Speed of Light Through a Medium?

Pete- “We know the blue light is refracted more than the red light.
This means that the blue light is slower than the red light.
This means that the blue light takes a longer time to travel.”

I know that blue light is refracted more and it is displaced more but how does that show that it took a longer amount of time to travel?

If two objects were measured the one that traveled farther in the same amount of time would be going faster. If the blue light covered more distance in the same time then it would be faster. So how do we know what the amount of time is?


This comes from the Fermat's Principle, right?

Could you explain explain the Fermat's Principle that light follows the path of least time.

Since the speed is constant, the minimum time path is simply the minimum distance path.

How do we know this? Is the speed of light constant in a medium?

 

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Hi, Mike,

I'm a little short of time at the moment but I can clear up one major point for you. We know beyond a doubt that it takes blue light longer because it has been tested time and again. Photo-detectors are set up on the exit side of the medium and are tuned to very precise frequencies. A burst of light is aimed at the medium and timed. The longer wavelengths (lower frequencies) arrive AFTER the higher ones while traveling through the exact same thickness of medium.

So, when the distance traveled is the *same* - the later arrivals *must* have been traveling slower.

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More later, perhaps.

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Mike, do you have any reason to think that blue light takes the same time as red light to pass through the prism?

Refracted more means slowed down more. Slower means it takes longer.

We know the time because we know the speed.
We know the speed because we know how much it is refracted.

We know how to get speed from refraction by Snell's law. We trust Snell's law because it makes good theoretical sense (see Huygens-Fesnel principle for the classical model) and it matches up with experiments (first done by Fizeau and Foucault).



If that's not enough, then direct measurements of the speed of red and blue light in various media should certainly be doable, and I wouldn't be at all surprised if they've been done, as Read-Only says.

 

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Another *very* quick post because I have to leave home in just a moment.

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Not have they made direct tests, they continue to be made. On every single large telescope lens during manufacture as a routine matter while checking for chromatic aberrations and other tiny flaws that would impair their use.

The physical measurements and calculations are fine indicators of quality - but nothing can replace actual tests for verification. (Remember the lens and reflector in the Hubble Space Telescope?)

 

I would have expected such tests to be measurements of refraction, rather than directly of speed?

 

That HAS to be my last post for a few hours. Wife is walking to the car. <grin>

Indeed, the majority of them are, Pete, just not all. And as you've already explained, refraction *does* indicate speed.

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The speed of light is not constant as it moves from medium to medium. When light enters a denser medium, like from air to glass, the speed and wavelength of the light wave decrease while the frequency stays the same. How much light slows down depends on the new medium's index of refraction.

Refraction indicates speed based from Fermat’s Principle, right? That assumes that the speed of light is constant but it is not constant as it travels through a medium. So I don't get it. I don't understand this principal.

Then I found this that says that the original statement of Fermat's principle was, "The actual path between two points taken by a beam of light is the one which is traversed in the least time." Snell's law and the law of reflection follow directly from this statement. It may be reformulated slightly in terms of optical path length as "Light, in going between two points, traverses the route having the smallest optical path length." In its original form however, Fermat's principle is somewhat incomplete and even slightly in error. Its modern form is "A light ray, in going between two points, must traverse as optical path length which is stationary with respect to variations of the path." In this formulation, the paths may be maxima, minima, or saddle points.

I tried to see if there was an experiment that showed that higher energy traveled slower and I did find one that showed that higher energy gamma rays traveled slower than the speed of light. This confuses me even more because the speed is supposed to be constant in a vacuum.

I really appreciate your help. Thank you!

 

Sort of.
I think that more fundamentally, it is based on experimental measurements, and on the Huygens-Fresnel principle.

Try this blog entry: Time is of the Essence
It describes two paths between A and B, that cross mediums at different speeds. The bent path is the fastest:

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Fermat's principle says that the path of a light ray between two points will always be the fastest path, and that's why it is bent (refracted) when it slows down.

That's not related to this thread, and seems to be bad journalism. There's a brief discussion of it at physicsforums.com.

 

I’m sorry. This is just really hard for me to understand. I will try to read more about the Fermat’s Principle and Huygens-Fresnel principle but if anyone else has an easy explanation I would really appreciate it.

Light moves slower through denser media because more particles get in its way. Each time the light bumps into a particle of the medium, the light gets absorbed which causes the particle to vibrate a little and then the light gets re-emitted. This process causes a time delay in the light's movement so the more particles there are (the more dense the medium), then the more the light will be slowed down.

