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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?

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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.

Helpful image to illustrate

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    $\begingroup$ Do you have a figure illustrating what you say here? That will make it a lot easier to understand. $\endgroup$
    – Bernhard
    Mar 14, 2012 at 21:58
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    $\begingroup$ Thanks that's pretty understandable, but why MUST the wavecrest bend just because it starts to slow down before the other part of the wavecrest? $\endgroup$
    – ODP
    Mar 14, 2012 at 22:03
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    $\begingroup$ That is the only way you can have the wavecrest segment inside the medium moving slow, the wavecrest segment outside the medium moving fast, while having the two segments meet. If the slow wavecrest is not bent, then a big gap will open up between them. $\endgroup$
    – user1631
    Mar 14, 2012 at 22:12
  • $\begingroup$ oh yeah of course haha $\endgroup$
    – ODP
    Mar 14, 2012 at 22:37
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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):

enter image description here

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.

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    $\begingroup$ That's a pretty cool and good analogy! Never seen it before $\endgroup$
    – ODP
    Mar 14, 2012 at 22:07
  • $\begingroup$ +1 for this analogy. I've never heard it before, is it in his lectures? I can't render the link on my phone, but I'll use it when I next present this introductory material for certain! $\endgroup$
    – kbh
    Jan 5, 2015 at 17:56
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    $\begingroup$ You have just restated the law in different terms. Why does the light wave choose the path it can traverse in the least time? Surely light waves don't want to reach their destination as fast as possible. They just go and hit something, or don't. $\endgroup$
    – Ville Laurikari
    Sep 22, 2016 at 10:10
  • $\begingroup$ i agree exactly with @VilleLaurikari, one can ask Why does the light wave choose the path it can traverse in the least time? it is not an intrinsic assumption. this does not answer the question, it just change it to another question $\endgroup$
    – S.Serpooshan
    Jul 30, 2017 at 9:23
  • $\begingroup$ If you look for an experimental proof you must put a sensor at the Q point.In fact,there is an undefined number of rays progressed from P to Q,but sensor detects the strongest=less absorbed:followed the shortest path.Light is not thinking,not choosing route. But what is the fastest route if light cannot reach Q? $\endgroup$
    – elias2010
    Dec 14, 2017 at 7:20
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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".

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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.

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