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We know light carries momentum, that's why solar sails work.

But when light goes towards a less denser medium at a shallow angle, it is reflected back. Since the momentum is conserved this light needs to impinge on something, but on what?

There is no actual massive mirror there, it's just a boundary between two media, how can that receive momentum?

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Total reflection at the boundary between a dielectric and vacuum means that no (average) energy or momentum of the wave will be transmitted into the vacuum. However, as you correctly observe, the momentum change of the photons requires that mechanical momentum must be imparted to something. This momentum can only be transferred to the dielectric medium where the wave propagates and is reflected at the boundary.

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  • $\begingroup$ This does not answer the question. The OP really wants to know what the momentum is impinging on. You just say “momentum can only be transferred to the dielectric medium where the wave propagates and is reflected at the boundary” that’s not answering why or how. One thing that is different at the boundary than anywhere else inside the material is that the electrons on the surface atoms are more crowded as they are pulled in toward the material. $\endgroup$ – Bill Alsept May 20 '18 at 16:03
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    $\begingroup$ @BillAlsept - Sometimes conservation laws are sufficient to solve a problem. But you are free to provide a deeper going and more elaborate answer. I am sure that many will be interested in a full microscopic explanation of the total reflection of a photon at the boundary between the dielectric and vacuum. $\endgroup$ – freecharly May 20 '18 at 20:08
  • $\begingroup$ I was just pointing out that your first and third sentence were general statements but did not explain anything. $\endgroup$ – Bill Alsept May 20 '18 at 20:44
  • $\begingroup$ @BillAlsept - If you read the third sentence attentively, you will discover that it gives an answer to the question as embodied in its the title. $\endgroup$ – freecharly May 20 '18 at 20:50
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    $\begingroup$ @BillAlsept - You can derive the momentum balance from simple electromagnetic wave theory. You don't need a photon (imagined like a billiard ball) impinging on something. Furthermore, when you consider the photon as a wave, the photon location is not well defined. $\endgroup$ – freecharly May 21 '18 at 2:53

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