# Does the amplitude of an electromagnetic wave affect brightness?

In sound waves, amplitude affects loudness. But just as a single person can sing loud, a choir can sound loud, even though each individual isn't singing loud. Can lights brightness be affected by amplitude as well as intensity?

• Rephrasing: Can intensity from several light sources be high while intensity from each source is low? Yes, but you have to be very careful with the sources. Sources need to be coherent and in-phase, which is difficult to achieve. For example, this happens in Young's two-slit experiment. – npojo Dec 26 '17 at 11:50

The energy transported by an electromagnetic wave is described by a quantity called the Poynting vector. Like many things in electrodynamics this can be a bit baffling for the beginner, but for the simple case of an infinite plane wave the Poynting vector is simply:

$$\langle S \rangle = \frac{1}{2\eta} |E|^2$$

where $|E|$ is the amplitude of the electric field and $\eta$ is a constant that depends on the medium through which the light is passing - for light in a vacuum $\eta = 377\Omega$.

The value of $\langle S \rangle$ is simply the energy transfer per unit area per unit time, and this is exactly what we mean by the intensity of the light. So the intensity is proportional to the amplitude squared

You use the word brightness but this turns out to be somewhat involved in optics. The brightness as perceived by the eye isn't simply the intensity because the response of the eye varies with the wavelength of the light. For more on this see the Wikipedia article on Lux. However if we ignore this and take the simplifying view that the brightness is just the intensity then the the brightness is also proportional to the amplitude squared.

• Thank you. So is the amplitude proportional to the wavelength in any way? – Zane Scheepers Dec 26 '17 at 12:54
• @ZaneScheepers: the amplitude and wavelength are independent properties of the light i.e. you can vary one without varying the other. There are circumstances in which they are related, but this isn't generally true. – John Rennie Dec 26 '17 at 13:35
• So red shift and drop in lux are seperate outcomes of expansion? – Zane Scheepers Dec 26 '17 at 13:52
• @ZaneScheepers Any light radiated outwards from a point source will have an intensity that decreases as $1/r^2$. So distant stars would be fainter as we looked farther away whether they were moving or not and in this sense the decrease in intensity is independent of the red shift. However the red shift does also decrease the intensity even further, as well as increasing the wavelength. – John Rennie Dec 26 '17 at 15:32