Colour depends on wavelength or frequency?

[NTesla]

Homework Statement

Kindly see the attached pic for the question.

Relevant Equations

$lambda = {c/v}$

This is the Question: It's from the book: Concepts of Physics by Dr. H C Verma.

The common observation is off course that a red light would appear red even when viewed from under the water (for eg in a swimming pool).

But, in the same book, it's been written that colour depends on wavelength, therefore, as wavelength changes after going in a medium, the colour should change, but it doesn't.
Here's the screenshot of that statement from this book:

Also, in Feynman's lecture, it is written that colour depends on wavelength. Here's the screenshot of that excerpt:

I have read various articles on internet, and there's no consensus as to what does the colour depend on. It just appears to me, that some people on net are insisting that the colour depends on frequency, only because that's what solves the question. But it doesn't make sense. If it's frequency in which the colour depends, then why did Feynman wrote that it's wavelength. And why did H C Verma Sir write the same.

Kindly help. Which does it depend on: wavelength or frequency. Though, according to the formula, $lambda = {c/nu}$, it could also be deduced that wavelength and frequency are interrelated. But, then again the same question arises, that why did Feynman and Dr. Verma choose to write that it's wavelength.

 

[anuttarasammyak]

You do not have to worry about it. $$\lambda=\frac{c}{\nu}$$

 

[NTesla]

I'm trying to learn how to type formulas in here. But seems it will take some more time.

 

[haruspex]

Since the receptors are within a constant medium, it makes no difference whether you consider them as tuned by wavelength or by frequency. The relationship is fixed in that context. Whatever changes to wavelength may have occurred on the way to the eye, by passing through glass, water etc., are not relevant.
If you could find some way of varying the wavelength received at the cone for the same frequency, my bet is that it still would change nothing and frequency wins.

 

[Hill]

Since molecular changes in light-sensitive proteins depend on energy of absorbed photons and not on their momenta, they depend on the frequency and not on the wavelength.

 

[NTesla]

Since molecular changes in light-sensitive proteins depend on energy of absorbed photons and not on their momenta, they depend on the frequency and not on the wavelength.

In response to your argument, can this argument not be made that wavelength and frequency both are interdependent(by the formula lambda = c*nu) , if one one changes, so does the other. So, why it would be correct to say that colour depends on the frequency, & not on wavelength.
I also would like to know as to why Feynman and Dr. H C Verma, both, have chosen to write that it's wavelength on which colour depends.

 

[Hill]

In response to your argument, can this argument not be made that wavelength and frequency both are interdependent(by the formula lambda = c*nu) , if one one changes, so does the other. So, why it would be correct to say that colour depends on the frequency, & not on wavelength.
I also would like to know as to why Feynman and Dr. H C Verma, both, have chosen to write that it's wavelength on which colour depends.

This is so only in vacuum. Otherwise, there are three variables, i.e. frequency, wavelength, and the speed of light.

 

[NTesla]

What's your opinion on the statements made by Dr. Feynman and Dr. Verma, that it's wavelength on which the colour depends.

 

[Hill]

What's your opinion on the statements made by Dr. Feynman and Dr. Verma, that it's wavelength on which the colour depends.

I think that Feynman talks about light in vacuum.

 

[anuttarasammyak]

Frequency is invariant when light goes through medium. If we feel bluish in pool water, we will know that not frequency but wavelength matters.

 

[kuruman]

why did Feynman and Dr. Verma choose to write that it's wavelength.

If you read carefully what they wrote and you have highlighted,, they both refer to what how light is perceived by a human observer. H C Verma Sir writes "The colour sensation to a human eye is related to the wavelength of light" whilst Richard P. Feynman writes about the "apparent" change in color. They do so to categorize the regions of the EM spectrum, e.g. microwave, visible, etc. on the basis of sensation assuming propagation in vacuum, as @Hill already suggested. I can only guess that those luminaries did not deem it necessary to specify that the medium of propagation is indeed vacuum.

Now for the meat of your question. Let's consider first the classical description of light in terms of oscillating EM waves. Consider the boundary condition at the interface of air and water. Surely you don't believe that how fast the electric field oscillates up down changes while the wave traverses from one medium to the other. So the frequency stays constant whilst the speed changes. This can only mean that the wavelength changes, not the frequency.

This brings me to what is your eye sensitive, wavelength, frequency or something else? A simple experiment would be to compare the color of an object in air and at the bottom of a pool with your head under water and your eyes open. You will see no color change.

So is the conclusion that the color perception depends on frequency? I think not. In the quantum description of light, a photon is absorbed and its energy is transduced by the appropriate receptor to an electrical signal that is interpreted by the brain as a specific color. If I had to answer the question in the title of this thread, I would say that (the perception of) color depends on neither wavelength nor frequency; it depends on photon energy, $\epsilon=\hbar \omega$ which is independent of the propagation medium.

