Sunday 22 December 2013

LIGHT WAVES: Principles, Laws, Properties, Numericals and FAQs

LIGHT WAVES: Principles, Laws, Properties, Numericals and FAQs

LIGHT WAVES: Principles, Laws, Properties, Numericals and FAQs
Principle of super position of waves
: -
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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