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. The distance between the first dark fringes on either side of the central bright fringe is

Options

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

Answer

D

Explanation

For diffraction through a single slit, the position of minima is given by
`d sin theta = nlambda`
IF `theta` is small, `sin theta = theta = (Y)/(D)`
Thus, the position of first minimum relative to centre will be given by
`d(y//D) = lambda, y = (D//d) lambda`
Here, D = 2m , `d = 1 xx 10^(-3)` and `lambda = 6 xx 10^(-7) m`
So `y = (2 xx 6 xx 10^(-7))/(1 xx 10^(-3)) = 1.2 mm`
`therefore` Distance between first minima on either side of central maxima,
`triangley = 2y = 2.4 mm.`