 

[Hill]

Frequency is invariant when light goes through medium. If we feel bluish in pool water, we will know that not frequency but wavelength matters.

This effect is consequence of different absorption rates of different light wavelengths by water.

 

[anuttarasammyak]

This effect is consequence of different absorption rates of different light wavelengths by water.

Thanks.
And I recall that our eys are always wet.

 

[NTesla]

@kuruman, @Hill, @anuttarasammyak: Appreciate your kind help in resolving the concept.

However, a followup question is coming to mind, that in red shift of light coming from distant galaxy, the light is travelling in vacuum. The light's wavelength increases due to expansion of spacetime itself. The frequency remains constant, and so does the energy. But if the energy remains the same, then it's colour should be same at the start and at the finish. But it's called red shift only because the light from distant galaxy does change in colour due to expansion of space-time.
But if what @kuruman is saying is correct, that the colour depends on energy, then the colour of light coming from distant galaxy must not have changed. But it does change.

How do I understand this ?

 

[Hill]

The frequency remains constant, and so does the energy.

This is incorrect. In the cosmological redshift, wavelength, frequency, and energy change.

 

[kuruman]

But if what @kuruman is saying is correct, that the colour depends on energy, then the colour of light coming from distant galaxy must not have changed. But it does change.

Yes, color depends on energy, but if the frequency changes because of galaxy recession, so does the energy which is proportional to frequency.

Read about the Pound and Rebka experiment for another example what happens to the energy of a photon when it is "dropped" from a tower.

 

[NTesla]

Yes, color depends on energy, but if the frequency changes because of galaxy recession, so does the energy which is proportional to frequency.

Read about the Pound and Rebka experiment for another example what happens to the energy of a photon when it is "dropped" from a tower.

The gist of Pound Rebka experiment that I understood, is that in a gravitational potential well, the energy of photon increases if it falls down the well, and vice a versa if it comes up.

Is the phenomenon of increase in energy of photon in a gravitational potential well, same as increase in energy of the photon when it is in deep space, free from any massive object & therefore free from a gravitational well, but the wavelength is increasing due to stretching of the space time fabric ?

 

[Orodruin]

This is incorrect. In the cosmological redshift, wavelength, frequency, and energy change.

This is a completely separate issue to what is being discussed here. Generally a light wave never has a definite invariant frequency without reference to an observer. But it is not what is being discussed.

 

[sysprog1]

But if what @kuruman is saying is correct, that the colour depends on energy, then the colour of light coming from distant galaxy must not have changed. But it does change.

The Doppler effect, to which we ascribe redshift, is a change in apprehended or perceived frequency that is attributable to a change in relative motion, i.e. to a change in kinetic energy.

 

[Hill]

This is a completely separate issue to what is being discussed here. Generally a light wave never has a definite invariant frequency without reference to an observer. But it is not what is being discussed.

I know this. In my post you have quoted, post #15, I replied to and have qouted a specific sentence in the OP's post #14.

 

[jbriggs444]

Is the phenomenon of increase in energy of photon in a gravitational potential well, same as increase in energy of the photon when it is in deep space, free from any massive object & therefore free from a gravitational well, but the wavelength is increasing due to stretching of the space time fabric ?

A falling photon light pulse gains energy and frequency while it decreases in wavelength. Technically, this assumes hovering observers.

A rising photon light pulse loses energy and frequency while it increases in wavelength. Again, assuming hovering observers.

Alternately, one can think of the frequency shift as a consequence of gravitational time dilation.

Alternately, one can adopt a free falling tangent inertial reference frame and approximately account for the shifts as a consequence of the Doppler effect because the "hovering" observer is undergoing proper acceleration. This is the equivalence principle in action.

Shifting to consider a photon light pulse crossing significant cosmological distances in an expanding universe...

The received photon has less energy, a lower frequency and a longer wavelength relative to the receiver than the emitted photon had relative to the emitter. It is "the same thing" as a gravitational well in the sense that general relativity makes both predictions. It is not "the same thing" because the universe is not a gravitational well. Expansion is not the same thing.

 

[Orodruin]

It is not "the same thing" because the universe is not a gravitational well.

I disagree. Both frequency shifts are exactly the same mathematically (although that math is far beyond "introductory physics homework"). The only difference between the cases is that one case assumes a stationary spacetime and the other a FLRW spacetime, which makes the computational methods somewhat different. However, both frequency shifts are related in exactly the same way to the propagation of a light pulse in a background spacetime with an emitting and a receiving observer.

 

[Orodruin]

The Doppler effect, to which we ascribe redshift, is a change in apprehended or perceived frequency that is attributable to a change in relative motion, i.e. to a change in kinetic energy.

No, it is attributable to relative motion between the source and observer. No velocity needs to be changing. The frequency of a light pulse is not something that is uniquely defined without reference to an observer.