Speed of Light Through a Medium?

[Mike Hawk]

Velocity is a vector, so it has direction. Speed is the magnitude of velocity, so it doesn't have direction.Speed is the rate of motion, or the rate of change of position. It is expressed as distance moved (d) per unit of time(t). Speed is a scalar quantity with dimensions distance/time. Speed is measured in the same physical units of measurement as velocity, but does not contain an element of direction. Speed is thus the magnitude component of velocity. Velocity contains both the magnitude and direction components.

My question is, since blue light is displaced more than red, through a medium, the blue light has traveled farther distance, so why would we say that blue light travels slower in a medium. Since it traveled farther in the same amount of time?

Wouldn’t that indicate that it traveled faster in a medium?

 

[Pete]

My question is, since blue light is displaced more than red, through a medium, the blue light has traveled farther distance, so why would we say that blue light travels slower in a medium. Since it traveled farther in the same amount of time?

Wouldn’t that indicate that it traveled faster in a medium?

Hi Mike, welcome to sciforums!
It sounds like you're thinking about white light refracting through a prism, right?

That's a great question - it shows that you're independently thinking about how things work to get a good understanding, rather than just taking the texts and teachers at face value.

Yes, the blue light is refracted more than the red light, because it travels slower in the medium.
Yes, this means that the blue light travels a greater distance through the prism.
But, your intuition that the blue light takes the same time to traverse the prism as the red light isn't quite right - it actually takes longer for the blue light to pass through.

Do you see why you wouldn't notice this time difference?

 

[Mike Hawk]

Thank you! No, I'm sorry. I don't see why. How do we know for sure that it takes longer to travel through the prism?

 

[Pete]

Because of what you said. It goes slower, and travels further. Therefore... it must take longer, right?

 

[Mike Hawk]

I'm sorry. I just don't get it. If it travels a greater distance in the same amount of time, then it would be faster. So, how do we know it isn't traveling a greater distance in the same amount of time?

 

[Neddy Bate]

If it travels a greater distance in the same amount of time, then it would be faster. So, how do we know it isn't traveling a greater distance in the same amount of time?

You could send two laser beams straight through an extremely thick plate of the optical medium. Let one laser beam be red, and the other blue. Put a photocell detector on the other side, and measure the transit times for both light beams.

I have a feeling that is not the kind of answer you were looking for, though.

 

[Mike Hawk]

Huygens died in 1695 and Newton died in 1726. Did they have photosensors and lasers back then?

The only thing that my teacher could say was that Huygens suggested wave behavior explained it better. All that Newton could say was that it was accelerated when it hit the surface because it went into (fits?) That’s why Huygen’s idea was accepted because the wave behavior made more sense.

But don’t all other waves, like sound waves, travel faster through a medium?

I just can’t understand how we know for sure that it hasn’t traveled a greater distance in the same amount of time? Suggesting that it travels faster through a medium. Have we measured the time it takes for each to travel through the prism and measured it with photosensors? Is that how they know?

 

[Neddy Bate]

Have we measured the time it takes for each to travel through the prism and measured it with photosensors? Is that how they know?

I don't know. That's why I said that my answer probably wasn't the kind of answer that you were looking for.

You raise interesting questions.

 

[Pete]

I'm sorry. I just don't get it. If it travels a greater distance in the same amount of time, then it would be faster. So, how do we know it isn't traveling a greater distance in the same amount of time?

OK, to answer your question properly means looking for reasons that a medium's index of refraction in Snell's Law is considered to be inversely proportional to the speed of light in that medium. Bear with me, because I'm an amateur. Check what I say against more reliable sources, and don't be afraid to call me out if something sounds wrong.

Theory:
There are some good models of light that suggest that a higher index of refraction follows from a slower speed of light in the medium.
Take a look at the Huygens–Fresnel principle, which describes wave propogation by considering each point in a wave front as a wave source:

And also check out Fermat's principle, which is another consequence of Huygen's principle which leads to the same conclusion.

