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Perpendicular (TE) polarization occurs when the electric field is perpendicular to the plane of incidence. I am having a hard time visualizing why that is the case in the following example. please let me know how you can figure where E or H is perpendicular or parallel to plane of incidence. what does the circle with the cross in it signify? it means that component is pointing out or in? also how do you use Right hand rule having E , H and propagation directions? Thanks enter image description here

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The circled cross means you're seeing the back of the arrow; while a circled dot would mean you're seeing the front of it. In your diagram axis "y" is therefore perpendicular to plane x-z and so is the electric field.

The plane of incidence is y-z and the electric field is parallel to it.

About the right hand rule you can put the right hand thumb in the direction of E, the index in the direction of H, and the third finger will point into the direction of propagation of the wave.

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