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OK, the light hits the subject, certain distinct wavelengths are absorbed, the light then travels thru oxygen, nitrogen, etc. Hits a prism, which is made out of carbon, I believe. And is then split, revealing the missing wavelengths. Why are the fingerprints of the oxygen, nitrogen, carbon etc. not showing up?

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  • $\begingroup$ They would show up if your detector were sensitive enough. $\endgroup$ – garyp Mar 20 '17 at 18:06
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I guess you talk a lab experiment on earth. Moreover, it is probably a glass prism so SiO would be the material, might be diamond, i.e. C, though. Concerning absorption of atmospheric gases as e.g. $\mathrm O_2$ NIST reports:

$\mathrm O_2$ is a weak light emitter, for most of its excited states, transitions to the ground state are strongly forbidden....

...Discrete bands of this allowed transitions span the region 5350-1750 Angstom; an even stronger dissociation continuum spans the region 1750-1300 Angstrom. Most other $\mathrm O_2$ transitions ... are forbidden by electric dipole selection rules...

So optically there is nothing to see. If it does not emit, it will not absorb. And additional research would probably show the same for the other gases you mention. The prism, as a solid, also has no lines in the optical region; that's why it is transparent.

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