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1.What is total energy of EM waves, as all got same speed?

  1. If two em waves has same energy, do they have same mass?

  2. If same mass and energy, do they have same frequency or wavelength still different EM waves or Color?

Qmechanic
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Raj Singh
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2 Answers2

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According to Maxwell's theory of electromagnetism, a light pulse (or generic electromagnetic wave) carries momentum, which can be transferred to an absorbing surface hit by the pulse. This momentum transfer is known under the name 'radiation pressure'.

Despite carrying momentum, light carries no mass. Yet a light pulse does carry energy. For a light pulse with momentum $p$ this energy is given by $E = p c$. Here, $c$ is the speed of light.

Note that frequencies or wavelengths do not enter this picture. So two distinct light pulses with the same energy (and hence the same momentum), do not need to have the same frequency (or the same wavelength).

When considering the quantisation (photon character) of light, frequency (or wavelength) does enter the picture. If two light pulses have the same energy (and therefore the same momentum) and each consist of the same number of photons, they must have the same frequency.

Johannes
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The total energy of a photon, the carrier of the electromagnetic force, is given by $ E=hf $ where $ h $ is Planck's constant and $ f $ is the frequency of the light. So yes, if two EM waves have the same energy, they will have the same frequency and wavelength, meaning they have the same colour.

Photons have no rest mass, but they do have a relativistic mass due to their momentum, given by $ m = \frac{h}{\lambda c} $. This isn't a rest mass in the sense that photons don't have a rest frame, but it behaves as an apparent mass in special relativity.

rupertonline
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    $E=mc^2$ doesn't work for photons (cf this post), you need to use $E=pc$. – Kyle Kanos Nov 09 '14 at 12:26
  • I was referring to relativistic mass – edited to clarify that more. – rupertonline Nov 09 '14 at 12:46
  • Ok, what is p's value, if you put both E value in your point 2 together considering E value of mc2 and E value of pc are same of same particle. – Raj Singh Nov 09 '14 at 13:11
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    "So yes, if two EM waves have the same energy, they will have the same frequency and wavelength". This is totally incorrect. Two photons have the same energy if they have the same wavelength. But a wave with 1 um wavelength can certainly have the same power as a wave with 500 nm wavelength, it will just be composed of twice as many photons. – The Photon Nov 09 '14 at 17:58