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I read that 2 light planes with same amplitude are set perpendicular to each other will create a circularly polarized light, but I am curious that when it is reflected back and is converted from left to right circularly polarized light what happens to the momentum?

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Suppose the mirror is in front of you and the electric field at the mirror surface is rotating in the clockwise direction as the light wave arrives there. For a light wave propagating into the mirror, that rotation is right-handed (using your right hand, make your thumb point along the direction into the mirror, then your curled fingers indicate the sense of rotation). After reflection the light propagates away from the mirror but it is still rotating in the same direction at the mirror surface. That rotation is now left-handed (make the thumb of your left hand point away from the mirror surface; the fingers are curling as before).

Thus the change from right-handed to left-handed circular polarization is not here associated with a change in angular momentum! The direction of propagation changes but the component of angular momentum along any fixed axis does not.

No angular momentum is transferred to the mirror in this process. (Some linear momentum is transferred).

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