Why does change in speed of a wave make it refract? When a light wave enters a medium with a higher refractive index (e.g. from air to standard glass) and its speed decreases, why does that make it refract/bend?
I understand that wavelength decreases and frequency stays the same and therefore its speed decreases, but I can't find anywhere whatsoever why the speed decrease cause the wave to refract. So could someone please explain this? 
 A: There are several ways to look at it. From what you have, the easiest is to understand it as deriving from Fermat’s principle:

the path taken between two points by a ray of light is the path that can be traversed in the least time

Because light travels slower in the medium of higer refractive index (as you stated), its course will be so that it travels a smaller distance in this medium than in the other. There's a commonly-used analogy for that (apparently from Feynman):

The rescuer wants to reach the drowning person as fast as possible. Because he runs faster than he swims, he won't take a straight path but his optimal path follows Snell's law.
A: The wave only refracts if it enters the medium at an angle.  Follow a single wavecrest; if the wave is entering the medium at an angle, then part of the wavecrest enters the medium first, and starts to slow down, while the other part of the wavecrest is still going fast, and therefore the wavecrest must bend.  If the wave enters at a right angle, then the entire wavecrest is slowed down simultaneously and no refraction occurs.  

A: The change in speed is deceleration due to a resistance force like friction.Photon is particle and it experiences resistance in its motion inside medium.If the ray enters vertical to the surface its not deflected and called "normal".Ray is photon's linear orbit.If photon enters at an angle,then resistance force is analysed in two components:one parallel and one vertical to the "normal".The last one pushes it towards the "normal".
A: The fact that the speed of a light wave on one side of a beam of light changes a little before the change in speed of light wave on its other side causes a change in direction of light if the light wave comes in on an angle.
