A beam of light of wavelength 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. What is the distance between the first dark fringe on either side of the central bright fringe?

Options

A. `1.2` cm
B. `1.2` mm
C. `2.4` cm
D. `2.4` mm

Answer

D

Explanation

In case of diffraction at a single slit, the position of minima is given by
`dsintheta=nlambda`
If `theta` is small, `sintheta~~theta=(y)/(D)`
So, the position of first minimum relative to centre will be given by `d(y//D)=lambda,i.e.,y=(D//d)lambda`
Here, `D=2m,d=1xx10^(-3) "m and" lambda=6xx10^(-7)m`
So, `y=(2xx6xx10^(-7))/(1xx10^(-3))=1.2"mm"`
`:.` Distance between first minima on either side of central maxima, `Deltay=2y=2.4"mm"`