If light is an electromagnetic wave and lightspeed is constant (we ignore spacetime or gravity for this question) why can't we slow down light with a few dozen wellplaced magnets and electricly charged objects ? Or electromagnetic mirrors ?
Light can be slowed if it interacts with something. For example just shining the light through glass or water slows it down. The ratio of the speed of light in the glass/water to the speed in vacuum is called the refractive index.
A more extreme example is to slow light by shining it through a Bose-Einstein condensate. In fact the light can be brought to a complete halt. However it's important to be clear that you're not really slowing the light. Your're creating an entangled light/something else system and this combined system has a velocity lower than light.
As far as I know light cannot be slowed by a magnetic field because it does not interact with the field in any way that could slow it.
Response to comment:
I'm not sure what you mean by effects at a distance; you'll need to clarify that.
I can't think of any interaction of light with magnetic fields in vacuum, though in the presence of a suitable material you can get the Faraday and Kerr effects. Actually the Faraday effect does slow light slightly, though I'm not sure if this counts as an interaction with the magnetic field, or whether it's really an interation with the medium it's passing through and that medium is affected by the magnetic field. Light principally interacts with electric dipoles.
You say I do not understand how it cannot be slowed down by an electromagnetic field of a massive object. Light can interact with some systems, like a BEC, so what is propagating is no longer a pure light wave but a quantum mechanical mixture of light with something else, and this mixture behaves as if it has a non-zero mass. I suppose you can argue about whether you've really slowed the light, because what you've really done is mix it with something else.
No need to use magnetic mirror or something else. Simply start MOVING away from light. The speed of light will not change, but it's wavelenghth will be increased (or energy/momentum of photons will be reduced) by this action compared to your initial frame of reference. This is called red shift.