Why do we restrict to electric field when describing light? Why do we restrict only to electric field when describing light as electromagnetic wave?
I mean from Maxwell equations we can derive wave equation for electric field and also for magnetic field but everyone uses electric field to further describe polarization of light and then phenomena like magneto-optical effects
 A: There reason I can think of is the strength of interaction. The force exerted by the electric field on a charged particle is $eE$ which is much stronger than the force by magnetic field  $ev\times B$. Magnetic force only get comparable to electric force when velocity of particle (usually induced by electric field) approaches light velocity. 
Due to this reason when light interact with any material the electrons starts to oscillate in the direction of electric field and if a wire grid is setup perpendicular to the electric field the electron motion experience high damping and absorb the light appreciably (principle of wire grid polarizer).
Consideration of magnetic field become important in very intense laser fields when the electron motion become relativistic. 
I hope this will help. 
A: Most materials used in optics experiments are not magnetic. By this we mean that the magnetic permeability is equal to that of free space. This results in a magnetic susceptibility of zero. $$\mu_r = \frac{\mu}{\mu_0}=1$$ $$\chi_m=\mu_r-1=1-1=0$$
Therefore the magnetic field of the optical wave generally does not interact with the things in the experiment. So we can typically ignore magnetic effects in our optics experiments.
