# Energy in light

Okay, I've spent a lot of time thinking about light, electromagnetic fields, and how everything interacts, and I think I finally understand the dynamics of light. Now I just have one thing I cant figure out. For light waves, amplitude and frequency, which of those represents/carries the light's energy? If its both, then which characteristic carries more.

• If you think of light as a single photon then the energy is due to the frequency. However, the amplitude of the EM wave more represents how many photons there are of that frequency (assuming only a single frequency for the EM wave). – K7PEH Feb 15 '17 at 6:03

The Planck-Einstein relation describes how much energy is carried by light. The energy is quantized, meaning it comes in discrete chunks, and each chunk carries an amount of energy proportional to the frequency. Discussions of wave amplitude become much more complicated in quantum mechanics compared to general physics, so I'd encourage you to read more about it if you're interested. It will be especially helpful to read about the photoelectric effect.

Assuming you are asking about a classical light wave the energy of the wave is described by the Poynting vector. This tells you both the direction and the magntide of the energy flux.

The Wikipedia article I've linked is rather detailed and probably somewhat confusing. However for a straightforward plane light wave the average energy flow (normally written as $\langle S \rangle$ is simply given by:

$$\langle S \rangle = \frac{|\mathbf E|^2}{2\eta}$$

where $\mathbf E$ is the electric field vector and $\eta$ is the impedance of the medium through which the light is passing ($\eta = 377\Omega$ in a vacuum). So the energy flow is just proportional to the electric field squared i.e. the intensity. It is not dependent on the frequency.

Some of the other answers mention that the energy carried in a single photon is proportional to the frequency. While this is true you need to be aware that a light wave is not simply a hail of little photons. See What is the relation between electromagnetic wave and photon? for more on this.

The frequency of the electromagnetic wave determines the energy carried by a single photon.

The energy carried by an photon in terms of its frequency is given by:

$$E = hf$$

where $E$ is the energy associated with a single photon, $h$ is the plank's constant and $f$ is the frequency of the wave.

When you talk about a single electromagnetic wave, you should consider it to be a particle, i.e: a photon. When you are talking about a collection of electromagnetic waves, you can understand them as waves of light. You can still treat light as a collection of particles, it depends on the context: choose the most appropriate concept.

When you consider light as a collection of waves, the amplitude of electric and magnetic fields are used to give a measure of energy per unit volume.

When we talked about light as a wave, we used to say that energy is the amplitude. Actually amplitude refers to the number of photons (intensity).

The actualy energy of the light (photons) is dependent on frequency. This is the energy/momentum that a single photon carries.

When light interacts with matter, for example, in photoelectric effect, the light (photon) energy decides whether the electron can gain enough energy to be ejected. Note that the intensity/amplitude is the number of photons so it decides the current.

So the answer depends on your understanding of the word 'Energy'. A low frequency but bright enough laser can damage, and a low intensity but high frequency laser can also cause damage. In Physics (which is the true quantum nature), the light energy is now meant to be the photon energy. The total energy for n photons is just n times energy of each photon, and n is the amplitude.

Questions?

Frequency

The wave's frequency represents the energy the light carries. The higher the frequency, the higher the energy it carries.

Amplitude

The amplitude represents the probabilities of finding the particle at a given place. If one of the amplitudes is relatively big, then the photon will more likely to appear at that location; in other words, the number of photons appearing will also be bigger.

• Hi Nicole. You are describing a wavefunction. A light wave is not a wavefunction so it does not describe the probability of finding a photon. – John Rennie Feb 15 '17 at 7:07