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Let a system be composed of two perfect linear polarizers, where the axis of the first one is perpendicular to the axis of the other, so they do not let any light pass through the second polarizer. Let a plane harmonic wave of initially unpolarized light incide on the system, such that after exiting the first polarizer, the light will now be linearly polarized in the direction perpendicular to the axis of the second one, so it will be completely absorbed by it. Now, if we were to cover the system of two polarizers with a box and study only the input and output of energy of the sytsem, we would conclude whatever is inside the box absorbs all the energy that is given to it, and that by definition is a black body.

My question is, is this result correct? If so, does the system emit thermal radiation as a black body? Interestingly enough, the black body-like behaviour of the system depends on the angle between the axis of the two polarizers. Naturally, the same behaviour could be obtained from using a single polarizer and a perpendicularly polarized beam of light, which is precisely the effect of the first polarizer.

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Black body is an object that absorbs all the radiation incident on it. Note that it does emit the radiation. The point is that nothing is reflected and we thus expect the black body to eventually come to equilibrium with the surrounding environment.

Note also that in quantum era black body has become an obsolete concept - since in terms of photons black body radiation can be simply defined as a radiation in thermal equilibrium.

A prior, polarizers do not necessarily absorb all the light incident on them - they simply let only one polarization through - the other is either absorbed or reflected.

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  • $\begingroup$ Thanks for your response! How come black bodies don't emit radiation? I've always been taught Planck's irradiance formula is preciselt the intensity per unit frequency emitted by a black body, and that a black body emits as thermal radiation all that it absorbs $\endgroup$
    – Lagrangiano
    Commented Nov 19 at 13:32
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    $\begingroup$ @Lagrangiano As the answer says: Note that it does emit the radiation. The point is that nothing is reflected [...]. Just in case there is a language problem: BB emits the radiation (does here is an affirmative particle, not a part of doesn't) $\endgroup$
    – Roger V.
    Commented Nov 19 at 13:34
  • $\begingroup$ "...they simply let only one polarization through - the other is either absorbed or reflected." And if it is absorbed? (AFAIK, most polarizers are the absorbing kind) Where does the energy go? $\endgroup$
    – Solomon Slow
    Commented Nov 19 at 15:21
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    $\begingroup$ @RogerV., Sure, but even if the system does not absorb all of the incident radiation, and even if "black body" is an outmoded way of describing the phenomenon, I still suspect that Lagrangiano is asking what becomes of the fraction of energy that is absorbed. $\endgroup$
    – Solomon Slow
    Commented Nov 19 at 16:14
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    $\begingroup$ The OP emphasized one phrase with bold-face type; "** does the system emit thermal radiation as a black body?**" I guess you focused on the "as a black body" part of it. I saw an implicit question about where the energy goes. $\endgroup$
    – Solomon Slow
    Commented Nov 19 at 16:39
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Consider this black body absorption spectrum compared to the "broad band" polarizer which operates in the wave-length range $300-2700~nm$ :

enter image description here

In short, for a black body :

  • It absorbs all incident wave-length ranges, it doesn't matter is it microwaves, radio waves, visible light, x-rays or gamma rays or something else - it swallows everything
  • Black body absorption spectrum is uniform,- it does not depend on black body temperature.

Now about a box with a pair of polarizers :

  • No polarizer operates in all of incoming radiation wavelengths,- usually just in small part of it.
  • Polarization efficiency may depend on polarizer temperature.

Due to these differences, pair of perpendicular axis polarizers is not even close to a black body definition.

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the box absorbs all the energy that is given to it...does the system emit thermal radiation as a black body?

If the polarizers absorb radiation, then they must convert that energy to heat. If the system is thermal equilibrium with its environment, and if the heat is not carried away by conduction or by convection, then the system must radiate as much energy as it absorbs. There's no place else where the energy can go. The temperature of the polarizers can't just keep increasing forever.

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