michelson interferometer and its uses

1. Michelson interfrometer
Prof. kamal abd El-kader
Physics department, faculty of science, suez canal university
Ismailia Egypt.
kamalmarei@yahoo.com

2. Interference
is the phenomenon in which two waves have the same direction, wavelength,
amplitude, state of polarization and path difference constant with time combined
to form bright and dark fringes
Classification of interference
Division wave front
The wave front originating from a common source is divided into two parts by
using two slits and the two wave fronts thus separated travels and finally brought
together to produce interference. Such as fresenels biprism
Division amplitude
The amplitude of the incoming beam is divided into two parts either by partial
reflection or refraction. These two parts travel in different paths and finally
brought together to produce interference. Such as Michelson interferometer

3. Michelson interferomerter used to
• Determine the wavelength of monochromatic source.
• Determine the difference between two wavelengths of
sodium light.
• Determine the refractive index of gas

4. He-Ne beam from the source falls on the beam splitter. It splits into
two perpendicular beams one to mirror M1 and the other to M2. The
two beams are then reflected back along their original path by two
separate mirrors M1 and M2 which are located at different distances
from the beam splitter. The two beams interfere and produces
interference fringes as shown in fig. 1 Whether the interference will
be constructive or destructive depends on the relative phase of each of
the combining light beams. This is determined by the path difference,
2d. With constructive interference, the wave amplitudes add in such
a way to produce a maximum intensity beam striking the screen. The
condition for maximum constructive interference is
Determination the wavelength of monochromatic source.

5. Fig.1

6. 𝟐𝝁𝒅 𝐜𝐨𝐬 𝜽 = 𝒏
Where µ is the refractive index of the medium for air=1
n is an integer ,  is the wavelength used.
When the path length difference is an integer multiple of the wavelength, the
recombining light beams will be in phase since both light beams originated
from the same source. The resulting amplitude of the combined beam is then
the sum of the amplitudes of each beam.
With destructive interference, the phases of the light beams are such that the
recombining beams cancel each other out. The condition for maximum
destructive interference is
𝟐𝝁𝒅 𝒄𝒐𝒔 𝜽 =
𝟐𝒏 + 𝟏
𝟐


7. When the path length is an odd half integer multiple of the wavelength,
the recombining light beams will be exactly out of phase. The resulting
amplitude of the combined beam will be the difference of the amplitudes
of each beam. Moreover, since the amplitudes of the split beams are
equal, the combined light beam will have zero amplitude.
By moving one of the mirrors, we can change the path length
difference As the path length difference changes, we would see both
constructive and destructive interference. Draw the relation between the
number of fringe (n) and distance (d) straight line will be obtained the
slope is equal /2. wavelength will be calculated.

8. To study the effect of heat on Michelson
interferometer
A source of heat in the form of a filament (Heater) was inserted in
the passage of one of the two interfering beams as shown in fig. 1
Plates1-4 illustrate an example of the visualization of fringe
shrinking and disappearance at the center. Five fringes crossed
the field of view when the temperature increased from 12 C to
23 C , the first fringe disappeared at temperature 20 C followed by
the remaining four fringes shrinking to the center and disappeared
successively, the recorded time and temperature for fringe
disappearance is given in table 1

9. Plates 1-4 shrinking fringe disappearing at the centre
Plate 1 Plate 2
Plate 3 Plate 4

10. Disappearance
temperature (C )
Disappearance
time(t min)
Fringe number
20
2.9
1
20.5
7.8
2
21.0
16.8
3
21.5
31.8
4
23
57.8
5
Table1

11. Switching off the thermal source, the disappeared interference started
to reappear again. The temperature at which each fringe crossed the
field of view and that at which each fringe reappeared were recorded .
Plates 5-8 show an example for the recorded reappearance fringe and
table 2 gives the recorded time and temperature
Table 2
Reappearance
temperature (C
)
Reappearance
time(t min)
Fringe number
19.5
10
5
19.0
15
4
18.5
21
3
18.0
30
2
16.5
59
1

12. Plate 5 Plate 6
Plate 7 Plate 8
Plates 5-8 fringe reaappearing at the centre