(a) In Young's double slit experiment, describe briefly how bright and dark fringes are obtained on the screen kept in front of a double slit. hence obtain the expression for the fringe width. (b) The ratio of the intensities at minima to the maxima in the Young's double slit experiment is $9:25$. Find the ratio of the widths of the two slits. OR (a) Describe briefly how a diffraction pattern is obtained on a screen due to a single narrow slit illuminated by a monochromatic source of light. Hence obtain the conditions for the angular width of secondary maxima and secondary minima. (b) Two wavelength s of sodium light of $590\,\mathrm{nm}$ and $596\,\mathrm{nm}$ are used in turn to study the diffraction taking place at a single slit of aperture $2 \times 10^{-6}$ $\mathrm{m}$. The distance between the slit and the screen is $1.5\,\mathrm{m}$. Calculate the separation between the positions of first maxima of the diffraction pattern obtained in the two cases.