Interference of light (perpendicular plains)

[Pagowen]

Hi,

Apologies if this is a really basic question, but I'm not a physicist by training. I was wondering how two waves of plane-polarised light will interfere if they have equal intensity, are completely in phase, but their planes of oscillation are perpendicular to one another?

 

[sophiecentaur]

Hello and welcome to PF. Not a bad question, at all, actually.
There will be a resultant of the addition of the two waves. The E field vectors will add together, according to the phases of each and the resultant, at any point, will be a new vector, in a different plane from the two planes you started with. According to the phases and amplitudes of the two sources, the resultant may have plane polarisation (in phase addition) or elliptical polarisation (sorry- a new idea, perhaps- but it's what you get when the two are not in phase).
It's hard to recommend a suitable link for you, as I don't know your level of knowledge but http://www.ece.mcmaster.ca/faculty/nikolova/4FJ4_downloads/lectures/L04_Polarization.pdf could be interesting as it has some good diagrams in it.
Many VHF f.m. sound transmissions (in the UK, at least) use circular or mixed polarisation and it is often achieved using a mixture of VP and HP transmitting aerials - which is just what your question is about, am.

 

[Pagowen]

Hello and welcome to PF. Not a bad question, at all, actually.
There will be a resultant of the addition of the two waves. The E field vectors will add together, according to the phases of each and the resultant, at any point, will be a new vector, in a different plane from the two planes you started with. According to the phases and amplitudes of the two sources, the resultant may have plane polarisation (in phase addition) or elliptical polarisation (sorry- a new idea, perhaps- but it's what you get when the two are not in phase).
It's hard to recommend a suitable link for you, as I don't know your level of knowledge but http://www.ece.mcmaster.ca/faculty/nikolova/4FJ4_downloads/lectures/L04_Polarization.pdf could be interesting as it has some good diagrams in it.
Many VHF f.m. sound transmissions (in the UK, at least) use circular or mixed polarisation and it is often achieved using a mixture of VP and HP transmitting aerials - which is just what your question is about, am.

Thanks for the reply! I'm currently looking over the slides in the link. I think I get it, but will just have to read through to make sure. One question, though: by plane polarisation, do you mean circular? Based on what I've just read in the link, won't two perpendicular light vectors with identical amplitude and phase interfere to produce circular polarlisation?

 

[sophiecentaur]

Thanks for the reply! I'm currently looking over the slides in the link. I think I get it, but will just have to read through to make sure. One question, though: by plane polarisation, do you mean circular? Based on what I've just read in the link, won't two perpendicular light vectors with identical amplitude and phase interfere to produce circular polarlisation?

You need to look at the link again. This polarisation thing takes a bit of getting used to - time and distance are involved with waves and it isn't obvious.
But if the two waves are in phase, their maxima will occur at the same time at the same point in space. That will produce a 'diagonal' vector and the vector will always lie in that diagonal plane, going through a zero and then a max in the other direction. That is plane polarisation and the p[lane is 45⁰ to each of the original polarisation planes.. The two waves need to be 90⁰ out of phase so that the resultant follows that spiral path - shown in one of the diagrams in the link. The maxes and zeros never coincide so the resultant vector is always the same amplitude but traces out a spiral of ' unit' radius. (Never passes through zero amplitude.) See the equation at the bottom of page 17 on the link. There is a π/2 constant in the second contribution. That means 90⁰ phase difference.
It may just be worth while (if your co-ordination is up to it lol) to try waving your hands about to simulate the two waves and then visualise their resultant. I just tried it (no one was watching!) and I think it made sense to me. But then again, I do know the answer already.