Im trying to calculate the impulse of the particles of a light ray in water assuming its freely traveling through and not bumping into any molecules.
This i what i tried:
We know that:
$$E=h \cdot f$$ $$p=\frac{h}{2\cdot \pi}\cdot k$$
Photons travel with the speed of light. In this case it should be the speed of light in water.
By Einstein: $$E=\gamma \cdot m \cdot c_{vacuum}^2 = h \cdot f$$ Also: $$p=\gamma \cdot m \cdot c_{water}$$
It follows: $$p=\frac{E \cdot c_{water}}{c_{vacuum}^2}=\frac{h \cdot f \cdot c_{water}}{c_{vacuum}^2}$$
But according to wikipedia: the dispersion relation is just $\omega = k \cdot c_{water}$ Then: $$p=\frac{h}{2 \cdot \pi} \cdot k = \frac{h \cdot f}{c_{water}}$$
So what is correct? And where did I go wrong? Can someone help me? Im so stupid i cant solve this at all :(
