Light of wavelength 550nm is incident as parallel beam on a slit of width 0.1nm. Find the angular width and the linear width of the principal maxima in the resulting diffraction pattern on a screen kept at a distance of 1.1m from the slit. Which of these width would not change if the screen were moved to a distance of 2.2m from the slit .....???

 See the first thing to occur diffraction wavelength of light should be comparable to the width of the slit. here I have used slit width is equal to 0.1 mm
Most of the light is diffracted between the tow first order minima. This minima occurs at an angle given by
$$\begin{gathered} \sin \theta =\pm \frac{\lambda }{b}; where b is theslit of width. \\ =\pm \frac{550\times {10}^{-9}}{0.1\times {10}^{-3}}=5.5\times {10}^{-3} rad \end{gathered}$$
so angular width of principle maxima=$5.5\times {10}^{-3} rad$
Now linear width is given by=$l=r\times \theta =1.1\times 5.5\times {10}^{-3}=6.05\times {10}^{-3}m$
if the screen were moved to a distance of 2.2m from the slit the angular width would remain same and linear width is given by=$l=r\times \theta =2.2\times 5.5\times {10}^{-3}=1.21\times {10}^{-2}m$