A double$-$slit experiment is illuminated, from a distant source, with monochromatic light of wavelength $.$ The width of the slits is $<<$ and the interference pattern is viewed on a distant screen. A thin piece of glass of thickness $,$ index of refraction n$,$ is placed between one of the slits and the screen, perpendicular to the optical light path, and the intensity at the central point P is recorded as a function of the thickness $.$ Assume that the glass does not absorb or reflect any light. a$)$ What is the intensity at the point P as a function of $?$ b$)$ For what values of is the intensity at P a minimum? $(10)(5)$ c$)$ Suppose that the width of one of the slits is now doubled while the other one remains unchanged. What is the intensity at the point P as a function of $?$