Use Huygen's principle to explain the formation of a diffraction pattern due to a single slit illuminated by a monochromatic source of light. When the width of the slit is made double the original width, how would this affect the size and intensity of the central diffraction band?

Consider a parallel beam of monochromatic light incident normally on a slit of width b as shown in the figure. Consider a particular point P on the screen that receives waves from all the secondary sources. All these waves start from different places and give the resultant intensity at the point P. At P0, all waves are traveling the same optical path. As all waves are in phase, thus the interference of maximum intensity is observed. The intensity at the point P is given by I = I₀sin²α/α, where α = πb sin θ/λ. For central maxima α = 0, thus I = I₀. Width of central maxima is given by β = 2Dλ/b. D = Distance between the screen and slit; λ = wavelength of the light and b = size of the slit. So with the increase in size of the slit, the width of the central maxima decreases. Hence, doubling the size of the slit would result in half the width of the central maxima.