Why don't windows and mirrors cancel light? So I understand that when light goes from a material of low index to a material of higher index it picks up a phase change of 180. Most glass has an index of around 1.5. I know that when light goes from a low index to a high index there is a phase change of 180. So light coming from air would reflect back off the glass with a phase change of 180. Also destructive interference takes place at 180 degrees of phase shift. I was thinking about this and I was wondering how we could even have reflections off of glass and why anti-reflective coatings are needed at all? Is is because of the polarization where only light polarized in the plane of incidence will have an interference? 
 A: What you have not taken account of is that the light wave reflected is travelling in the opposite direction. The incoming and outgoing waves may interfere with each other, but they will not completely cancel each other out - in fact a standing wave may be formed as described below.
Now - the way an antiflection coating works is to reflect the wave back twice so that the two reflected waves which travel in the same direction are 180 degrees out of phase and these two cancel each other out by destructive interference (this is the simplest form of antireflective coating).
Standing wave formation
There can be interference between an incoming and outgoing wave. In general if a wave hits a barrier and reflects back the way it came there may be a standing wave formed by the addition of the forward and backward waves. The waves appear to 'pass through' each other. 
A nice description with pictures to show how standing waves are set up is here. In brief the two waves going in opposite directions look like the picture below...

combine by constructive and destructive interference to form a standing wave that looks like the picture below, where A is the amplitude of the wave and N are the null-points which are always at zero.

Antireflective coating
For an antireflective coating the two reflected waves produced are out of phase by 180 degrees as in the picture below

