A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000Å and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is _______ mm.

Options

A. 3 mm
B. 9 mm
C. 4.5 mm
D. 1.5 mm

Answer

B

Explanation

a = 0.1 mm = `10^(-4)cm`,
`lamda=6000xx10^(-10)cm=6xx10^(-7)cm,D=0.5m`
for `3^(rd)` dark band, a `sintheta=3lamda`
or `sintheta=(3lamda)/a=x/D`
The distance of the third dark from the central bright band
`x=(3lamdaD)/a=(3xx6xx10^(-7)xx0.5)/10^(-4)=9mm`