Is the index of refraction constant for a given medium?

[Phys12]

If we have a medium (say, glass) with an index of refraction, n=1.33, the speed of light in it will be c/1.33. However, blue light travels slower in glass than does red light. Since c is constant and the speed of light is changing, doesn't that mean that the index of refraction will vary based on the frequency of the incident light?

 

[anorlunda]

The refractive index of many materials (such as glass) varies with the wavelength or color of the light used, a phenomenon known as dispersion.

 

[Phys12]

Okay. Also, since the wavelength of light remains constant when it passes through a medium, the frequency has to decrease in order to have a lower velocity, correct?

 

[Vanadium 50]

Also, since the wavelength of light remains constant when it passes through a medium

Why do you think that?

 

[Phys12]

Why do you think that?

Actually, I got it the other way around. My statement should've read: "since the frequency of light remains constant when it passes through a medium, the wavelength has to decrease in order to have a lower velocity, correct?"

But when I think about it again, frequency is the number of times a certain wave of a given wavelength passes through a point and if we're changing the velocity of the wave, that should change the frequency and not the wavelength.

Edit: on another thought, the energy of the photon stays the same in vacuum and in water so we need to keep E=hf (where f is the frequency) constant. E is also equal to hv/lambda (v is the speed of light, lambda is the wavelength), but if we want to keep the frequency constant and we're changing v, we must change lambda too.

 

[olivermsun]

Actually, I got it the other way around. My statement should've read: "since the frequency of light remains constant when it passes through a medium, the wavelength has to decrease in order to have a lower velocity, correct?"

Write down the relationship between frequency, wavelength, and velocity and you will have the answer.

But when I think about it again, frequency is the number of times a certain wave of a given wavelength passes through a point and if we're changing the velocity of the wave, that should change the frequency and not the wavelength.

See above and figure out which two of the three quantities have to be constant across a change in medium.

Edit: on another thought, the energy of the photon stays the same in vacuum and in water so we need to keep E=hf (where f is the frequency) constant. E is also equal to hv/lambda (v is the speed of light, lambda is the wavelength), but if we want to keep the frequency constant and we're changing v, we must change lambda too.

So what's your answer?

 

[Phys12]

So what's your answer?

I'm going to say this one: The energy of the photon stays the same in vacuum and in water so we need to keep E=hf (where f is the frequency) constant. E is also equal to hv/lambda (v is the speed of light, lambda is the wavelength), but if we want to keep the frequency constant and we're changing v, we must change lambda too.

Because we can change the wavelength and still keep the frequency constant by changing the velocity.

 

[sophiecentaur]

Because we can change the wavelength and still keep the frequency constant by changing the velocity.

Whilst the Maths of that statement is correct - you can re-arrange an equation to put any variable on the left - the Physics of it are the wrong way round. Once a wave has been launched, you cannot change its frequency (in an inertial frame). All you can do it change the velocity by choosing the right medium and that will result in a wavelength change.
The description of how an EM wave moves through a substance is very non-trivial in terms of photons so best not to try until the rest of the basics have been totally sorted out, along with the Quantum mechanics that are involved.