# Q & A: Refraction Saves Light some Time

Q:
What happens when light refracts? We know somehow it bends, but why, and when does this happen? Thanks!
- Mrs. Smith’s third grade class
Glenfield, NJ
A:
The light path is the one that lets it travel quickest from the start point to the endpoint. (This is called Fermats principle.)

Light slows down when it passes through materials. The amount it slows down depends on the material. That means that the time it takes to get somewhere isn't always shortest on a straight path. The quickest path is one that travels more distance through the fast regions (say air) and less through the slow regions (say water), so the light path bends as it goes from air to water.

Why does light take the quickest path? Remember that light is a wave. It actually travels in a bit of a spread-out way, like other waves.  In order to show up somewhere, it can't arrive with crests and troughs all jumbled together, because they would mostly cancel. Whether a crest or trough arrives at some time depends on exactly how long the trip took. So the places where the light shows up are ones where a range of nearby paths all give the same travel time. That usually means that the travel time along the central path is either at a maximum or a minimum. Otherwise, little shifts in path would increase or decrease the travel time. Typically the paths are ones with minimum travel times.

(published on 10/22/2007)

## Follow-Up #1: acceleration of light?

Q:
Folks: If light 'slows down', where does it get the energy to speed back up again? And how would you describe the acceleration of the light as it leaves the 'slowing' medium? That is, how long does it take for this 'slowed' light to speed back up again - zero time? Or does it take some time (and therefore distance) in air? Can the acceleration of light be infinite? Thanks
- PLawton (age 50)
Rockville, MD
A:
Let's use a simplified picture- classical light waves and a sharp edge of a homogeneous  material with an index of refraction, where the light travels more slowly. As the light wave leaves the material, it does so continuously. So you could say that the wave accelerates suddenly on leaving the the material, but the wave is only gradually leaving. Thus the rate of change of the average velocity over a wave packet only changes continuously, without any sudden jumps. Adding further realistic details, such as the gradual tailing off of the electronic wave at the edge of the material, just smooths the picture out even more.

As for the energy, it goes as the frequency times the photon number, which are the same in and out of the material, allowing for some photons that reflect. Since the wave in the material is moving slower, it has a smaller wave packet. Its energy density is higher than that in the vacuum, but the energy is the same. You can think of some of the energy in the material as being in the electrons, oscillating around the positions they'd be in if there were no wave coming by.

Mike W.

(published on 04/06/2012)