A scientist is investigating the spectral lines of a new gas. They use a grating

with $5000$ lines per centimeter. A screen is placed a distance $12\mathrm{.}1$ cm from the

grating and is parallel to the grating. If the gas produced visible light of just

two wavelengths, $500$ nm and $419$ nm$,$ how far apart do the m $=2$ order maxima

appear for these two wavelengths? Report your answer in units of mm$.$