1. (Worth 6 points total.) Derive the on-axis intensity (p2 = 0) as a function of 2: for an incident uniform plane wave of field amplitude E0 and wavelength A diffracting through a circular aperture of radius (1. Give the expressions for the exact HuygensFresnel solution (meaning not in the paraxial approximation), as well as the solution in the Fresnel approximation and in the Fraunhofer approximation. Give the conditions for the validity of each approximation, and produce a plot showing the on axis intensity as a function of z for all three expressions