A diffraction grating having $190$ lines$/$mm is illuminated with a light signal containing only two wavelengths, lambda$\_\{1\}=412$ nm and lambda$\_\{2\}=515$ nm$.$ The signal is incident perpendicularly on the grating. $($a$)$ What is the angular separation between the second$-$order maxima of these two wavelengths? $($b$)$ What is the smallest angle at which two of the resulting maxima superimposed? $($c$)$ What is the highest order for which maxima for both wavelengths are present in the diffraction pattern?