1
optics
CHAPTER-01
UNIT-I
INTERFERENCE
1.1 Introduction: -
Optics is the branch of physics that studies the behaviour and properties of light,
including its interactions with matter and the construction of instruments that use
or detect it. Optics usually describes the behaviour of visible, ultraviolet,
and infrared light. Because light is an electromagnetic wave, other forms
of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit
similar properties.
Light and its optical properties: -
Light is a form of energy which is in the form of an electromagnetic wave and is
almost everywhere around us. The visible light has wavelengths measuring between
400–700 nanometres. Sun is the primary source of light by which plants utilize this to
produce their energy.
In physics, the term light also refers to electromagnetic radiation of different
kinds of wavelength, whether it is visible to the naked eye or not. Hence by this, the
gamma rays, microwaves, X-rays and the radio waves are also the types of light. Light
exhibits various properties which are given below
Reflection: -
Reflection is one of the primary properties of light. Reflection is nothing
but what you see the images in the mirrors. Reflection is defined as the change
in direction of light at an interface in-between two different media so that the
wave-front returns into a medium from which it was originated. The typical
examples for reflection of light include sound waves and water waves.
Speed of light: -
The rate at which the light travels in free space is called as Speed of
light. For example, the light travels 30% slower in water when compared to
vacuum.
Refraction: -
The bending of light when it passes from one medium to another is
called as Refraction. This property of refraction is used in a number of devices
like microscopes, magnifying lenses, corrective lenses, and so on. In this
property, when the light is transmitted through a medium, polarization of
electrons takes place which in-turn reduces the speed of light, thus changing
the direction of light.
Total internal reflection: -
When a beam of light strikes the water, a part of the light is reflected,
and some part of the light is refracted. This phenomenon is called as Total
internal reflection.
Interference
, 2
optics
Dispersion: -
It is a property of light, where the white light splits into its constituent
colours. The phenomenon of dispersion can be observed in the form of a prism.
Applications of Optics: -
The properties of optics are applied in various fields of Physics.
1) The refraction phenomenon is applied in the case of lenses (Convex and
concave) for the purpose of forming an image of the object.
2) Geometrical optics is used in studying of how the images form in an
optical system.
3) In medical applications, it is used in the optical diagnosis of the
mysteries of the human body.
4) It is used in the therapeutically and surgeries of the human tissues.
1.2 Principle of superposition: -
The principle of superposition, states that when two waves of the same kind
meet at a point in space, the resultant displacement at that point is the vector sum of
the displacements that the two waves would separately produce at that point.
Interference refers to the superposing of two or more same kind of waves to
produce regions of maxima and minima in space, according to the principle of
superposition.
1.3 Coherent sources & coherence: -
Coherent sources: -
The sources of light which emit light waves continuously of same wavelength,
and time period, frequency and amplitude and have zero phase difference or constant
phase difference are called coherent sources.
Consider the two coherent sources which are close to each other and the two
sources emits the light waves then these lights waves gets interacted to each other i,e;
the superposition of the two or more waves of same kind will gives the phenomenon
of interference.
Coherence (Coherent wave): -
A wave from the coherent source and which appears to be a pure sine wave for
an infinitely large period of time or in an infinitely extended space be said to be a
perfectly coherent wave. In such a wave there is a definite relationship between phase
of wave and a given time and at a certain time later for at a point and at a certain
distance away.
Coherence describes all properties of the correlation between physical quantities
of a single wave or between several waves or wave packets. Actually, there is no light
to emits a perfect coherent wave. Light wave which are pure sine waves, and only for
a limited period of time or in a limited space, are partially coherent waves.
There are two types of Coherence:
i. Temporal coherence
ii. Spatial coherence
Let us discuss each of them.......
Interference
, 3
optics
i. Temporal Coherence: -It's a measure of the average correlation between the
value of a wave and itself delayed by T, at any pair of times. Temporal
coherence tells us how monochromatic a source is. Example of temporal
coherence: A wave containing only a single frequency is perfectly correlated
with itself at all time delays. On the other hand, a wave whose phase drifts
quickly will have a short coherence time.
Similarly pulses of waves which naturally have a broad range of
frequencies also have a short coherence time since the amplitude of the wave
changes quickly.
Finally, white light which has very broad range of frequencies is a
wave which varies quickly in both amplitude and phase since it consequently
has a very short coherence time it is often called incoherent.
ii. Spatial Coherence: -The spatial coherence is the phase relationship between
the radiation field at different points in space.
In some system such as a water waves or optics wave-like states can
extend over one or two dimensions. Spatial coherence describes the ability
for two points in space in the extent of a wave to interfere when averaged
over time
The spatial coherence is the cross-correlation between two points in a
wave for all times if a wave has only 1 value of amplitude over an infinite
length it is perfectly spatially coherent.
