Momentum in AD.
In AD, momentum, as in Newton, is the product of "mass" times "velocity."
pi = Initial momentum before penetrating the refractive medium, v = particle velocity
In the present case m is the particle rest mass equal to m0 because the particle is not decaying and consequently does not vary.
The Photonic emission has a momentum equal to
pp= Photonic momentum, N = Number of Photons, h = The Planck's constant, = Frequency, c = Light Velocity
Consequently, the equivalent momentum as function of mass is
vR = Light Velocity in a Refractive medium.
j being the angle between pm and pi, we have, according to Fig. 1
Energy and Momentum Conservation
Equalizing equations (11) and (15), after changing, in equation (11), the velocity b by b n as the valid velocity to calculate the real Kinetic Energy that will be converted to Photonic Energy h n , we have
The classical equation was found and this solution works perfectly, but given a substantive difference in Kinetic Energy's proportion to get Photonic Energy when the Refractive Index is larger, even though there are few anomalies regarding n and v, which could drive to impose a "selection rule" in those values beyond the universal condition that v need always to be larger than vR.
Of course more complete research starting from the Energy's partition is open to AD's equations regarding the Electrodynamics derived from the Maxwell's equations applied to the medium where the phenomena happen.