However, other waves like sound travels faster in liquids and non-porous solids than it does in air.

So just because it traveled more distance and is bent more how do we know this means it is slower?

If the blue light is slowed down more does it remain slower forever? Did it lose speed or energy?

The high energy article is over my head so don’t worry about it.

Thanks again!

 

As the photons move from electron to electron, they still move at the constant c. We say the light is slowed, but it isn't. It just takes longer through a medium because of the absorbtion and re-emission.

The method of propagation of sound is different than light. Sound wave are compression waves where one molecule bumps another. The denser the medium, the shorter the distance between bumps and the faster the propagation. In a helium atmosphere, sound travels slower than it does through air.

With light, the denser the medium, the more times a photon is absorbed and re-emitted, so the longer it takes a photon to pass through it.

The blue light itself isn't slower, it just takes longer to pass through the medium. If it's bent more, it travels through more of the prism, which means there are more absorbtions and re-emissions. The photons themselves still travel at the constant speed c.

 

Okay. That makes sense but my teacher should have said that.

So light never loses any energy or speed and technically it always travels at c. It is always a constant even in a medium, right? So technically light never slows down no matter what. They should tell you this right up front, don’t you think?

Thank you so much!!!

 

The photons never lose any speed, but they can, and do lose and gain energy. They do so by changing frequency. Higher frequency photons (the blue end of the spectrum) have more energy than lower (red) photons.

 

Alex, you're confusing things. Mike is struggling to grasp the classical wave model. He doesn't need to worry about quantum theory.

 

I thought that they already had their frequency in the white light and that the prism just dispersed them. So are you saying that the prism changed their frequency?

 

I'm not an authority on optics and there's a chance that I'm wrong but, moving through the prism does not change the frequency of anything, it simply separates the already existing photons (with their already existing energy levels) from each other. I believe Alex was mentioning that photons can lose and gain energy in other situations.

I think the experiment that would answer your main question would be to take Pete's prism in post #2 and replace it with a sheet made of the same material but of uniform thickness, standing straight up. Now, strike the material with a ray of white light at a perpendicular angle (straight in from the side). The light would experience no refraction (there would be white light coming out the other side), but before that happened the color of light coming out the other side would not be of uniform color...in other words the red would "come out first".

 

Thank you but now I'm really confused. So are you saying that light doesn't lose any energy when traveling through a medium? It only loses energy in other situations? Like what?

It says that assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to the frequency that waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.

It also says that the wavelength is decreased in a medium with higher refractive index. So does this mean that since the wavelength is decreased in a prism that also the frequency is decreased in a higher refractive index? Does light traveling through a prism lose energy? When it says that the wavelength is decreased in a medium. Do they mean it becomes shorter with higher frequency or longer with lower frequency?

I can understand that it may not lose speed because in air (close to a vacuum) all the energies travel at c but does it lose energy? If it does, how does it lose energy?

 

Technically the energy isn't "lost" at all. If it were, the light would change colors as it exited the other side, even when not refracted. Someone already gave a fine explanation on this, and that is that the photons are being "absorbed and re-emitted" by the atoms in the prism which is a process that takes time, while the speed of the photon's travel between those atoms is the same as it is in a vacuum, c.

Think of it like this: a bunch of different colored photons arrive at a party and want to reach the keg in the kitchen. In an empty room, they would all reach the keg at the same time. However, in a crowded room, running into people consumes time (to say hi, excuse me, etc). Blue has more energy so his lateral movements are more pronounced than red. Larger lateral movements increase his chances of bumping into people. Therefore, red reaches the keg first.:cheers:

 

Okay. Technically light never loses any energy or speed when traveling through a medium it always travels at c. It is always a constant even in a medium. So technically light never slows down no matter what. So light never loses speed or energy when traveling through a medium.

That's the finally correct answer, right?


It only loses energy in other situations that I don't know about, right? Could you just give me one example of the other situations?

 

Sure, gravity affects the energy of photons just as you expect it would. A photon leaving a gravity source loses energy which is known as "red-shifting", and a photon headed for a gravity source gains energy which is known as "blue-shifting". The reason for these names make sense if you think about them.

 

Great! Thank you! But is this answer correct? I want to print it to show my teacher.

Okay. Technically light never loses any energy or speed when traveling through a medium it always travels at c. It is always a constant even in a medium. So technically light never slows down no matter what. So light never loses speed or energy when traveling through a medium.

That's the finally correct answer, right?