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Constructive Interference

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The particle nature of light is well known and has important applications. There are two accepted behaviors of light to explain the dual nature of light. In some cases, light acts like a particle and in others, it acts like a wave. The proof of the wave nature of the light came with the discovery of interference of light and diffraction. When light waves from two light sources are mixed, the waves are said to interfere. The principle behind the interference is nothing but the superposition principle. If two waves are in same phase and they are interfere with each other, the resultant amplitude will be larger than the previous waves this process is known as constructive interference.

Definition

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The change or modification inthe uniform distribution of light intensity in a medium due to the superposition of light waves is known as interference of light. The point at which the interfering waves are in phase, the resultant intensity and the displacement become maximum, these points are termed as maxima and this type interference is known as constructive interference, because in this case both the waves add to the effect of each other.

Constructive Interference

Equation

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The intensity of light is maximum if the constructive interference occurs whereas the intensity is zero in the case of destructive interference. The intensity can be measured in terms of amplitudes of the waves which is superimpose each other. So, the equation of constructive interference is,
I = $a_{1}^{2}$ + $a_{2}^{2}$ + 2$a_{1}a_{2}cos\phi$
If $\phi$ takes the values 2n$\pi$ where n = 0,1,2,3,......we get the maximum intensity, which is given by
$I_{max}$ = $(a_{1} + a_{2})^{2}$
Where $I_{max}$ is the maximum intensity, $a_{1}$ is the amplitude of the first wave, $a_{2}$ is the amplitude of the second wave.

Example 

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Some of the examples of constructive interference are:

Stereo speakers: If two speakers are kept near to each other with playing same music at same time, the resultant sound will be very high.

Tidal waves: While tsunami, two large amplitude waves interfere together and produce a big wave

Beats are also an example of constructive interference.

Constructive and Destructive Interference

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Constructive Interference

As mentioned above, in the case of constructive interference the amplitudes of waves add up and the resultant amplitude is the sum of the amplitudes of these waves.

Destructive Interference

At those points orĀ  positions of the medium where the two interfering waves reach in opposite phase, the resultant displacement and hence the resultant intensity become minimum. Such positions are called minima and this state is known as destructive interference because in this case one wave destroys the effect of the other.

Destructive Interference