Sneaky photons

Classical Mechanics Level 5

Light travels with different velocities and different wavelengths (and hence wave vectors) in different media. Since light is made out of photons, individual photons change their momentum as they change the media. One way to actually derive Snell's law is from the behavior of photons at the boundary between different dielectrics.

A photon is travelling from a medium with the refractive index \(n_1 = 1\) (air) to a medium with the refractive index \(n_2 = 1.5\) (glass). Its incident angle is \(60^\circ\), measured from the normal to the boundary between the two surfaces. For how much does the momentum of the photon change in \( 10^{-30}~\mbox{kg m/s}\)?

Details and assumptions

  • The incident photon is green, i.e. its wavelength is \(555~\mbox{nm}\).

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