Abstract
We rigorously prove that when a bounded light beam is incident on an interface, a part of its plane wave components propagate according to the reverse mode of the ordinary reflection and transmission. Based on the two propagation modes, we propose the definition of the generalized reflection and transmission. With this definition, we solve the controversy about the Goos-H\"anchen shift approaching the grazing incidence limit, and release the angular expansion method from the precondition which requires that the beam spread angle should not exceed the complement of the incident angle. Then the spectrum superposition effect is investigated for the incidence circumstance whose beam spread angle exceeds the complement of the incident angle.
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