# Does reflection change the frequency of light?

1. Mar 2, 2015

### Reallyfat

Note that I am not addressing only specular reflection here, but both kinds.

Anyway, so if I had light of a certain frequency incident upon a surface, will the light that reflects off that surface also have the same frequency? That would imply that it had retained the full 100% of its energy, which would violate the first law of thermodynamics, since it has changed its momentum and presumably also that of the surface on which it was incident.

2. Mar 2, 2015

### jbriggs444

Are you working in a frame of reference where the reflecting surface starts at rest, one in which it ends at rest or one in which total momentum is zero?

3. Mar 2, 2015

### Reallyfat

We would have to use a frame where the reflecting surface would have an initial momentum of zero, if we were to try and apply this in a realistic situation. Its momentum would have to change, of course, even if very slightly.

4. Mar 2, 2015

### jbriggs444

One certainly could use such a frame, though there is no requirement to do so.

In this frame, what is the relevant mirror velocity for purposes of calculating the Doppler effect?

5. Mar 2, 2015

### Reallyfat

That would be variable from mirror to mirror and surface to surface. I'm not looking for a calculation to a specific case though, but just a general explanation. If I had a glass block, for example, from which an incident white ray was reflected, would the reflected ray not have a frequency shifted toward the red side of the spectrum (since it must have lost some energy, particularly if some light was absorbed by the block)?

6. Mar 2, 2015

### jbriggs444

My apologies -- I am not trying to ask for a calculation. I am trying to get you to think about the question. If the reflecting surface is moving, this will affect the frequency of the light that is reflected, right?

If the reflecting surface starts at rest and if momentum is transferred, does it end at rest?

7. Mar 2, 2015

### Reallyfat

The reflecting surface: yes, though that change in frequency would be due to the Doppler effect and not the conservation of energy explanation that I am trying to point to. What I would like to know is this: If a ray of light were to reflect off any surface, would the total energy of the reflected ray not be lower than that of the incident ray? It will, of course, cause an initial change in momentum to the reflecting surface, though that would be negligible and would very quickly opposed by repulsion from other nearby atoms in the surface, bringing the net change to zero. Yet, the light has initially caused the momentum of the atoms it was incident upon to change, right? The momentum of the light has changed too, at least in terms of its direction. Now, since the light has caused the reflecting surface's momentum to be changed slightly, that means it has done some work. The individual photons should thus have lost some energy, and that would mean that they have a lower frequency than they did in the incident ray.

I guess it boils down to just one thing: is the reflection of a light a 100% efficient process?

8. Mar 2, 2015

### jbriggs444

A change in frequency is a change in energy. You still have not correctly answered the question in post#2 above.

9. Mar 2, 2015

### Reallyfat

I know that a change in frequency is a change in energy, that is the point I am trying to make here. That frequency should change even without the Doppler effect.

Which question have I not answered correctly?

10. Mar 2, 2015

### jbriggs444

What frame of reference are you using?

11. Mar 2, 2015

### Reallyfat

The reflecting surface is initially at rest. And the incident light will cause some change in momentum to the incident area, but that is going to be opposed by other nearby atoms in the surface, which will bring it to rest again if it should move.

12. Mar 2, 2015

### jbriggs444

"at rest" is not a frame-independent statement.

13. Mar 3, 2015

### Soren

From the best of my knowledge, no frequency does not change. However, the amplitude would change if the reflection coefficient was <1. Frequency of light is a property of the refractive index and can go up and down depending on the media it is propagating.

14. Mar 3, 2015

### jbriggs444

The motion of a mirror does affect the frequency of the reflected light. The Doppler effect applies.

The back-and-forth in this thread is addressing the nit-picky question of how the tiny sliver of momentum transferred into the mirror figures into that motion -- do we count the motion of the mirror pre-collision, post-collision or in the middle of the collision.

15. Mar 3, 2015

### christopher.s

So what you are asking is if a beam of light (monochromatic) is incident on a surface that is not perfectly reflecting (i.e. some absorption, or transmission,) and loses some energy, does the corresponding wavelength of light change? I think the answer is in most cases is no, as Soren said it is the amplitude of the beam that will change. However, you will have some local effects that will emit and absorb light at different wavelengths although I think it would be more of a near field effect and mostly non-radiative. The bulk effect is to retain the original "frequency" of light, or its ability to impart momentum.