Spectroscopy is a process for analyzing the electromagnetic emission spectrum emitted by matter. A basic spectrometer uses a diffraction grating to separate incoming light into narrow bands of color. Different wavelengths of light diffract at different angles onto a screen placed behind the grating. The image illustrates the first$-$order emission spectrum of visible light from a tube of energized hydrogen gas.

Consider a setup using a diffraction grating with $579$ lines $\frac{?}{mm}$ and an observation screen placed $1\mathrm{.}2$ cm behind the grating. Determine the distance $d$ of separation on the screen in centimeters between the first$-$order $656$ nm red light and the first$-$order $434$ nm blue light.

$d=$ cm