Every source I have referred to says red light is faster in water than blue light. However, nearly all descriptions/explanations depend on refractive indices and 'bending' to show that blue light is slowed to a greater extent. Instead, I'm wondering if a more precise explanation based on dispersion is possible b/c every time I attempt to reason out this fact based on group velocities, I get the opposite conclusion. My reasoning: Water is a dispersive material so frequency w is non-linear wrt wave number k. Group velocity is dw/dk and always less than c [sanity check] but the slope of the graph increases with k so group velocity is higher at lower wavelengths [k inversely proportional to lambda] which seems to imply that wave packets of lower wavelength should have a faster speed in water... Am I using the dispersion relationship of w-k wrongly or is the group velocity not the same as the velocity of propagation [I'm fairly confident it is since number sources cite it as the speed that energy/information of the wave travel]? Should I use phase velocity w/k instead? I have strong doubts given a) it always exceeds c and b) that dispersive wave means that w/k not equal to dw/dk = v. However, if I do use it, I get the correct connection of greater phase velocity for great wavelength. I have a feeling that though I understand the terms and concepts to some degree, I can't draw the connection I want to b/c I'm lacking some other tool. Can you even draw the conclusion that vred > vblue in water knowing only w-k relationship?