  Attempts to explain the refraction of light in dispersive media in terms of a
photon or "corpuscular" model have heretofore been unable to account for the
observed decrease in the speed of light as it passes from air into a region of
higher refractive index n such as water or glass. In the present work it is
argued on the basis of the quantum mechanical relations p = k and E = h omega
that the energy of photons satisfies the equation E = pc/n. It is possible to
obtain an exact prediction of the observed speed of the photons in a given
medium by application of Hamilton's equations of motion to the above formula,
but at the same time to conclude, in agreement with the arguments of Newton and
other classical physicists, that the photon momentum increases in direct
proportion to n, thereby producing the well-known bending of light rays toward
the normal when entering water from air. The corresponding relativistic
particle theory of light indicates that the potential V encountered by the
photons in a given medium is attractive for n > 1 and is momentum-dependent,
which suggests the microscopic interactions responsible for the refraction of
light are non-Coulombic in nature and are instead akin to the spin-orbit and
orbit-orbit terms in the Breit-Pauli Hamiltonian for electrons moving in an
external field. The present theory concludes that the reason photons are slowed
down upon entering water from air is that their relativistic mass p/v increases
faster with n than does their momentum, which in turn requires that Einstein's
famous E = mc^2 formula does not hold for light dispersion because the energy
of the photons is expected to be the same in both media.
