Maybe this has been asked before, but I didn't find anything about it. I am wondering about the momentum of light in media with refractive index n>1 (so to say, not in vacuum). There are two approaches to this problem I think, but they lead to different results.
First, one can take the equation $p = \frac{h}{\lambda}$ Because it holds $\lambda = \frac{\lambda_0}{n}$, one gets $ p = n \frac{h}{\lambda_0} = n\cdot p_0$. So momentum is larger than in vacuum.
Second, one can take the eqation $p = m \cdot v$. Because $v= c$ for phonons and in medium it holds $c=\frac{c_0}{n}$, one arrives at $p = \frac{m c_0}{n} = \frac{p_0}{n}$, which is clearly smaller than $p_0$.
These two results dont fit together. So which result is right and why?
