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On Wikipedia: In the physics of wave propagation, a plane wave (also spelled planewave) is a wave whose wavefronts (surfaces of constant phase) are infinite parallel planes.

In my understanding, an electromagnetic wave plane is an electric field perpendicular to a magnetic field which both form a surface plane that propagates in direction normal to the plane.

Is my understanding correct?

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Yes,in a plane emw the electric and magnetic field vectors oscillate in a plane, perpendicular to one another and the wave propagates in a direction perpendicular to that plane

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