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 + $${1\over 2}$$)$$\lambda$$  m = 1,2,.... constructive

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

Note:

• The above formulas are valid whenever an odd number of phase changes occur. If an even number of phase changes occur then the original, unmodified formulas must be used.
• The phase change does not happen when light is reflected off a less dense medium, i.e. for total internal reflection.