# Do Light Waves Have Amplitude?

1. ### peter.ell

43
Waves in general have three properties: frequency (related to wavelength), amplitude, and speed. When referring to light as a wave, it's wavelength and speed are always referenced but never its amplitude, and I was wondering if light has a fixed amplitude for all wavelengths or if it changes.

Sound waves, for example, get louder in two cases: when there's more of them (multiple speakers) or when the amplitude of the sound waves is increased (more volume). Obviously having more light waves (multiple light sources) will result in increased brightness, but can the amplitude of a light wave change as well?

Since I've never heard the amplitude of a light wave referred to, plus the fact that higher frequency (shorter wavelength) light is referred to as more energetic, I was wondering if perhaps the intensity of light is only related to how much of it there is, and maybe the amplitude of a light wave is set. After all, how would a light wave of a given wavelength increase its amplitude? If an electron falls a greater distance, the light emitted won't be more intense, it will actually have a higher frequency, right?

Thanks for clearing this up for me!

### Staff: Mentor

I think I remember reading that the amplitude was planks constant or something related to it. Intensity of light refers to the number of photons and the energy of each is based on its frequency.

3. ### sweet springs

575
Hi,　peter.ell

Brightness of light corresponds to amplitude. Amplitude of light from two light bulbs are larger than that from one light bulb. Amplitude of light from each bulb is additive.

Regards

### Staff: Mentor

Brightness does not correspond to the amplitude of each photon. Instead it corresponds to the number of photons.

5. ### sweet springs

575
...And number of photons also corresponds to amplitude of light, doesn't it?

Regards.

### Staff: Mentor

If by amplitude you mean how bright something like a light bulb is sure. However when speaking of individual photons, which is what I think the OP is asking about, that is not correct.

7. ### JaWiB

289
I don't think you can define "amplitude" for a single photon. In the classical picture, light is an electromagnetic wave and the amplitude of the electric/magnetic fields is the property you talk about. In the quantum picture, light is made up of photons and the number of photons describe the amplitude. That's my understanding.

### Staff: Mentor

Yes, I agree that we generally use amplitude to mean the number of photons. However in terms of a single photon I am unsure whether we can define amplitude or not. I swear I remember reading something about planks constant having something to do with the amplitude though.

9. ### HallsofIvy

40,957
Staff Emeritus
Where did "photons" come into this? The original post was about the amplitude of light waves, not photons.

### Staff: Mentor

This plus the context of the OP's post suggests he is talking about a photon, not a large collection of photons. Unless I am missing some sort of difference between "light wave" and "photon".

11. ### sweet springs

575
Hi,　I write down energy density of monochoromatic light of frequency ν as

1/2 (ED + BH) = ε0 E^2 = N h ν

where E is electric field, D is density of electric flux, B is density of magnetic flux, H is magnetic field intensity, ε0 is electric permittivity in vacuum, h is Planck constant and N is number density of photon.
Amplitude of light, E, undertakes superposition or interference of lights from various sources.
Lights of frequency v1 and ν2 can have same amplitude E or same energy density when N1 h ν1 = N2 h ν2, higher the frequency of light, fewer the number density of photons. However, quality differs, for example, hundreds of green color photons entertain us but one X-ray photon of same energy may harm our cell.

Regards.

Last edited: Sep 16, 2011

### Staff: Mentor

Of course, but can you define amplitude for a single wave or photon as the OP is asking?

13. ### sweet springs

575
How about N = 1, say single photon in unit volume, in the formula 1/2 (ED + BH) = ε0 E^2 = N h ν?

Last edited: Sep 16, 2011

### Staff: Mentor

But what is the amplitude referring to in this equation? The amount of energy found in N photons?

15. ### sweet springs

575
E in this formula is amplitude of light,　say square root of h ν / ε0　for single photon in unit volume.

Regards

Last edited: Sep 16, 2011

### Staff: Mentor

Amplitude of light meaning that it is the energy of N photons?

17. ### Naty1

Photons exhibit wave particle duality, right?? What doesn't?? ..so they DO have amplitude and wavelength...and experience wave inteference and polarization, for example.

Einstein's photon model accounted for the frequency dependence of light's energy, E = hv.
I n a sound wave, extra energy is louder, in light, it's a higher frequency....say X-ray instead of visible.

See here for an illustration of an electromagnetic wave: note the amplitude is given by the amplitude of the electric (E) and magnetic (B) field vectors....amplitudes vary.

"intensity" is one thing to the human eye, another to objective instruments. Maybe lumens is most closely related to "brightness" or "intensity"....I'm not sure that's the BEST term.

Symmetry777 likes this.
18. ### Philip Wood

1,172
When we have large numbers of photons, the photon stream behaves as an e-m wave, in which energy is spread out over broad wavefronts. A natural meaning to give to amplitude is the maximum value, Emax of the electric field strength, as the wave passes a point. Alternatively, it could be the maximum value, Bmax of the magnetic field strength. One would know which one from the units. In any case, they are related very simply:
Emax = cBmax.

The wave intensity, i.e. the wave energy per unit area per second passing through an area normal to the waves' direction of travel is $\frac{1}{2}c\epsilon_{0} E_{max}^{2}$. So, assuming monochromatic waves of frequency f, for which the photon energy is hf, the photon flux density (i.e. the number of photons per unit area per second passing through an area normal to the waves' direction of travel) is $\frac{1}{2}\frac{c\epsilon_{0}}{hf} E_{max}^{2}$. So the photon flux density is proportional to Emax2, i.e. to amplitude2.

Last edited: Sep 17, 2011
19. ### Redbelly98

12,053
Staff Emeritus
Yes, exactly. The amplitude refers to the peak electric or magnetic field strength.

It is not necessary to bring photons into the discussion, the original question was about the classical description of light as a wave.

20. ### klimatos

455
It has always been my understanding that the frequency, wavelength, and energy content (amplitude of a sort) can be rigorously related by two equations:

The first equation relates frequency to wavelength to the speed of light; that is, the speed of light in meters per second is equal to the frequency in cycles per second times the wavelength in meters.

The second equation relates the energy content of the photon to both frequency and wavelength. This energy content is equal to Planck's Constant in Joule seconds times the frequency and is also equal to Planck's Constant times the speed of light, the product divided by the wavelength.

I believe that these two equations will work if you consider a single wave to be the equivalent of a photon.