How do refraction of light follows the law of conservation of energy and conservation of momentum?
When a light of energy E incidents on a refracting surface a part of the energy is reflected from (R) the surface, a part gets transmitted (T) along the refracted ray and yet another part is absorbed by the medium (A).
Now if we add the energies T + A + R we get the total energy E.
T + A + R = E. So, total energy remains constant.
Conservation of momentum of refraction of light is difficult as there are two definitions of momentum of light in a refractive medium. However, when the light is incident on a medium a part of its relativistic momentum is absorbed by the medium and thus the momentum of light becomes less and hence it slows down. Still, it can be shown using relativity and quantization of radiant energy that momentum of light remains conserved.