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 ?

Answer

`1.1 xx 10^(-2) rad ; 12.1 mm`. Former will not change

Explanation

Here, `lambda = 550 nm = 5.5 xx 10^(-7)m`,
`a = 0.1 mm = 10^(-4)m, D = 1.1 m`
Angular width of principal maximum,
`2 theta = (2 lambda)/(a) = (2 xx 5.5 xx 10^(-7))/(10^(-4)) = 1.1 xx 10^(-2) rad`
Linear width pf principal maximum
`x = (2 theta) D = 1.1 xx 10^(-2) xx 1.1`
`= 1.21 xx 10^(-2)m = 1.21 mm`
When the screen os moved. `D` is changed linear width changes, angular width does not change