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I have now been learning about interference through slits, and we considered a phasor approach to this. I notice that the intensity detected on the screen was the square of the net phasor at that point. On the other hand when I learned about superposition of waves before in phenomena such as beats, the measured amplitude was the projection of the net phasor onto the real axis.

Now this is what is confusing me. On the one hand we took the resultant amplitude as the real projection/component when considering beats, and on the other hand we are using the whole magnitude of the net phasor when considering light intensity.

My two thoughts about this were

  • Perhaps this has to do with the fact that light consists of orthogonal electric and magnetic purturbations? I'm not too familiar with the equations for light as I am yet to cover these in my course, but perhaps the fact that we use the whole phasor length for light due to the fact that light has both components? Now this got me thinking: when we measure light and we measure the intensity of light, are we measuring the magnetic or electric components or both? Say we had a detector that was able to record on very small time sclae and we had light of a very long wavelength, would the detector reading change as the light wave passed, or not because the intesnity detected depends on the sum of the squares of the electric and magnetic components which remains constant? Could we build a detector which detects only one of these and not the other?
  • My second idea is that perhaps we are considering the whole amplitude of the vector because the 'intensity' we have been talking about in classes is the intensity of the time average of the superposed wave? I'm not quite sure about this.
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I notice that the intensity detected on the screen was the square of the net phasor at that point.

This is correct and usual.

On the other hand when I learned about superposition of waves before in phenomena such as beats, the measured amplitude was the projection of the net phasor onto the real axis.

This is not correct. The amplitude of the signal is given by the magnitude of the phasor. The intensity is proportional to the square of the amplitude, and that's why the intensity is related to the squared magnitude of the phasor.

Where you will see the projection onto the real axis used is if you multiply the phasor by $e^{i\omega{}t}$ and project onto the real axis, you'll get the instantaneous electric field strength.

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