The document describes the Fabry-Perot interferometer. It consists of two parallel glass plates separated by a small air gap. Light reflects multiple times between the plates, producing an interference pattern of bright and dark fringes. The pattern results from the optical path difference between light rays undergoing different numbers of reflections. Applications include wavelength references, narrow bandwidth filters for astronomy, and precision measurement in fields like gravitational wave detection and laser control.

1. FABRY-PEROT
INTERFEROMETER

2. *Christian Huygens-1680-light propagates in the
form of waves.
*Thomas Young-1801-wave theory of light
received first experimental evidence.

3. Light Wave
*A light wave is a harmonic
electromagnetic wave.
*It consists of periodically varying
electric and magnetic fields.

4. Superposition of Waves
*When two or more waves overlap, the resultant
displacement at any point and at any instant
may be found by adding the instantaneous
displacements that would be produced at the
point by the individual waves if each were
present alone.

5. Interference
*It is an important consequence of superposition
of coherent waves.
*Coherent waves-waves of same frequency and
constant phase difference.
*Redistribution of light energy due to
superposition of light waves from two or more
coherent sources.

6. *Constructive interference:-two waves are in-
phase.
AR=A+A=2A
IRαAR
2
IR>2I
*Stationary bright band.

7. *Destructive interference:-two waves in
opposite-phase.
AR=A-A=0
IRαAR
2
IR<2I
*Stationary dark band

8. Conditions for Interference
*Conditions for sustained interference
1. The waves from two sources must be of the
same frequency.
2. The two light waves must be coherent.
3. The path difference between the overlapping
waves must be less than the coherence
length of the waves.
4. If the two sets of waves are plane polarized,
their planes of polarization must be the
same.

9. *Condition for formation of distinct fringe
pattern
1. The two coherent sources must lie close to each
other in order to discern the fringe pattern.
2. The distance of the screen from the two sources
must be large.
3. The vector sum of the overlapping electric field
vectors should be zero in the dark regions.

10. Techniques of obtaining interference
1.Wavefront splitting.
2.Amplitude splitting.

11. Wavefront splitting
*By passing light through two slits closely
spaced side by side.
*Two parts of the same wavefront travel through
different paths and reunite on a screen to
produce fringe pattern.

12. Amplitude splitting
*Reflected and transmitted components by
partial reflection at the surface.
*Two wave parts travel through different parts
and reunite to produce interference fringes.

13. Interferometer
*Instruments based on the principle of
interference of light.
*Fabry-parot interferometer-multiple beam
interference.
*Multiple beam interference: when the
reflected or transmitted beams meet

14. Fabry-Perot Interferometer
*Improved version of Michelson Interferometer.
*Invented by Charles Fabry & Alfred Perot.
*High resolving power instrument.
*Fringes of equal inclination.
*Multiple reflections in an air film.

15. *A combination of mirrors is used mounted
parallel to each other.
*If one of the mirrors is movable-
interferometer.
*Otherwise-etalon.
*In a broad sense it is still an interferometer.

17. How does it works
*Consists of two glass plates with parallel plane
surfaces separated at a distance d.
*Media between glass plate is air.
*When monochromatic wave falls upon the plate
multiple reflections are generated.
*Reflections in the glass plate are negligible.
*Only interference produced by multiple beam
are observable.

20. *Intensity of interference pattern is
Where a-amplitude of the incident wave
r-reflection coefficient of the coating
film
-phase difference between two
consecutive waves
I = 𝑎2
1+
4𝑟2
1−𝑟2 2 𝑠𝑖𝑛2 𝛿
2
𝛿

21. *Optical path difference,
Δ=2dcosθ
*Also we know that,
δ=
2π
λ
Δ
*Intensity depends on d,r,λ,𝑎2and θ.
*If light comes from an extended source and
geometry depends only on θ,intensity pattern
exhibit rotational symmetry.

22. *The intensity maximum,
𝐼 𝑚𝑎𝑥 = 𝑎2
, if 𝑠𝑖𝑛2 𝛿
2
= 0.
*Thus, ∆= 2𝑑𝑐𝑜𝑠𝜃 = 𝑚λ ,m=0, ±1, ±2 … .
*The intensity profile exhibits a sequence of
maxima and minima.
*Consequently, interference pattern is
characterized by light circles.

23. Finesse
*Quantitative measure of interferometer’s
ability to resolve closely spaced transmission
peaks.
F=
𝑺𝒆𝒑𝒂𝒓𝒂𝒕𝒊𝒐𝒏 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝒇𝒓𝒊𝒏𝒈𝒆𝒔
𝑭𝒖𝒍𝒍 𝒘𝒊𝒅𝒕𝒉 𝒂𝒕 𝒉𝒂𝒍𝒇 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒐𝒇 𝒓𝒆𝒔𝒐𝒏𝒂𝒏𝒕 𝒑𝒆𝒂𝒌

24. Resolving Power
*Describes the minimum difference between the
two wavelengths that can be distinguished.
*Resolving power=Finesse*order of interference

25. Interference fringes, showing fine
structure, from a Fabry–Perot etalon. The
source is a cooled deuterium lamp.

26. The transmission of an etalon as a function of
wavelength. A high-finesse etalon (red line) shows
sharper peaks and lower transmission minima than a
low-finesse etalon (blue).

27. Fabry–Perot interferometer, using a
pair of partially reflective, slightly
wedged optical flats

28. Applications
*Highly specialised etalons for DUV photolithography
sources
*Air-spaced etalons used to control the centre
wavelength and bandwidth of UV-NIR lasers
*Large solid and air- spaced etalons for government
research projects
*Etalons for telecommunications solutions
*Air-spaced etalons for astronomy as narrow bandwidth
filters
*Wavelength reference etalons used in LiDAR sensing
instruments for atmospheric research

29. *In astronomy an etalon is used to select a
single atomic transition for imaging.
*In gravitational wave detection(LIGO).
*Optical wave meters and some optical
spectrum analysers use Fabry–Perot
interferometers with different free spectral
ranges to determine the wavelength of light
with great precision.