$E = h\nu$ and $P = h\nu/c$ in vacuum. If a photon enters water, its frequency $\nu$ doesn't change. What are its energy and momentum: $h\nu$ and $h\nu/c$ ? Since part of its energy and momentum have been transferred to water, it should be less.
If water's refractive index is $n$, are the energy and momentum equal to $h\nu/n$ and $h\nu/c/n$ ?
It's a non-trivial problem, which also involves how you define a photon in a medium - as a interacting particle and treating excitation of medium separately, or as a "dressed particle", including the interaction.
From Abraham–Minkowski controversy Wikipedia page:
The Abraham–Minkowski controversy is a physics debate concerning electromagnetic momentum within dielectric media.
[...]
- The Minkowski version: $$p=\frac {n h \nu}{c}$$
- The Abraham version: $$p=\frac {h \nu}{n c}$$
[...]
A 2010 study suggested that both equations are correct, with the Abraham version being the kinetic momentum and the Minkowski version being the canonical momentum, and claims to explain the contradicting experimental results using this interpretation
- Stephen M. Barnett, Resolution of the Abraham-Minkowski Dilemma, Phys. Rev. Lett. 104, 070401 (2010), free pdf here
Look also (Google Scholar?) at "electromagnetic momentum in a medium" or "electromagnetic energy in a medium", as essentially its related to a classical problem.
A photon doesn't transfer part of its energy to water. Either it is absorbed or it is not. The energy is always $E=h\nu$.
A photon doesn't transfer part of its momentum to the water either. If it is absorbed, it transfers all its momentum to an electron of course.
If not, then there are several explanations about what happens and none of them are particularly enlightening. One is the microscopic view, put forth by Mark in the comments below, that the photon is traveling in mostly empty space, punctuated every now and then by a charged particle, and so its momentum doesn't change at all.
This is technically the most correct, but in my opinion not much use if you are looking at macroscopic scales. In that case, we have the Abraham-Minkowski controversy about whether the photon's momentum is higher or lower in a medium. Steve Barnett purports to have solved this controversy in a 2010 paper, as mentioned in the Wikipedia article, and I find that paper easily readable and enlightening. According to Barnett, the Abraham momentum, $P=h\nu/cn$, corresponds to the kinetic momentum of the photon (which is the momentum one usually thinks of when considering a macroscopic body in motion); and the Minkowski momentum, $P=nh\nu/c$, is the canonical momentum (which is defined as Planck's constant divided by the de Broglie wavelength of the body).
The answer is really that "the momentum" of a photon in a medium is not a well-defined concept, so you need to specify what you are talking about.
Working mostly with plane waves myself, I prefer to say $\vec{p}=\hbar\vec{k}$ (which indeed grows by a factor of $n$ in a medium) since this allows me to intuitively explain several other phenomena in terms of conservation of momentum. I will freely admit that this is a gross oversimplification, and also not intuitive in the sense that there is no good explanation why the photon's momentum should be higher, only the unsatisfying mathematical explanation that since the speed of light is "effectively" lower in water, the momentum is "effectively" higher.
A new solution to this controversy has just (June 2017) been published:
"in a transparent medium each photon is accompanied by an atomic mass density wave. The optical force of the photon sets the medium atoms in motion and makes them carry 92% of the total momentum of light, in the case of silicon." (my emphasis)
https://phys.org/news/2017-06-atomic-mass-photon-momentum-paradox.html
The rather long abstract of the paper itself is very enlightening:
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.063850
