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Phase Change on Reflection

Idea: When light is reflected off a more dense medium with higher index of refraction, crests get reflected as troughs and troughs get reflected as crests. The wave is said undergo a 180 o change of phase on reflection. The net effect of the phase change is that the reflected ray ``jumps ahead" by half a wave length. Thus, if one of the rays undergoes an odd number of phase changes, the conditions for constructive and destructive interference must be modified:

r1 - r2 = (m + $\displaystyle{1\over 2}$)$\displaystyle\lambda$  m = 1,2,.... constructive

r1 - r2 = (m)$\displaystyle\lambda$  m = 1,2,... destructive