How does light get energy when moving from one medium to another?

Question

It is said that the speed of light increases when moving from optically denser medium to rarer medium but as light can be considered as a particle how does it get the energy to increase it velocity

Answer 1

Light can be considered a particle, known as a photon, but the energy of each photon is not related to its velocity. Instead, it is given by the Planck formula, $$ E=h\nu, $$ where $h$ is Planck's constant and $\nu$ is the frequency of the light. Since the frequency of the light remains constant as it travels from one medium to another, the energy of those photons is also unchanged.

Answer 2

I would just add to Emilio Pisanty's comment by saying that the frequency remaining a constant as light travels across a boundary separating two media is required because it is required that the tangential component of E be continuous across the boundary.

In turn, that the tangential component of E must be continuous across the boundary separating two media can be found by computing the line integral along any path through the two media and using Stoke's theorem.