:.` Linear width of central maximum
=`D|2 theta|`
`=(2Dlambda)/(a)" " [ :.` for small angle `sin theta ~~ theta]`