PHYSICS
UNIT - 1
Chapter 1 : INTERFERENCE OF LIGHT
Geometric path (L) and Optical path (Δ)
The shortest physical distance between two points between which light travels is known as the
geometric path (L). The geometric path is independent of the medium in which light travels.
Since light travels in different media with different velocities, the
optical path travelled by light between two points will be
different for different media.
Optical path = Geometric path x refractive index of medium
i.e. ∆ = µL
Eg: Geometric path from I to E, L = IO + OE
Optical path from I to E, ∆ = µair x IO + µglass x OE
= IO + µ . OE (since µair = 1)
Optical Path difference (Δ)
The optical path difference between two rays of light is the difference in the optical paths
travelled by the two rays.
Phase difference (δ)
The relative difference in phase of two waves is called the phase
difference between them.
Waves completely in phase
Two waves are said to completely in phase with each other when
the crests and troughs of one wave come exactly over the crests
and troughs of the other wave.
For two waves to be in phase, the phase difference between
them must be zero or even integral multiple of π.
i.e. for waves in phase, δ = 2nπ ……eqn.1
where n = 0, 1, 2, 3……
Waves completely out of phase
Two waves are said to completely out of phase with each other
when the crest of one wave comes exactly over the trough of the
other wave and vice versa.
For two waves to be out of phase, the phase difference between
them must be an odd integral multiple of π.
i.e. for waves out of phase, δ = (2n+1)π …..eqn.2
where n = 0, 1, 2, 3……
Relation between phase difference (δ) and path difference (Δ)
2π
δ= Δ ……eqn.3
λ
where λ = wavelength of light
Using the values of δ from eqn.1 & eqn.2 in eqn.3 we get,
For waves in phase, Δ = n λ where n = 0, 1, 2, 3……
i.e. the path difference between them is an integral multiple of the wavelength.
Interference of Light Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 1
, Similarly, for waves out of phase, Δ = (2n+1) λ/2 where n = 0, 1, 2, 3……
i.e. the path difference between is an odd integral multiple of half wavelength.
Change of phase on reflection
When a light wave is reflected at the surface of an optically denser medium, it suffers a phase
change of π or a path change of λ/2.
Interference of light
When two light waves superimpose then the resultant amplitude or
intensity in the region of superposition in different from the
amplitude of the individual waves. This modification in the
amplitude in the region of superposition is called interference of
light.
a) Constructive Interference
When the two waves arrive at a point in phase, the amplitudes add
up to get larger amplitude (bright spot or maxima). This is called
constructive interference.
Thus for constructive interference, waves must be in phase.
i.e. Phase difference, δ = 2nπ OR
Path difference, Δ = n λ
where n = 0, 1, 2, 3……
b) Destructive Interference
When the two waves arrive at a point out of phase, the amplitudes
cancel each other to get zero or almost zero amplitude (dark spot or
minima). This is called destructive interference.
Thus for destructive interference, waves must be out of phase.
i.e. Phase difference, δ = (2n+1)π OR
Path difference, Δ = (2n+1) λ/2
where n = 0, 1, 2, 3……
Condition to get Steady Interference Pattern
To get a steady interference pattern (pattern which does not change with time), the two
interfering sources of light must be coherent. i.e. the phase difference or path difference
between them must remain constant.
Note: Two separate sources of light cannot be coherent, since, they being independent of each
other, changes taking place in one source may not simultaneously take place in the other source.
Hence the phase or path difference between them will not remain constant.
Coherent sources can be obtained by spitting a single source into two or more sources. This can
be done by various methods.
Types of Interference
Depending upon the method by which coherent sources are obtained, interference is classified
into two categories: (i) Interference by division of wavefront, and (ii) Interference by division of
amplitude
(i) Interference by division of wave front
Here the wave is physically divided into two coherent sources by the use of a double slit, a
mirror, or a biprism.
A narrow or point source is required for this method, hence, the interference pattern is not
bright.
