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Because a reflection reverses the direction of the component of the wave vector of the light hitting the reflecting surface which is orthogonal to the surface. The component parallel to the surface will not change.

This means the light going towards a mirror, will go away from the mirror after reflection. But if it went from the left to the right, it will continue to go from the left to the right. Same with up and down.

In three dimensions this is the same as changing the handedness of the image.

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