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Billyneutron

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The photon before encounter with the mirror is [A>, then afterwards it evolves according to U to become [B> + i[C> (where C is the reflected light). The imaginary factor "i" is said to arise because of a net phase shift by a quarter of a wavelength which occurs between reflected and transmitted beams.

I'm confused with this last part- Why, again, is "I" used? I'm unclear about the phase shift by 1/4 wavelength. Can anyone explain this in laymens?