Consider the interference/ diffraction pattern from a three-slit arrangement as shown. Take d=3.5a. The wavelength of the monochromatic light incident upon the slits is ?=0.5a. The amplitude of the electromagnetic wave hitting the middle slits is half as much as those hitting the other two slits.
a. Derive an expression for the intensity I as a function of θ and other relevant parameters. Express the answer in terms of I?,the maximum intensity on the screen. Making sure to include the effects of both interference and diffraction.
b. At what angle θ1 is the first diffraction minimum away from the center of the screen?
c. How many interference maxima are present within the central diffraction peak?(Do not count the "clipped" maxima, if any)