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P-State Lightwave question

by paul11273
Tags: lightwave, pstate
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Mar13-05, 05:18 PM
P: 156
I do not even really know where to begin with this problem.
Any help would be great.

Q. Write an expression for a P-State (linearly polarized) lightwave of angular frequency [tex]\omega[/tex] and amplitude [tex]E_{0}[/tex] propogating along a line in the xy-plane at 45 degress to the x-axis and having its plane of vibration corresponding to the xy-plane. At t=0, y=0 and x=0 the field is zero.

Like I said, I don't even know where to start. This prof is miserable, and the book is light on examples and explanations.

I am figuring the equation will be of the form [tex] \vec{E}=(\tilde{i}E_{0x}+\tilde{j}E_{0y})cos(kz-\omega t) [/tex]
This would be a wave traveling along the z-axis, so I expect that I have to change this term with a vector specifying the path 45 degrees from the x-axis. But how to do this? The prof did give a hint that we need to perform an operation of taking the dot product of two vectors, say k dot r. He was very vague, in fact down right confusing after that.

Thanks in advance.
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Mar15-05, 06:09 AM
P: 156
No takers on this question?
I know I have shown no work, but I am completely stuck.
Can anyone gander atleast a starting point?
Mar15-05, 08:11 AM
Sci Advisor
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P: 2,002
A plane wave with wavenumber k travelling in an arbitrary direction given by the unit vector [itex]\hat k[/itex] can be represented as:

[tex]A\cos(\vec k \cdot \vec r - \omega t - \varphi_0)[/tex]
where [itex]|\vec k|=k[/itex].

Try to see why this is true. Draw a diagram or so. I think you'll learn the most by understanding this general case. Solving your problem is then easy.

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