Radiation Pressure of Light in a Dispersive Medium

R. V. Jones
1978 Proceedings of the Royal Society A  
An elem entary discussion is given regarding the momentum associated with a photon in a dispersive medium. The results of the Jones-Richards (1954) and the Jones-Leslie (1978) experiments are taken to confirm that, if the momentum of the photon in vacuo is p, the total momentum asso ciated with the same photon in a dispersive medium of phase refractive index n^ is n^p (as the Minkowski energy-momentum tensor would imply). I t is then argued th a t a portion p /n g of this momentum may be
more » ... entum may be regarded as 'electrom agnetic' ( pace the Abraham tensor) and t nq,p(l -l/n^ng) as 'mechanical' and bodily present in the medium, where ng is the 'group refractive index'. This leads to plausible results for an artificial dielectric where n< jfng = 1, and suggests an element of reci procity between the 'd rag ' of light on the medium through which it is passing and the 'aether drag ' of a moving medium on light, since the drag coefficient (1 -l/n^n g)enters into both cases. Jones & Richards (1954) observed th a t the radiation pressure exerted by a beam of light of constant intensity on a mirror suspended in a liquid was directly pro portional, within about 1 %, to the refractive index of the liquid. This observation has been refined by Jones & Leslie (1978) to a precision of better than 0.1%, supporting the conclusion th a t it is purely the classical refractive index (phase velocity ratio) th a t is involved and not the group velocity ratio, despite the fact th a t energy is propagated with the group velocity. This simple result had been expected (Jones 1951) on the naive arguments of Newtonian corpuscles, and of Maxwell's result th a t the radiation pressure would be equal to the energy density in a parallel beam of light, and of the relation p = h/A for a photon. I t is also consistent with Barlow's experiment (1912) if, as J . J. Thomson concluded (1904), the reaction on the refracting boundary is always normal, irrespective of the angle of incidence. Although the Jones-Richards experiment had been noted by Brevik (1970) as providing support for the Minkowski formulation for the tensor relating energy flow and momentum in an electromagnetic field in a refracting medium, relatively little notice was taken until B urt & Peierls (1973) concluded th a t A braham 's formulation for the tensor was to be preferred. And they argued from the Abraham tensor th a t the radiation pressure exerted by a beam of light in a refracting medium should be inversely proportional to the refractive index rather than directly as [ 365 ]
doi:10.1098/rspa.1978.0073 fatcat:aqibna5nuvgorkkqnp5yg64ffu