# 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?

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– Qmechanic Mar 14 '12 at 22:12

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.

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Do you have a figure illustrating what you say here? That will make it a lot easier to understand. – Bernhard Mar 14 '12 at 21:58
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? – ODP Mar 14 '12 at 22:03
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. – user1631 Mar 14 '12 at 22:12
oh yeah of course haha – ODP Mar 14 '12 at 22:37

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.

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That's a pretty cool and good analogy! Never seen it before – ODP Mar 14 '12 at 22:07
+1 Fermat's principle at it's beauty! – Stefan Bischof Mar 4 '13 at 19:25
+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! – kbh Jan 5 '15 at 17:56

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 light wave on one side of beam of light changes a littel before the change in speed of light wave on its other side causes a change in direction of light.

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## protected by Qmechanic♦Mar 4 '13 at 9:26

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