How do we measure the frequency of light?

[lenfromkits]

Do we essentially measure its wavelength and calculate the frequency?

I thought we figured out frequencies by refracting the light into its many frequencies - (ie, like we see when looking at a Doppler shift). But, refraction formulas are based on VELOCITY, not wavelength and light travels at a constant speed.

So, given a hypothetical situation of slowing down light (possible through denser mediums), would the colours refract at the same angles - since the wavelengths are the same, or would they refract differently since the speeds are different (assuming you manage to keep the transition from one medium to another the exact same ratio)

Thanks!

 

[NobodySpecial]

Do we essentially measure its wavelength and calculate the frequency?

It's generally easier, at optical frequencies, to calculate wavelength, you can do it with a couple of flat microscope slides and a ruler. Since you know the velocity you can get the frequency

So, given a hypothetical situation of slowing down light (possible through denser mediums), would the colours refract at the same angles - since the wavelengths are the same, or would they refract differently since the speeds are different (assuming you manage to keep the transition from one medium to another the exact same ratio)

The frequency doesn't change with refractive index, but the speed changes and so the wavelength must change

 

[K^2]

There are no direct ways of measuring frequency, because there are no recording devices capable of operating anywhere near optical frequencies.

Indirect methods are many, however. First, yes, you can measure wavelength. Michelson Interferometer is the simplest way and gives good results. You can also combine two beams with similar frequencies and use beats to measure the difference. In some media, you can use known absorption spectra to determine dependence of refraction index on frequency and measure the former to determine the later. And so on.

 

[Cthugha]

There are no direct ways of measuring frequency, because there are no recording devices capable of operating anywhere near optical frequencies.

Strictly speaking, this is not true. You can in principle even have measurements of the oscillating electromagnetic field itself. See for example E. Goulielmakis et al, Science 305, 5688, 1267-1269 (2004).

But of course I agree that such techniques are too complicated and not really useful for everyday usage.

 

[sophiecentaur]

It should be possible to use the beats between a known, reference optical frequency and an unknown frequency to produce a measurable RF frequency. Or is that a cop-out?

 

[NobodySpecial]

At optical wavelngths the LO frequency would still probably need to be a light source so you don't know it's frequency directly - you also have to find some sort of non-linear optical effect to get them to mix.

 

[lenfromkits]

The frequency doesn't change with refractive index, but the speed changes and so the wavelength must change

Hi, thanks Mr NobodySpecial-but-very-helpful.

Okay. This makes sense. What happens to this slower light then as it hits a denser medium at an angle? So...if a certain frequency refracts at a certain angle going from air to glass, and somehow we create that exact same 'ratio' between mediums while light is slowed down, will it refract at the same angle or different?

In other words, you mention the frequency is the same, so will it refract the same, or will it refract based on the wavelength or speed? This is the main question I'm after answering.

Thanks!

 

[NobodySpecial]

The change on going from one refractive index to another only depends on the ratioof their indexes.
So going from air (n=1) to water (n=1.3) the light will slow down to c * 1/1.3 and the light will bend, then going from water into say diamond (n=2.4 almost twice as much) it will slow down by almost the same factor again c * 1.3/2.4 and bend by the same angle.

 

[lenfromkits]

The change on going from one refractive index to another only depends on the ratioof their indexes.
So going from air (n=1) to water (n=1.3) the light will slow down to c * 1/1.3 and the light will bend, then going from water into say diamond (n=2.4 almost twice as much) it will slow down by almost the same factor again c * 1.3/2.4 and bend by the same angle.

Thanks. Okay, just to clarify, if we we pretend that those two ratios are identical for a moment then the refraction would be the same - based on 'velocity.' It sounds like it is entirely based on velocity by what you are saying, so that if we had a higher frequency beam of light with a longer wavelength - but the exact same speed as the beam you are describing, then it also would bend along the same path (even though it has a totally different frequency and wavelength)?

If that is not the case for 'light,' then what about other 'normal' waves?

(so, I'm really trying to figure out exactly which variable - frequency/wavelength/speed causes the angle of refraction, and it should be determinable because we can always keep anyone variable constant while changing the other two and then looking to see how it refracts)

 

[NobodySpecial]

Yes, refractive index changes the velocity, frequency stays the same so wavelength must change. You can measure the change in speed directly with a clock. (In practice there is a slight extra complication that the refractive index of most real materials also varies with wavelength)

The bending is caused only by change in speed - it's called Fermat's principle and it's one of the cleverest things in physics.
What it says is that the light takes the path through the two materials that minimises the total time to get from A-B.

You can even picture it in the 'real' world.
Suppose you had to rescue somebody in the ocean further down a beach.
You could jump in and swim directly to them, BUT you can run faster than you can swim, so it makes sense to run along the beach and then at some point get into the water and swim diagonally out toward them.

The ratio of how far you run and how far you swim - and so the point you enter the water - and therefore the angle between your running path and swimming path - only depends on the ratio of how fast you swim and how fast you run.
You pick them to minimise the time to the swimmer - just as the photon does.

How the photon 'knows' which path to take is the basis of quantum mechanics.

 

[lenfromkits]

You can even picture it in the 'real' world.
Suppose you had to rescue somebody in the ocean further down a beach...

Wow - what an awesome answer. Thanks!

 

[lenfromkits]

Yes, refractive index changes the velocity, frequency stays the same so wavelength must change. You can measure the change in speed directly with a clock. (In practice there is a slight extra complication that the refractive index of most real materials also varies with wavelength)

The bending is caused only by change in speed - it's called Fermat's principle and it's one of the cleverest things in physics.
What it says is that the light takes the path through the two materials that minimises the total time to get from A-B.

You can even picture it in the 'real' world.
Suppose you had to rescue somebody in the ocean further down a beach.
You could jump in and swim directly to them, BUT you can run faster than you can swim, so it makes sense to run along the beach and then at some point get into the water and swim diagonally out toward them.

The ratio of how far you run and how far you swim - and so the point you enter the water - and therefore the angle between your running path and swimming path - only depends on the ratio of how fast you swim and how fast you run.
You pick them to minimise the time to the swimmer - just as the photon does.

How the photon 'knows' which path to take is the basis of quantum mechanics.

Hmm. It seems to me that in the "real" world, the scenario would be that if there were 5 people drowning and you headed straight for one, you would "end up" rescuing the one that took the least time to get to, not the one you set out to rescue, yet everyone would wonder how you managed to figure out the exact place to jump into the water to meet this person. In other words, whatever clever "intent" that the light has about what path to take, never pans out. Someone with intelligence would have to understands fermats principle and intentionally alter the angle of the light-emitter in order to hit the "actual" intended target.

I think saying the light always chooses the correct path is like saying I have amazing precise aim for hitting a location precisely 3 inches below the dart board, even though I was aiming for a bullseye. Here it would only be amazing if I "meant" to hit this spot, hence the term," ah, I meant to do that"