1.4 Interference and types of interference: -
Interference: -
When the two light waves from different coherent sources meet together, then
the distribution of energy due to one wave is distributed
by the other wave gets modified. This modification in
the distribution of light energy due to superposition of
two light waves is called “interference of light” As
shown in the figure, we noticed that the point on a wave
with maximum value or upward displacement within a
cycle is called crest, and the point on a wave with
minimum value or downward displacement within a
cycle is called trough.
The distance between two successive crest or two successive troughs is called
wavelength of the wave(λ). And as shown in the figure, the distance between
maximum to minimum points on the wave is known as amplitude(a).
The following are the condition for the interference
The two sources of light should emit continuous waves of the same
wavelength and the same time period, i.e; the two sources should be
coherent sources.
Interference
, 4
optics
The two sources of light should be very close to each other.
The distance of the screen from the two sources be quite large.
The waves emitted by two sources should either have zero phase
difference or no phase difference.
If the interfering waves are polarised, they must be in the same state of
polarisation.
The two sources should give monochromatic light.
The background should be dark.
Types of interference: -
There are majorly two types of interferences. Those are constructive &
destructive interferences.
1. Constructive interference: -
When two light waves superpose with each other in such a way that crest of
one wave falls on the crest of the second wave, and trough of one wave is falls on
the trough of the second wave, then the resultant wave has larger amplitude and it
is called Constructive interference.
In this interference, the resultant wave amplitude(a) is sum of the individual
amplitudes of the first wave(a1) and the second wave(a2)
i,e; 𝑎 = 𝑎1 + 𝑎2
or in terms of displacements we can write;
𝑦 = 𝑦1 + 𝑦2
Constructive interference occurs when the phase difference between the
waves is an even multiple of π such as 2π, 4π, 6π.... etc.
2. Destructive interference: -
When two light waves superpose with each other in such a way that the crest
of one wave coincides with trough of the second wave, then the amplitude of the
resultant wave becomes zero and it is called Destructive interference.
In this interference, the resultant wave amplitude(a) is difference of the
individual amplitudes of the first wave(a1) and the second wave(a2)
i,e; 𝑎 = 𝑎1 − 𝑎2
or in terms of displacements we can write;
𝑦 = 𝑦1 − 𝑦2
Interference
optics
CHAPTER-01
UNIT-I
INTERFERENCE
1.1 Introduction: -
Optics is the branch of physics that studies the behaviour and properties of light,
including its interactions with matter and the construction of instruments that use
or detect it. Optics usually describes the behaviour of visible, ultraviolet,
and infrared light. Because light is an electromagnetic wave, other forms
of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit
similar properties.
Light and its optical properties: -
Light is a form of energy which is in the form of an electromagnetic wave and is
almost everywhere around us. The visible light has wavelengths measuring between
400–700 nanometres. Sun is the primary source of light by which plants utilize this to
produce their energy.
In physics, the term light also refers to electromagnetic radiation of different
kinds of wavelength, whether it is visible to the naked eye or not. Hence by this, the
gamma rays, microwaves, X-rays and the radio waves are also the types of light. Light
exhibits various properties which are given below
Reflection: -
Reflection is one of the primary properties of light. Reflection is nothing
but what you see the images in the mirrors. Reflection is defined as the change
in direction of light at an interface in-between two different media so that the
wave-front returns into a medium from which it was originated. The typical
examples for reflection of light include sound waves and water waves.
Speed of light: -
The rate at which the light travels in free space is called as Speed of
light. For example, the light travels 30% slower in water when compared to
vacuum.
Refraction: -
The bending of light when it passes from one medium to another is
called as Refraction. This property of refraction is used in a number of devices
like microscopes, magnifying lenses, corrective lenses, and so on. In this
property, when the light is transmitted through a medium, polarization of
electrons takes place which in-turn reduces the speed of light, thus changing
the direction of light.
Total internal reflection: -
When a beam of light strikes the water, a part of the light is reflected,
and some part of the light is refracted. This phenomenon is called as Total
internal reflection.
Interference
, 2
optics
Dispersion: -
It is a property of light, where the white light splits into its constituent
colours. The phenomenon of dispersion can be observed in the form of a prism.
Applications of Optics: -
The properties of optics are applied in various fields of Physics.
1) The refraction phenomenon is applied in the case of lenses (Convex and
concave) for the purpose of forming an image of the object.
2) Geometrical optics is used in studying of how the images form in an
optical system.
3) In medical applications, it is used in the optical diagnosis of the
mysteries of the human body.
4) It is used in the therapeutically and surgeries of the human tissues.
