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Imagine a plate beeing irradiated from all sides with a specific wavelength. One side of the plate is smoth and reflects most of the incoming radiation, the other side is covered in grooves with the right depth and width tunned to absorb most of the incoming radiation.

Does the plate feel an unbalanced force towards any direction?

Doesn’t the answer to the previous question (yes or no) violates either the first law of thermodynamics or Newton’s third law?

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    $\begingroup$ Hello, sorry it is not clear why it should be a paradox. If the radiation is isotropic but the plate is not, then you can expect some unbalance. However, why this should be a paradox? Total conservation law apply to the whole system (incomjng and reflected radiation + plate). $\endgroup$
    – Quillo
    Nov 28, 2021 at 14:33
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    $\begingroup$ Hi Pedro. Please consider editing your question title to reflect the content of your question. $\endgroup$
    – J. Murray
    Nov 28, 2021 at 16:12
  • $\begingroup$ @J.Murray Any particular sugestion? $\endgroup$
    – Pedro
    Nov 28, 2021 at 16:19
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    $\begingroup$ Perhaps "Apparent radiation pressure paradox" or similar. $\endgroup$
    – J. Murray
    Nov 28, 2021 at 17:38
  • $\begingroup$ @J.Murray Done. Thanks for the suggestion $\endgroup$
    – Pedro
    Nov 29, 2021 at 15:45

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Does the plate feel an unbalanced force towards any direction?

Yes. The change of EM momentum on the reflective side is twice the change of EM momentum on the absorptive side. So the radiation pressure is twice as large on the reflective side, leading to a net force pointing from the reflective to the absorptive side.

Doesn’t the answer to the previous question (yes or no) violates either the first law of thermodynamics or Newton’s third law?

Of course not. Thermodynamics is irrelevant here since the radiation is not thermal. There is no temperature associated with monochromatic radiation, so nothing in thermodynamics prevents it from doing work. Moreover, the energy removed from the radiation is proven equal to the energy gained by the matter.

A more interesting question would have been to make the absorptive side a black body and to irradiate both sides with thermal radiation at temperature T. This will provide a force, as before, but now the force will depend on the difference in temperature between the plate and the radiation. The force will go to zero as the temperatures become equal. In other words, it is a heat engine.

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    $\begingroup$ "The force will go to zero as the temperatures become equal" - namely this is because at temperature equilibrium, absorbing and reemiting (black side) produces the same effects as reflecting immediately (silvery side). $\endgroup$ Nov 28, 2021 at 16:46

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