Eg: Young’s Double Slit, Lloyd’s Mirror, Fresnel’s Biprism
Interference of Light Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 2
UNIT - 1
Chapter 1 : INTERFERENCE OF LIGHT
Geometric path (L) and Optical path (Δ)
The shortest physical distance between two points between which light travels is known as the
geometric path (L). The geometric path is independent of the medium in which light travels.
Since light travels in different media with different velocities, the
optical path travelled by light between two points will be
different for different media.
Optical path = Geometric path x refractive index of medium
i.e. ∆ = µL
Eg: Geometric path from I to E, L = IO + OE
Optical path from I to E, ∆ = µair x IO + µglass x OE
= IO + µ . OE (since µair = 1)
Optical Path difference (Δ)
The optical path difference between two rays of light is the difference in the optical paths
travelled by the two rays.
Phase difference (δ)
The relative difference in phase of two waves is called the phase
difference between them.
Waves completely in phase
Two waves are said to completely in phase with each other when
the crests and troughs of one wave come exactly over the crests
and troughs of the other wave.
For two waves to be in phase, the phase difference between
them must be zero or even integral multiple of π.
i.e. for waves in phase, δ = 2nπ ……eqn.1
where n = 0, 1, 2, 3……
Waves completely out of phase
Two waves are said to completely out of phase with each other
when the crest of one wave comes exactly over the trough of the
other wave and vice versa.
For two waves to be out of phase, the phase difference between
them must be an odd integral multiple of π.
i.e. for waves out of phase, δ = (2n+1)π …..eqn.2
where n = 0, 1, 2, 3……
Relation between phase difference (δ) and path difference (Δ)
2π
δ= Δ ……eqn.3
λ
where λ = wavelength of light
Using the values of δ from eqn.1 & eqn.2 in eqn.3 we get,
For waves in phase, Δ = n λ where n = 0, 1, 2, 3……
i.e. the path difference between them is an integral multiple of the wavelength.
Interference of Light Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 1
, Similarly, for waves out of phase, Δ = (2n+1) λ/2 where n = 0, 1, 2, 3……
i.e. the path difference between is an odd integral multiple of half wavelength.
Change of phase on reflection
When a light wave is reflected at the surface of an optically denser medium, it suffers a phase
change of π or a path change of λ/2.
Interference of light
When two light waves superimpose then the resultant amplitude or
intensity in the region of superposition in different from the
amplitude of the individual waves. This modification in the
amplitude in the region of superposition is called interference of
light.
a) Constructive Interference
When the two waves arrive at a point in phase, the amplitudes add
up to get larger amplitude (bright spot or maxima). This is called
constructive interference.
Thus for constructive interference, waves must be in phase.
i.e. Phase difference, δ = 2nπ OR
Path difference, Δ = n λ
where n = 0, 1, 2, 3……
b) Destructive Interference
When the two waves arrive at a point out of phase, the amplitudes
cancel each other to get zero or almost zero amplitude (dark spot or
minima). This is called destructive interference.
Thus for destructive interference, waves must be out of phase.
i.e. Phase difference, δ = (2n+1)π OR
Path difference, Δ = (2n+1) λ/2
where n = 0, 1, 2, 3……
Condition to get Steady Interference Pattern
To get a steady interference pattern (pattern which does not change with time), the two
interfering sources of light must be coherent. i.e. the phase difference or path difference
between them must remain constant.
Note: Two separate sources of light cannot be coherent, since, they being independent of each
other, changes taking place in one source may not simultaneously take place in the other source.
Hence the phase or path difference between them will not remain constant.
Coherent sources can be obtained by spitting a single source into two or more sources. This can
be done by various methods.
Types of Interference
Depending upon the method by which coherent sources are obtained, interference is classified
into two categories: (i) Interference by division of wavefront, and (ii) Interference by division of
amplitude
(i) Interference by division of wave front
Here the wave is physically divided into two coherent sources by the use of a double slit, a
mirror, or a biprism.
A narrow or point source is required for this method, hence, the interference pattern is not
bright.
Eg: Young’s Double Slit, Lloyd’s Mirror, Fresnel’s Biprism
Interference of Light Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 2
