  On the base of the Hamilton theory for the time-like photon in isotropic
dielectric with refraction index n (S.Antoci, et.al, 2007), we suggest
generalization of the Einstein-Plank-Richardson law for the value of the light
energy quantum in medium:E=h*nu*n, where h is the Plank's constant, and nu is
the light frequency. By use of this new quantum law, we resolve the famous
contradiction between de Broglie and Einstein's theories, related with the old
Abraham-Minkowski dilemma in the definition of the photon momentum value p (in
the medium for n>1). We show that the same value p=p_a=E/(c*n)(c is the speed
of light in vacuum) follows now from the both theories of de Broglie and
Einstein, which complies with the theory of Abraham, but not with the theory of
Minkowski (where p=p_m=E*n/c). Based on the corpuscular approach with p=p_a and
E=h*nu*n^2, we give new inference for the Snellius refraction law and resolve
more old corresponding corpuscular-wave Newton-Huygens dilemma. We show that
even for n-1<<1 the Abraham and Minkowski theories (with different p=p_a and
p=p_m)may lead to very different conclusions. Thus, only the theory with p=p_a,
contrary to the theory with p=p_m, allows the conclusion about the
Vavilov-Cherenkov radiation realization in the photon gas of the background
cosmic radiation, for which n-1=10^(-42) in the current epoch.
