DSR, Optics and Electrodynamics

We investigate some interesting solutions in the DSR theories. These solutions have important features in optics and mechanics. We use these similarities for a better understanding of these theories. We know that, the vacuum in the DSR has an effective refractive index which depends on the frequency of the light. We find this modified refractive index which leads us to a modified Electrodynamics with some new interesting aspects, for example near the Planck energy the electric field can be stronger or weaker than the usual case. Also, we will find a new modified Lorentz transformations in the first order of the Planck length which are very similar to the usual Lorentz transformations.