A chemist identifies compounds by identifying bright lines in their spectra. She does so by heating the compounds until they glow, sending the light through a diffraction grating, and measuring the positions of first$-$order spectral lines on a detector $15\mathrm{.}0$ cmcm behind the grating. Unfortunately, she has lost the card that gives the specifications of the grating. Fortunately, she has a known compound that she can use to calibrate the grating. She heats the known compound, which emits light at a wavelength of $421$ nmnm$,$ and observes a spectral line $9\mathrm{.}95$ cmcm from the center of the diffraction pattern.

Part A

What is the wavelength emitted by compound AA that have spectral line detected at position $8\mathrm{.}55$ cmcm$?$

Part B

What is the wavelength emitted by compound BB that have spectral line detected at position $12\mathrm{.}15$ cmcm$?$

Express your answer with the appropriate units.