INTERFERENCE OF LIGHT Light is an electromagnetic radiation we can see with our eyes light has the properties of a wave. One of these properties is interference, caused by the addition of waves Introduction: If two or more waves cross one another in the same medium, each wave produces its own effect totally independent of the effects due to the other. Principle of superposition tells that at any instance the resultant displacement is equal to the vector sum of the individual displacements produced by each wave. This is based on the theory of interference of light discovered by Thomas Young in 1801. With single source of light the energy distribution in the surrounding medium is uniform. But when there are two adjacent sources of light giving out light waves of the same wavelength, amplitude and having zeroed or constant phase difference, the distribution of energy is no longer uniform. At some points where the crest of one wave falls upon the crest of the other or the trough of one wave falls on the trough of the other, the resultant amplitude is large and hence the intensity become maximum. At other points where the crest of one wave falls on the trough of the other wave and vice versa, the resultant amplitude is reduced to zero and intensity is minimum. The modification in the distribution of light energy due o superposition of two or more waves of light is called interference of light. It should be noted that in this phenomenon there is only transference of energy from one region to another. The energy missing at one region reappears at the other region. There is no creation destruction of energy in any region as a result of the superposition of the waves of light.
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Interference of Light & It's Applications (Interferometry)
Academic work submitted to VTU under Bachelor of Engineering course during 8th semester. A Research on Interference of light and it's applications in the field of Flatness Measurement of Metrology Instruments
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INTERFERENCE OF LIGHT
Light is an electromagnetic radiation we can see with our eyes light has the
properties of a wave. One of these properties is interference, caused by the addition of
waves
Introduction:
If two or more waves cross one another in the same medium, each wave produces
its own effect totally independent of the effects due to the other. Principle of
superposition tells that at any instance the resultant displacement is equal to the
vector sum of the individual displacements produced by each wave. This is based on
the theory of interference of light discovered by Thomas Young in 1801.
With single source of light the energy distribution in the surrounding medium is
uniform. But when there are two adjacent sources of light giving out light waves of the
same wavelength, amplitude and having zeroed or constant phase difference, the
distribution of energy is no longer uniform. At some points where the crest of one wave
falls upon the crest of the other or the trough of one wave falls on the trough of the other,
the resultant amplitude is large and hence the intensity become maximum. At other points
where the crest of one wave falls on the trough of the other wave and vice versa, the
resultant amplitude is reduced to zero and intensity is minimum.
The modification in the distribution of light energy due o superposition of
two or more waves of light is called interference of light.
It should be noted that in this phenomenon there is only transference of energy
from one region to another. The energy missing at one region reappears at the other
region. There is no creation destruction of energy in any region as a result of the
superposition of the waves of light.
Because of interference there are alternate bright and dark regions observed and
they are called interference bands or interference fringes. The color pattern observed
on soap bubbles and oil on the wet roads are due to interference of light. If a convex lens
of large radius of curvature is placed on a glass plate and illuminated with
monochromatic light source, alternately bright and dark concentric rings (called as
Newton’s rings) are observed because of interference. Similarly if a wedge shaped air
film between two plane glass plates (air wedge) is illuminated with monochromatic light,
alternate bright and dark bands are formed because of interference, the bands being
parallel to the edge of the wedge.
Concepts:
Light travels in waves.
Sometimes, two or more waves join together.
Interference is the addition, or coming together, of several waves.
Constructive Interference happens when two or more waves come together to
form a larger and stronger wave, matching their crests and troughs.
Destructive Interference is when two or more waves come together and cancel
each other out to make a weaker wave.
Principles:
Since light has wave properties, it will experience interference (the addition of
waves).
This interference is like that seen with water waves.
Whether you get constructive or destructive interference depends on the
wavelength (color) of the light.
White light is made up of many colors. These different colors have different
wavelengths.
We can see the many colors of light on bubbles.
The separation of white light into many colors on a bubble happens because of
interference.
Thomas Young’s double slit Experiment:
One of the most important experiments of wave theory is that of Young's double
slits. It is a clear example of the diffraction of light conducted with essentially basic
scientific equipment.
Thomas Young was a not only a physicist but also a physician and Egyptologist, who was
responsible for deciphering the Rosetta stone. He devised an experiment in the early
1800's that proved that light is a wave. The experiment has been used subsequently to
show that wave behaviors exists in many other areas of nature and therefore it is worth
spending a little time going into the experiment in detail.
When two light beams interact they create interference which can be constructive or
destructive as we have discussed earlier. The places where constructive and destructive
interference occur are subject to constant change, since electromagnetic waves emitted
are capable of varying phase. Using one light source and splitting it into two beams you
can create two coherent sources, meaning they are of identical frequencies and have a
constant phase difference (the distance between a peak of wave 1 and wave 2 is always
the same) It is also important to use monochromatic light for this experiment as the
location of interference occurs is wavelength dependent.
Interference
pattern on
completely
flat surface
The apparatus consists of a source matching the above requirements, a screen with two
very thin identical slits or the order of a wavelength in width, and a screen to view the
interference on.
In principle, a light bulb, or lamp can be used, but the light must be reduced to a
monochromatic source with filters. It can also be done by splitting the light into its
various frequencies using a prism, a frequency can be selected by channeling the light
with a further screen with only a pin prick in it to allow the light out. These days’ lasers
are used to provide the light source.
When the light is switched on, it travels up to the first screen and is split into two beams
by the slits, we have seen that when this happens waves are diffracted and bulge outwards
causing two curved wave fronts to propagate the other side of the slits, at many places
between the slits and the viewing screen there are areas of constructive interference and
by moving the viewing screen it is possible to get a picture of where they are occurring
Conditions for Sustained Interference:
Light waves from two sources can form a sustained (well defined and observable)
interference pattern where they meet, only if they satisfy the following conditions:
Two light waves superposing at a point must have the same wavelength or
frequency
The amplitude of superimposing light waves should be equal or almost equal.
Two light waves superposing at a point should either have the same phase or
constant phase difference.
The two sources emitting light waves should be very narrow.
The sources emitting light waves should be very close to each other.
Coherent Sources:
Any two sources of light continuously emitting light waves having zeroed or
constant phase difference are called coherent sources. Thus coherent sources have a
definite phase relationship between them and emit light waves of equal frequency or
wavelength.
Interference can occur only with coherent sources. But two independent sources
cannot be coherent because even though they may emit light waves of equal wavelength
and equal amplitude, they may not have constant phase difference. Therefore, to obtain
two interfering beams, a single source is used and its beam is split into two by following
ways:
Division of wave front:
In this case the wave front is divided into two parts by reflection, refraction or
diffraction so hat those two parts reunite at a small angle and produce
interference.
(Example: Fresnel’s biprism, Lloyd’s mirror)
Division of Amplitude:
In this case the wave front is split up into two parts by partial refraction and
reflection at a surface and these two parts are later made to reunite to produce
interference.
(Example: Air wedge, Newton’s Rings)
Air Wedge:
Newton’s Rings:
Newton’s Rings Explanation:
Given a hemisphere of radius R resting on a plane, monochromatic light falling
normally on the top of the hemisphere reflects off both the plane and the hemisphere.
Near the center of the hemisphere, refraction can be neglected, and the rays create rings
of interference. On the curved surface, a point a distance r from the center will be a
height d above the plane
(1)
(2)
Reflection from hemisphere undergoes a phase change of . Reflection from the
plane gives a phase change of . The phase difference between rays reflected off
the plane and hemisphere is therefore
(3)
for , and the interference pattern goes as .
Constructive interference occurs when with m = 0, 1, 2, ..., i.e.,