A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observe on screen 1 m away. It is observed that the first minimum is at a distance of `2.5 mm` from the centre of the screen. Find the width of the slit.

Options

A. 0.2 mm
B. 0.3 mm
C. 0.4 mm
D. 0.5 mm

Answer

A

Explanation

Distance of first minima in diffraction pattern due to a single slit is
`x_(1)=(Dlambda)/(a)`
It is given that
`D=1m, lambda=500 mm=500xx10^(-19)m`
`x_(1)=2.5mm=2.5 xx 10^(-3)m, a=?`
`therefore a=(Dlambda)/(x_(1))=(1xx500xx10^(-9))/(2.5xx10^(-3)) m `
`=200xx10^(-6)m=0.2 mm`