# Wave theory of light

## Main Question or Discussion Point

For wave theory of light, it said that energy of light is depend only on its brightness and independent of its frequency.
I would like to ask which equation shows that wave energy is independent of frequency..??

thank you.

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ZapperZ
Staff Emeritus
2018 Award
For wave theory of light, it said that energy of light is depend only on its brightness and independent of its frequency.
You should cite this source. That is the one thing we try to make people do when they talk about something they read or heard.

I would like to ask which equation shows that wave energy is independent of frequency..??
Actually, it DOES! Maybe the energy PER CYCLE or per period isn't dependent on frequency in classical wave theory of light, but energy in a unit time does! Think about it. The higher the frequency, the more cycles in that unit time that you measure, the more energy you will get. So yes, even in classical wave theory of light, frequency does matter IF you are looking at it per unit time.

Zz.

For wave theory of light, it said that energy of light is depend only on its brightness and independent of its frequency.
I would like to ask which equation shows that wave energy is independent of frequency..??

thank you.
Then energy of light actually is dependant on frequency by the relation $$E=hf$$ where h is Planck's constant.

ranger
Gold Member
Then energy of light actually is dependant on frequency by the relation $$E=hf$$ where h is Planck's constant.
That can be restated:

The energy of a photon is dependant on the frequency. I think its incorrect to say the energy of light with respect to that equation.

That can be restated:

The energy of a photon is dependant on the frequency. I think its incorrect to say the energy of light with respect to that equation.

But the light is made up of photons. The only way this dependancy couldn't be extended to light frequencies in general is if there were less photons in high frequency light than in low frequency light. Is this true?

the equation of light intensity

the equation of average intensity
I = .5 nceεo sqr(E)
n refractive index of medium
c velocity of light
εo permativity of medium
E max value of Electric filed
as we know that light is an electromagnetic wave has 2 perpendicular fields electric and magnetic

ranger
Gold Member
But the light is made up of photons. The only way this dependancy couldn't be extended to light frequencies in general is if there were less photons in high frequency light than in low frequency light. Is this true?
It doesnt mean less or more photons, it means photons with lower/higher energy levels.

ranger, that wasn't what he said. He's saying that the only way kkmans' scenario would work is if the numbers of photons were intrinsically related to the frequency of the light 'beam'/ray/whatever. This is quite obviously not true.

ranger
Gold Member
Sojourner01, I thought thats what I said in my previous reply.

You said exactly opposite that:

ranger said:
It doesnt mean less or more photons

Does one not measure brightness/intensity in units of power per area?

The intensity is proportional to the square of the amplitude, not dependent on the wave frequency.

When one later discovers light quantised in packets of energy proportional to frequency, one must infer (to avoid contradiction) that for a red and blue light source of equal measured brightness there will be a higher rate of photons received from the lower frequency source.

When one later discovers light quantised in packets of energy proportional to frequency, one must infer (to avoid contradiction) that for a red and blue light source of equal measured brightness there will be a higher rate of photons received from the lower frequency source.

This is what I was trying to say in my earlier post, I'm sorry if I wasn't clear.

>You should cite this source. That is the one thing we try to make people do when they talk about something they read or heard.
oops, I read this from wikipedia.

let's forget about the light, what about other waves like sound and water ?
If we consider wave as the particles performing SHM, their energy is depends on the frequency.
Is there anything wrong with my concept..??

thank you.

ZapperZ
Staff Emeritus
2018 Award
>You should cite this source. That is the one thing we try to make people do when they talk about something they read or heard.
oops, I read this from wikipedia.

let's forget about the light, what about other waves like sound and water ?
If we consider wave as the particles performing SHM, their energy is depends on the frequency.
Is there anything wrong with my concept..??

thank you.
Why did you quoted one part of my response while ignore the rest that would have answered your question here?

ZapperZ said:
Actually, it DOES! Maybe the energy PER CYCLE or per period isn't dependent on frequency in classical wave theory of light, but energy in a unit time does! Think about it. The higher the frequency, the more cycles in that unit time that you measure, the more energy you will get. So yes, even in classical wave theory of light, frequency does matter IF you are looking at it per unit time.

Zz.

hmm..I understand if I consider it per unit time, the intensity is directly proportional to the energy, not the frequecy.
My problem is that is the expression of "energy" include frequency ?
Like other waves, the particles are performing SHM, and their energy is proportional to the square of the frequceny.

Like other waves, the particles are performing SHM, and their energy is proportional to the square of the frequceny.
No. No no no. The energy of a photon is directly proportional to its frequency. Not the square. Linear dependence. No question about it.

