$35\mathrm{.}11$ Two thin parallel slits that are $0\mathrm{.}0116$ mm apart are illuminated by a laser beam of wavelength $585$ nm$.($a$)$ On a very large distant screen, what is the total number of bright fringes $($those indicating complete constructive interference$),$ including the central fringe and those on both sides of it$?$ Solve this problem without calculating all the angles! $($Hint: What is the largest that can be$?$ What does this tell you is the largest value of $)($b$)$ At what angle, relative to the original direction of the beam, will the fringe that is most distant from the central bright fringe occur?