Experiment:
The most direct measurement might be with the Fizeau-Foucault apparatus which can measure the speed of light as it bounces off a rotating mirror. By placing a tube of water in the path of the light beam, Fizeau showed that light travels more slowly in water than in air, which helped to disproved Newton's corpuscular theory of light.
I think that interferometry would provide more precise measurements. For example, Fizeau used his eponymous interferometer to measure the speed of light in moving water:

 

[Mike Hawk]

I apologize. I was just giving you the only answer that my teacher gave me.

I believe that light does slow down through a medium. There are lots of experiments to prove it. I even found one that showed that they stopped light completely.

I just don’t understand how we know for sure that longer wavelengths travel faster through a medium than shorter wavelengths.

Red 6220-7800
Blue 4920-5770

What if the blue travels this greater distance in the same the amount of time as the red? Then blue would be faster. Am I missing something regarding speed vs. velocity, or distance vs. displacement? Why do we assume because the blue traveled a greater distance, that it is slower. If it traveled farther in the same amount of time, wouldn’t this indicate it was faster?

Thank you!

 

[Pete]

No need to apologise!

I can't answer your question.
My own understanding is simply that the index of refraction has been shown to correlate with the speed of light in the medium, ie that a greater speed difference across the boundary causes more refraction.

What if the blue travels this greater distance in the same the amount of time as the red? Then blue would be faster.

Yes, it would.
But is there any reason to think that it does travel that distance in the same time?

Why do we assume because the blue traveled a greater distance, that it is slower.

We don't say that it is slower because it traveled a greater distance - we say that it must be slower because it is refracted more. More slowdown leads to more refraction.

 

[Pete]

I imagine that quantum mechanics should predict how fast certain wavelengths of light travel through a medium as well, but that's beyond my ken.

 

[Mike Hawk]

In optics, Fermat's principle or the principle of least time is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time.

So, it is all based on this principle, right? But in all the stuff I’ve learned about speed vs. velocity. It states that if something has more displacement in the same amount of time it is faster.

I'm sure there is a simple explanation but I just can't find it.

Thank you!

 

[prometheus]

The speed of light in a medium is given by the following: $$v= \frac{c}{n}$$ where n is the refractive index. I imagine you've seen examples like the refractive index of water is 1.33 or something, however (as always) this is a simplification. Refractive index is not just a constant but depends on the wavelength of the light, and therefore the speed of light for different wavelengths in a medium will be different. From a quick look on wikipedia it looks like that n is bigger for blue light than it is for red light, so red light is actually faster than blue light in a medium.

Another way to see this is that, looking at pete's picture in post #2 the red light is deflected less than the blue light, meaning that the change in speed for red light as it passes into the medium is smaller, or that it is closer to c than the blue light.

 

[James R]

From a quick look on wikipedia it looks like that n is bigger for red light than it is for blue light, so blue light is indeed faster than red light in a medium.

Shouldn't that be the other way around? Blue is refracted more than red. That's in glass, anyway.

 

[prometheus]

So, it is all based on this principle, right? But in all the stuff I’ve learned about speed vs. velocity. It states that if something has more displacement in the same amount of time it is faster.

Thank you!

Another thing I've just thought of is this: suppose there is a red photon and a blue photon that enter the prism together. You're assuming they also have to exit together, but there's no reason to assume this is so. This is why the polarization of the light after it exits the prism will in general be different to the polarization of the light that entered. For this reason you can use prisms as polarizers.

 

[prometheus]

Shouldn't that be the other way around? Blue is refracted more than red. That's in glass, anyway.

see edited post. I was getting mixed up between wavelength and frequency.

 

[Pete]

So, it is all based on this principle, right? But in all the stuff I’ve learned about speed vs. velocity. It states that if something has more displacement in the same amount of time it is faster.

Yes, if something has more displacement in the same time, that means faster.

I'm sure there is a simple explanation but I just can't find it.

The time is not the same.
Blue light takes longer to go through the prism than red light.

 

[Mike Hawk]

Pete-"The time is not the same.
Blue light takes longer to go through the prism than red light."

You said the time is not the same. That’s what I want to know. How do we know this. How do we know the amount of time?

Red 1.33
Blue 1.343

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?

 

[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.