$8.$ The figure shows the interference pattern obtained in a double$-$slit experiment using light with a wavelength of $450$nm$.$ The slits are $2\mathrm{.}0$ um apart with a $12\mathrm{.}5$ m wide viewing screen that is $3\mathrm{.}0$ m away from the slits to produce $9$ bands on the viewing screen as shown below.c$)$ From center to center of the bands, what is the distance from band E to band B$?$d$)$ How many bands would there be if we shined light with a wavelength of $800$nm instead?e$)$ How would the picture change if we replaced the double slit with a different refraction grading with $500$ lines per mm$?$