Wave Interference and Polarization

[jaumzaum]

I'm studying wave interference and having trouble to understand some concepts. I would like to ask what would happen in the 2 situations below

Image 1


Image 2


Both waves are identical, have the same frequency, amplitude and velocity. They are polarized on the direction shown (first one oscilates going out of the screen, second one on the plane of the screen). At the red circle they interfere construtively (that means A.Cos(...) are equal). The waves have perpendicular propagation directions. What will be the amplitude on the red points?

I would say 2A for the first image and A √2 for the second. Is it right?

I'm asking because on the slit experiment (OEM interference) my book (and everybody) seems to treat constructive interference as 2A, ignoring the angle between the waves. Why is that?

 

[Redbelly98]

You're correct about the amplitudes. But I would not consider the second example to be constructive interference, I only associate that term if the waves are polarized in the same direction.

Or put another way, try to imagine setting up destructive interference (amplitude is zero) for your plane-polarized example. It can't be done.

Hope that helps.

 

[jaumzaum]

I helps :)

try to imagine setting up destructive interference

You are right, I used "constructive" because I didn't have other world to use. The amplitude should range from A to A√2, so there will never be a destructive interference.

In the previous post I wrote OEM where I should have written EMW (in portuguese "onda elétromagnética), in english "electromagnetic wave"), sorry for that

Now come the second question. For the second wave we had to consider the angle between them because the wave was oscilating on the plave of the screen. An EMW has 2 fields (electic and magnetic) that are perpendicular to each other, so there will always be a component of one (or both) fields that will be on the plane of the screen. So in the double slit experiment, why they ignore the angle between the waves when they find the phase shift? Is it because the angle is too small?

 

[Redbelly98]

Yes, exactly.

(Sorry about the delay in responding.)

 

[sardar]

Firstly, let's clarify the concept of wave interference. When two waves meet, they can either constructively interfere (where the amplitudes of the waves add up) or destructively interfere (where the amplitudes cancel each other out). The result of this interference depends on the phase difference between the two waves. In the case of constructive interference, the phase difference is 0, meaning the peaks and troughs of the waves align perfectly.

In the first image, the two waves are polarized in the same direction and have the same propagation direction. This means that at the point of interference (red circle), they will constructively interfere with an amplitude of 2A, as you correctly stated. This is because the two waves are perfectly aligned and have a phase difference of 0.

In the second image, the two waves are polarized in different directions, but still have the same propagation direction. This means that at the point of interference, they will still constructively interfere, but with an amplitude of A√2. This is because the two waves are not perfectly aligned, and there is a phase difference between them due to their different polarizations.

Now, for the slit experiment, the waves are not polarized, and they are coming from different directions. This means that the phase difference between the waves is not 0, but rather depends on the angle between the two waves. In this case, the resultant amplitude at the point of interference is given by the formula √(A1^2 + A2^2 + 2A1A2cosθ), where θ is the angle between the two waves. When θ = 0, this formula reduces to 2A, which is why the book treats constructive interference as 2A.

In summary, the amplitude at the point of interference depends on the phase difference between the waves, which is affected by their polarization and propagation directions. In the first image, the waves are perfectly aligned, so there is no phase difference, resulting in an amplitude of 2A. In the second image, there is a phase difference due to the different polarizations, resulting in an amplitude of A√2. And in the slit experiment, the phase difference varies with the angle between the waves, but when the angle is 0, the amplitude is 2A. I hope this helps clarify the concept of wave interference and its application in different situations.