LIGHT WAVES: Principles, Laws, Properties, Numericals and FAQs
When two or more than two waves
come to a particle of a medium together then the displacement of the particle
will be equal to the vector sum of displacements due to different waves
reaching to the point. The waves coming to the particle will be going further
without any change in them. Let the displacement in the particle due to one
wave be y1 and it is y2 due to the second wave. Then
resultant displacement of the particle will be ‘y’.
Frequency and amplitude of superposed waves will depend on
Frequency And Amplitude Of Superposed Wave Will Depend On
1)
Frequencies of waves coming.
2)
Amplitudes of waves coming.
3)
Phase difference between the
waves coming.
4)
Direction of waves coming.
Interference
When two waves of equal
frequency, equal velocity and going in a direction in a medium are having
superposition then they produce effect of interference.
Interference
Of Light Waves: -
Definition: -Redistribution of energy in light waves due to superposition of
waves is said to be interference of waves. Or,
when two waves of equal frequency going in a medium in a direction with
a velocity are having superposition they effect the energy distribution of each
other. At certain point where the waves meet in
a phase the displacement or amplitude /of the particle becomes more or
intensity of light will be more but at the other certain points where the waves
meet in opposite phase displacement/ amplitude of particle reduces and
intensity of light reduces. In this way the increases and decreases in energy
of light at different points in medium due to superposition of waves is said to
be interference of waves.
Types of interference: -
1) Constructive
interference: - When the waves are superposed in a phase or displacement or
intensity increases than it said to be Constructive Interference.
2) Destructive
Interference: -When the waves are superposed in a opposite phase or displacement or intensity decreases than it
said to be Destructive Interference.
Condition for
interference: -
1)
The waves coming for
superposition must be from the coherent sources, the wave must meet in a phase
or have constant phase difference.
2)
The waves coming for
superposition must be having equal frequency, wavelength or velocity.
3)
The wave must be propagating in
a medium in direction
4)
If the amplitude of waves are
equal than the interference will be clear or distinct
5)
If the path difference between
the wave for reaching to any point in the medium is complete multiple of l say l, 2l, 3l, … ,nl or the phase difference between the waves is 0,2p,4p,6p,… or T, 2T, 3T,… then the point will be point of
constructive interference.
6)
If the path difference
between the waves reaching to a point is odd multiple of l/2, say l/2 ,3l/2, 5l/2,… ,(2n+1)l/2 or the phase difference is p,3p, 5p … or T/2, 3T/, 5T/2,…then the point will be destructive interference
Mathematical
Analysis of interference
Consider the waves having the same frequency and going along the x
direction. Let the amplitude of the waves be a1 and a2
the phase difference between them is f then the wave equation will
be
y1 = a1 sin wt
y1 = a1 sin (wt ± f)
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