(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 wavelengths of sodium light 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture 2 x 10⁻⁶m. The distance between the slit and the screen is 1.5 m. Calculate the separation between the positions of first maxima of the diffraction pattern obtained in the two cases.

(a)The phenomenon of diffraction of light around the sharp corners of an obstacle and spreading into the regions of geometrical shadow is called diffraction.From the diagram, approximate path difference is given by:BN=ABsin(θ)=asin(θ)For BN=nλ, constructive interference occursHence,nλ=asin(θn)This is the nth bright fringe.tanθn=yn/DFor small θn,sinθn≈tanθnyn=nλD/aWidth of the secondary maximum, β=yn−yn−1=λD/aFollowing same lines, width of secondary minimum comes out to be the same (b)For first maximum,y1=λD/aFor 590 nm,y1,590=590×10⁻⁹×1.5/(2×10⁻⁶)y1,590=0.4425mFor 596 nm,y1,596=596×10⁻⁹×1.5/(2×10⁻⁶)y1,596=0.447mSeparation isy1,596−y1,590=0.0045m