I've read that greenhouse gases absorb and reemit sunlight, and that the infrared portion is what bounces off Earth back to space. When sunlight bounces off the Earth, why isn't the entire spectrum reflected rather than just the infrared portion?

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2Um, I am not sure you read that correctly. The Earth does reflect a great deal of light over the entire EM spectrum. – honeste_vivere Jan 22 '16 at 14:50
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The atmosphere and planet also absorb a lot of of the EM spectrum. The average energy of the planet corresponds to a blackbody temperature in the IR range, thus the planet emits most radition in infrared. The problem occurs when the atmosphere becomes opaque to that frequency range, because the planet can no longer radiate away energy into space. So it warms up until its blackbody temperature corresponds to a frequency range that is not absorbed by the atmosphere... – honeste_vivere Jan 22 '16 at 14:53
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4Possible duplicate of How does carbon dioxide or water vapour absorb thermal infra red radiation from the sun? – John Rennie Jan 22 '16 at 16:02
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I don't see how this is a duplicate. The linked question is asking how two gases absorb infrared radiation while this question asks why the whole spectrum isn't reflected. – Kyle Kanos Jan 23 '16 at 18:35
2 Answers
The reflectivity of the atmosphere, and of the surface itself, is strongly wavelength-sensitive. So while some percentage of any given wavelength is reflected -- and some percentage is absorbed rather than transmitted, the variation over wavelength is what leads to the somewhat misleading statement you refer to. Here's an example of atmospheric absorption, as can be seen at wikipedia
There are also curves of reflectance. $transmittance+absorptance+reflectance = 1$, in case you were wondering :-) .
The reason all this matters is that shorter-wave energy, e.g. visible and some UV, that is absorbed either in the atmosphere or by the ground, is re-emitted at different wavelengths in accordance with black-body theory. In general this leads to a lot of IR-radiation, so if the atmosphere is reflective at these wavelengths, the energy is retained rather than re-emitted to space.

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It does. Consider this: you can see the Earth from space. Therefore, not just infrared light gets reflected but also light on the visible spectrum.
Here's a graph (by NASA) of various planet's radio emissions. The ways that Earth can release radio waves is a bit limited. Because of that, it is safe to assume that at least some come from the Sun.

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How so? He asks why infrared is the only light reflected on the spectrum, and I'm answering that other light IS reflected. – DevilApple227 Jan 22 '16 at 15:19
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Because a partial answer is often worse than no answer. It doesn't take much effort to explain a bit about spectral reflectivity and absorption, which is what the "greenhouse effect" is all about. (even I managed to post) – Carl Witthoft Jan 22 '16 at 15:28
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Personally, I feel that my answer answers the question in the simplest terms, no physics background required. When I'm looking for answers, I prefer the "Explain it like I'm 5" approach, not the "Explain it like I work for NASA" – DevilApple227 Jan 22 '16 at 15:31
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@DevilApple227 - From where did you get that image? Where was the measurement made (i.e., on Earth or in space)? It matters because the frequencies one can observe are different depending upon the observation location (due to cutoffs at different plasma frequencies). – honeste_vivere Jan 22 '16 at 21:08
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