# Determining the polarisation state of the waves.

1. Apr 24, 2012

### Raphisonfire

1. The problem statement, all variables and given/known data
$$E(z,t) = E_{0x} \sin (kz - wt - \frac{\pi }{12}) - E_{0y} \cos (kz - wt + \phi + \frac{\pi}{12})$$
$$E(z,t) = E_{0x} \sin (kz - wt - \frac{\pi }{3}) - E_{0y} \sin (kz - wt + \frac{\pi}{6})$$

3. The attempt at a solution

For the first and second problem, I set t and z both to 0, so the only things that are left within the equations are the angles.

I've reduced the first equation down to
"$$E(z,t) = -E_{0x} \sin ( \frac{\pi }{12}) - E_{0y} \cos (\phi + \frac{\pi}{12})$$"

And I've worked out that there is a phase shift of $$\frac{\pi}{2}$$ between the waves, but I'm not sure where $$\phi$$ comes into it.

For the second question, I've done the same process to reduce down z and t. and I've gotten $$E(z,t) = -E_{0x} \sin ( +\frac{\pi }{3}) - E_{0y} \sin (\frac{\pi}{6})$$

When I get here, I'm not really sure on what to do from here. I know sin's are in phase, but the angle's aren't... is it just a matter of minusing a phase angle from one another?

I am fine with determining the actual state of polarisation because I have a table and I can also use mathematica to plot the functions out to determine it, but I'd rather use mathematics, because of how I will be examined on this.

2. Apr 24, 2012

### ehild

What does "polarization state" mean?

ehild

3. Apr 25, 2012

### Raphisonfire

I know what polarisation state means.

My problem is, I don't know how to work through the phase shifts, to actually find the polarization state of that specific wave.