Problem $3.$ Diffraction gratings with $10,000$ lines per centimeter are readily available. Suppose you have one, and you send a beam of white light through it to a screen $2\mathrm{.}00$ m away. $($a$)$ Find the angles for the first$-$order diffraction of the shortest and longest wavelengths of visible light $(380$ and $760$ nm$).($b$)$ What is the distance between the ends of the rainbow of visible light produced on the screen for first$-$order interference?