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When I use a sinusoidal function to describe a lightwave what do I actually have as units of measurements on the X and the Y curve?

Physics Asked by Agnete Thomsen on January 30, 2021

I need some help to understand what would be the standard units of measurements on the Y-axis when representing lightwaves as a sinusoidal function.

I understand how light works in that different perceived colors of visible light have different energy levels and that this is due to the different wavelenths of light. I also understand that this is really a simplified representation of a threedimensional function with a magnetic and electric field oscilation along a distance or time axis.

I also see that most examples of the function put nm or some other distance measure on the x axis to represent wavelength. However I am struggling to understand what unit of measurement is on the Y axis.

I’ve spent 2 days at this point trying to look at different examples of the sinusoidal function but many explain that the amplitude is in meters which makes no sense for lightwaves, and others show the general shapes of the different types of light curves but don’t give any units of measure on the Y axis. Some explain that the amplitude gives us the intensity of the light. But they still don’t say how they are measuring this, whether in lumen, in volts, in watts (I am listing here, bear with me, I know some of these may make no sense).

So what I need to know is:

  1. What is on the Y-axis? Some measure of energy I assume, I imagine that it would be electrical?
  2. What units of measurement of energy would make sense then to use?
  3. Do all different visible colors have curves with the same amplitude on the Y axis? if not, what causes changes in the amplitude of the curve (hence the intensity).
  4. Is there a minimum measurement I can use? Such as "the energy of one photon" or something like this? To describe the simplest function of a lightwave?

I really appreciate your time, especially if you can point to any good medium level resources apt to be shared with highschool level students.

Thanks.

One Answer

The EM waves consist of electric and magnetic fields. So for each point of space and time corresponds a value of that fields.

Note that strictly speaking it is impossible to visualize them, because it would be necessary more than 3 dimensions for that. But considering plane waves, for all points of a plane perpendicular to the direction of propagation, the fields have the same value. So the y and z axis are used to indicate the fields value. But it is only a visualization trick, because they don't have length units.

The units are V/m (volts/meter) for the electric field and Tesla for the magnetic field in the SI.

Answered by Claudio Saspinski on January 30, 2021

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