$1$:Consider a standard double slit experiment as shown. Monochromatic $($say $=532$ nm$),$ coherent, laser light is incident from the left and forms our double slit interference pattern. Ignore single slit diffraction in this problem. The locations of the first three maxima are indicated for reference$\mathrm{.}1.$a$)$ Consider placing the entire apparatus within a fluid with n $=1\mathrm{.}5.$ Describe and sketch the resulting interference pattern that and briefly describe why it takes this form$\mathrm{.}1.$b$)$ Consider placing a material that has a wildly fluctuating index of refraction, n$($t$),$ where changes occur on the order of $1014$ Hz$.$ Describe and sketch the resulting interference pattern that would be seen by your eyes and briefly describe why it takes this form. $1.$c$)$ Consider placing polarizers behind each slit, H is behind the upper slit and V behind the lower. Describe and sketch the resulting interference pattern and briefly describe why it takes this form$\mathrm{.}1.$d$)$ Consider placing polarizers behind each slit, H is behind the upper slit and P behind the lower. Describe and sketch the resulting interference pattern and briefly describe why it takes this form. $1.$e: Monochromatic, coherent, laser light passes through a number of narrow, equally$-$spaced, slits and forms the interference pattern shown. Ignore single slit diffraction $($though a portion of it is displayed in the figure$).$ How many slits did the light pass through? $($Think about what the phase difference is for each principal maxima is $($taller peaks$)$ and the number of minima between two principal maxima.$)$