Review your ideas of what 'intensity' is. I sense some confusion of concepts creeping in here.

The higher the frequency, the more cycles in that unit time that you measure, the more energy you will get. So yes, even in classical wave theory of light, frequency does matter IF you are looking at it per unit time.
Do you have a reference to support that?

>energy is proportional to the square of the frequceny
If we consider waves as particle performing SHM, then their energy
= 1/2m ω^2 A^2, where ω = 2πf

Can I use this concept in wave theory of light ?

ZapperZ
Staff Emeritus
2018 Award
Do you have a reference to support that?
No I don't. Rather, look at a mass-spring system. Find the energy per second of the system at a particular amplitude. Now replace the spring so that you have a system that doubles the natural frequency. Now measure again the amount of energy of the system per second with the SAME amplitude. Are you telling me you need a "reference" to figure out that the amount of energy in that unit time has increased?

Zz.

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The thing I consider confusing in this thread is the way frequency is being thought of. It simply is a number of an event in an amount of time. In this case we are talking about waves. Therefore, the number of oscillations per unit time, be it light waves or mechanical waves the same principals apply. The relation to energy in the quantum mechanical formula E=hf i think is being miss interpreted. Here the frequency is just a multiplier where as Planck's constant is a number related to the most discrete quantisation of energy. Remember where this formula was derived from.

ZapperZ
Staff Emeritus
2018 Award
I think people are forgetting the OP. The original question is based on the wave theory of light. We are not bringing in any quantum effect of light here.

Zz.

No I don't. Rather, look at a mass-spring system. Find the energy per second of the system at a particular amplitude. Now replace the spring so that you have a system that doubles the natural frequency. Now measure again the amount of energy of the system per second with the SAME amplitude. Are you telling me you need a "reference" to figure out that the amount of energy in that unit time has increased?
According to both Griffiths Electrodynamics (p.381) and Saleh & Teich Photonics (p.44), the intensity of a monochromatic light wave is proportional to the square of the amplitude and independent of frequency (just like the average of $cos^2\ \omega t$ over $t$). Energy per second is simply intensity, integrated over an area.

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Do you have a definitive piece of reasoning that makes you certain that the power of a beam is equivalent to the energy residing in the photons that comprise it? It sounds obvious but isn't necessarily, so be careful.

ZapperZ
Staff Emeritus
2018 Award
According to both Griffiths Electrodynamics (p.381) and Saleh & Teich Photonics (p.44), the intensity of a monochromatic light wave is proportional to the square of the amplitude and independent of frequency (just like the average of $cos^2\ \omega t$ over $t$). Energy per second is simply intensity, integrated over an area.
I have the 2nd Edition of Griffiths, and pg. 381 has nothing of that sort.

If you look in the section titled "Energy and Momentum of Electromagnetic Waves" (section 8.2.2 in Griffiths 2nd Edition), you would have seen that the energy of a monochromatic plane wave is

$$U = \epsilon_0 E^2_0 cos^2(\kappa x - \omega t + \delta)$$

This clearly has a frequency term. The confusion comes in when you are looking at the total energy that has been integrated over the volume of space that is relevant to the problem. THEN you have integrated out the effects of frequency or the spatial extent of the oscillation. You then no longer have either the time dependent, or the volume dependent. Now all you care about is how much of that goes through an area that you are looking at.

Again, look at the simplest wave equation, of which a mass-spring system is the simplest visual example. The amount of energy in a particular time that the system makes clearly depends on the frequency if you fix the amplitude. This is the most transparent example I can give.

Zz.

I have the 2nd Edition of Griffiths, and pg. 381 has nothing of that sort. If you look in the section titled "Energy and Momentum of Electromagnetic Waves" [..]
In the 3rd edition, a section with that name derives that for a monochromatic wave with electric field amplitude $E_0$ the intensity is $\frac 1 2 c \epsilon_0 E^2_0$ (eq. 9.63).

$$U = \epsilon_0 E^2_0 cos^2(\kappa x - \omega t + \delta)$$This clearly has a frequency term.
And just as clearly, if you average this over unit time (as you https://www.physicsforums.com/showthread.php?p=1224951#post1224951" specify, rather than integrating over just one cycle), that frequency term will dissappear.

Again,[..] a mass-spring system is the simplest visual example.
Regardless of the behaviour of such a system, the fact it contains non-zero rest-mass is enough for me to doubt the equivalence. It seems more analogous to a free electron in an electric field.

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