$37.$ A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence of $\backslash (50\mathrm{.}0^\{\backslash$circ$\}\backslash ).$ The index of refraction of quartz is $1\mathrm{.}455$ at $600$ nm $($red light$),$ and its index of refraction is $1\mathrm{.}468$ at $410$ nm $($violet light$).$ Find the dispersion of the slab, which is defined as the difference in the angles of refraction for the two wavelengths.