Febry-perot Interferometer
Febry-Perot Interferometer: In this case the interference phenomenon was observed between the reflected wave from the first surface and transmitted wave after getting reflected from the second surface. The path difference 
between these wave had been 
, where
was angle of refraction in the case when two surfaces were parallel to each other, d is separation between the two surfaces. For near normal incidence, (
is small), = 2d, phase difference = 
.
However, in general, if both the surface are partially silvered, transmitted wave from the first surface undergoes multiple reflections at both the interfaces. Each time this wave reaches an interface, it gets partially reflected and partially transmitted (Fig.A).
The resultant waves in two mediums 1 & 3 are actually the sum of several waves which have path difference (thus phase difference) among them selves. The interference pattern is then observed in both the medium 1 (reflected wave) and medium 3 (transmitted wave). Fabry-Perot interferometer and Fabry-Perot Etalon are based on the principle of multiple beam interferometry. Before discussing the Fabry perot Interferometer, we will first find out the resultant intensity of reflected and transmitted wave and determine the interference conditions. We will also be dealing with the complex representation of light wave (light wave is a transverse electromagnetic wave). Let, for simplicity assume that medium 3 is same as medium 1.
Fig. A : Multiple reflection and transmission from partially silvered surface.
Let the incident light wave at the point of incidence(near normal condition) at first plane be represented by 
and let 
be the magnitude of the wave vector of this wave. The wave gets partially reflected and partially transmitted at the first interface. If r1 and r2 be the reflection coefficients for reflection medium 1 and medium 2 respectively and t1 and t2 be the transmission coefficients for transmission in medium 2 and medium 1 and 3 respectively.
Let us represent the waves in medium 1 by a's, medium 2 by b's and medium 3 by c's. The first reflected wave in medium 1 will be 
. The first wave in medium 2 will be 
.
The transmitted wave in medium 2, ( 
) will again undergo a partial reflection ( 
) in medium 2 and partial transmission (
) in medium 3 which is same as medium 1. The reflected wave upon reaching interface 1, again undergoes partial reflection and transmission and the process goes on. If d is the thickness of medium 2, then each time the wave crosses this medium it undergo a phase change given by 
The resultant wave in medium 1 is
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