$($a$)$ Young's double$-$slit experiment is performed with $565-$nm light and a distance of $2\mathrm{.}00$ m between the slits and the screen. The tenth interference

minimum is observed $7\mathrm{.}00$ mm from the central maximum. Determine the spacing of the slits $($in mm $).$

mm

$($b$)$ What If$?$ What are the smallest and largest wavelengths of visible light that will also produce interference minima at this location? $($Give your

answers, in nm$,$ to at least three significant figures. Assume the visible light spectrum ranges from $400$ nm to $700$ nm $.)$

smallest wavelength

xxnm

largest wavelength

nm