# Febry-perot Interferometer

The reflected flux density is given by

------------------------(4)

Where I_{inc} is the incident flux density () and is co - efficient of finesse .

If no observation takes place the net transmitted intensity in medium 3 is given by

------------------------------(5)

Thus we see that the resultant intensity in medium 1 (reflected wave) and medium 3 (transmitted wave) is a function of (phase difference introduced by medium 2). Also, when the intensity is maximum for reflected wave, it is minimum for transmitted wave. Thus interference in reflected waves is complementary to that in transmitted waves. These can be used to make more precise study of the contour of the surfaces. So far, we have assumed that no absorption takes place, while the wave transmits through the surfaces so that . If there is some absorption by the surfaces, this relation does not hold and transmitted intensity as given in Eq.(5) is to be multiplied by , where t_{1}t_{2 } and *r ^{2}* are the factors of intensity transmitted and reflected by a single surface.

**Fabry – Perot Interferometer and Fabry Perot-Etalon**

The Fabry- Perot interferometer is based on the fringes produced by the phenomenon of multiple beam interference in transmitted light. Here two plate (partialy silvered on inner surfaces) are separated by a distance d such that the inner surfaces are parallel to each other. The separation d between the inner surface is large (usually 0.1 – 10 cm) and the observations are made near the normal direction. Light ray from a point P_{1} of the broad source S is incident on plate E_{1 }at an angle and a series of parallel rays are emergent after the plate E_{2} . The rays are brought to focus at a point P_{2} using a lens. The condition for a maxima is given by

Where *n* is the refractive index of the medium between the two plates (which is usually air.)

This condition of maxima is fulfilled by all the point on a circle through P_{2} with their center at ‘*O*'. ( *O * is the point of intersection of axis of lens with the screen). Different order maxima are obtained by varying .

We thus have a series of concentric rings similar to those obtained with Michelson interferometer when mirrors M_{1} and M_{2 }are parallel to each other. The interferometer can be used to determine the wavelength of monochromatic light and the difference between the two closely spaced wavelengths by varying the separation between plates as discussed in the case of Michelson interferometer. The interferometer is frequently used to determine the detailed structural lines.

**Fabry-Perot Etalon : **

In a Fabry –Perot interferometer, it is essential that the two inner surfaces remain parallel to each other. In order to avoid any mismatch during the process of changing separation between the two plates, the two plates with inner surfaces exactly parallel to each other are fixed for a given d . The whole assembly is now enclosed such that the two plates can not be moved separately and only their inclination with respect to incident light can be changed. The assembly is known as Fabry Perot Etalon and is used to determine the refractive index of the medium between the plates.