Light of `lambda = 550 nm` is incident as parallel beam on a slit of width `0.1 mm`. Find the angular width and linear width of the principal maximum in the diffraction pattern on a screen at a distance of `1.1m` from thw slit. Which of these widths will not change if the screen were moved to a distance of `2.2 m` from the slit ?

Explanation

Given, wavelength of light,
`lambda = 550 nm = 550 xx 10^(-9) m`
Width of slit, `b = 0.1 mm = 0.1 xx 10^(-3)m`
Distance of screen from the slit, `D = 1.1m`
Angular width of central maximum is
`2 theta = (2 lambda)/b = (2 xx 550 xx 10^(-9))/(0.1 xx 10^(-3)) = 0.011 rad`
Linear width of central maximum is
`beta_0 = (2 Dlambda)/(b) = D xx 2 theta = 1.1 xx 0.011`
`= 0.0121m = 12.1 mm`
Angular width will not change on moving the screen away from the slit because it is independent of D.