A single slit of width 0.25mm is illuminated successively by red light of wavelength 700nm and blue light of wavelength 460nm. The screen is kept 1.8m from the slit.
(a) Derive an expression for the ratio of the linear widths of the central diffraction maxima produced by the two wavelengths in terms of the given quantities.
(b) Using the expression obtained in part (a), calculate the numerical ratio and determine the actual linear widths for both colours.
(c) Comment on how the result illustrates the dependence of diffraction on wavelength and its relevance for resolving closely spaced objects of different colours.