1.2 Principle of superposition: -
The principle of superposition, states that when two waves of the same kind
meet at a point in space, the resultant displacement at that point is the vector sum of
the displacements that the two waves would separately produce at that point.
Interference refers to the superposing of two or more same kind of waves to
produce regions of maxima and minima in space, according to the principle of
superposition.
1.3 Coherent sources & coherence: -
Coherent sources: -
The sources of light which emit light waves continuously of same wavelength,
and time period, frequency and amplitude and have zero phase difference or constant
phase difference are called coherent sources.
Consider the two coherent sources which are close to each other and the two
sources emits the light waves then these lights waves gets interacted to each other i,e;
the superposition of the two or more waves of same kind will gives the phenomenon
of interference.
Coherence (Coherent wave): -
A wave from the coherent source and which appears to be a pure sine wave for
an infinitely large period of time or in an infinitely extended space be said to be a
perfectly coherent wave. In such a wave there is a definite relationship between phase
of wave and a given time and at a certain time later for at a point and at a certain
distance away.
Coherence describes all properties of the correlation between physical quantities
of a single wave or between several waves or wave packets. Actually, there is no light
to emits a perfect coherent wave. Light wave which are pure sine waves, and only for
a limited period of time or in a limited space, are partially coherent waves.
There are two types of Coherence:
i. Temporal coherence
ii. Spatial coherence
Let us discuss each of them.......
Interference
, 3
optics
i. Temporal Coherence: -It's a measure of the average correlation between the
value of a wave and itself delayed by T, at any pair of times. Temporal
coherence tells us how monochromatic a source is. Example of temporal
coherence: A wave containing only a single frequency is perfectly correlated
with itself at all time delays. On the other hand, a wave whose phase drifts
quickly will have a short coherence time.
Similarly pulses of waves which naturally have a broad range of
frequencies also have a short coherence time since the amplitude of the wave
changes quickly.
Finally, white light which has very broad range of frequencies is a
wave which varies quickly in both amplitude and phase since it consequently
has a very short coherence time it is often called incoherent.
ii. Spatial Coherence: -The spatial coherence is the phase relationship between
the radiation field at different points in space.
In some system such as a water waves or optics wave-like states can
extend over one or two dimensions. Spatial coherence describes the ability
for two points in space in the extent of a wave to interfere when averaged
over time
The spatial coherence is the cross-correlation between two points in a
wave for all times if a wave has only 1 value of amplitude over an infinite
length it is perfectly spatially coherent.
1.4 Interference and types of interference: -
Interference: -
When the two light waves from different coherent sources meet together, then
the distribution of energy due to one wave is distributed
by the other wave gets modified. This modification in
the distribution of light energy due to superposition of
two light waves is called “interference of light” As
shown in the figure, we noticed that the point on a wave
with maximum value or upward displacement within a
cycle is called crest, and the point on a wave with
minimum value or downward displacement within a
cycle is called trough.
The distance between two successive crest or two successive troughs is called
wavelength of the wave(λ). And as shown in the figure, the distance between
maximum to minimum points on the wave is known as amplitude(a).
The following are the condition for the interference
The two sources of light should emit continuous waves of the same
wavelength and the same time period, i.e; the two sources should be
coherent sources.
Interference
, 4
optics
The two sources of light should be very close to each other.
The distance of the screen from the two sources be quite large.
The waves emitted by two sources should either have zero phase
difference or no phase difference.
If the interfering waves are polarised, they must be in the same state of
polarisation.
The two sources should give monochromatic light.
The background should be dark.
Types of interference: -
There are majorly two types of interferences. Those are constructive &
destructive interferences.
1. Constructive interference: -
When two light waves superpose with each other in such a way that crest of
one wave falls on the crest of the second wave, and trough of one wave is falls on
the trough of the second wave, then the resultant wave has larger amplitude and it
is called Constructive interference.
In this interference, the resultant wave amplitude(a) is sum of the individual
amplitudes of the first wave(a1) and the second wave(a2)
i,e; 𝑎 = 𝑎1 + 𝑎2
or in terms of displacements we can write;
𝑦 = 𝑦1 + 𝑦2
Constructive interference occurs when the phase difference between the
waves is an even multiple of π such as 2π, 4π, 6π.... etc.
2. Destructive interference: -
When two light waves superpose with each other in such a way that the crest
of one wave coincides with trough of the second wave, then the amplitude of the
resultant wave becomes zero and it is called Destructive interference.
In this interference, the resultant wave amplitude(a) is difference of the
individual amplitudes of the first wave(a1) and the second wave(a2)
i,e; 𝑎 = 𝑎1 − 𝑎2
or in terms of displacements we can write;
𝑦 = 𝑦1 − 𝑦2
Interference
