Interference of a light wave

 Interference of a light wave



In previous topic we have learned reflection of a light in form of wave which was explained by Huygens' . If the light propagates as waves then it must exhibit interference effect in medium of propagation . Thus in 1801 ,Thomos Young performed his experiment and demonstrated interference of light.

The modification in the intensity of light produced by bthe superposition of two or more light wave s is called interference of light

If two or more light passes through a medium , and interfere with each other, then the resultant light has intensity which is governed by Principle of Superposition of wave.

Superposition of Wave

When to or more waves overlap, the resultant displacement at any point and at any instant is equal to the vector sum of instantaneous displacements that would be produced at the point by individual waves if each wave is present alone.



From the above figure, there are two light source A and B emitting waves in forward direction .These circular waves travel out in form of trough and crests .Let continuous lines represent the crest and dotted lines represent troughs. The points at which a crest falls upon crest and a trough an trough are marked by (x) crosses . At such points the resultant displacement is maximum , the waves interfere is called constructive interference.

While other points where a crest falls upon a trough and trough falls on crest are marked as (0).These are the points on the surface and the resultant is zero and the resultant effect at these point is called destructive interference.
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Condition for interference

Consider two source of light P and Q as shown in fig below, Both the source at very close to each other.


Both the source is emitting light in forward direction having wavelength λ and having same frequency . At point O both wave reaches at same time without any phase difference. Hence they will produce constructive interference and the point O will be bright. In this case both wave travels equal distance  and path difference (QR - PR) is zero.
Constructive Interference


Consider a point R on the screen. The path difference between both wave at R is (QR-PR) .The point R will be bright if both wave arrive at point R with
phase difference of : 0 , 2π , 4π, 6π,-----------nπ
                              or 
path difference is 0,2 λ /2  ,  4λ /2  , 6λ/2--------------2n (λ/2)

i.e  even multiple of λ/2

Destructive Interference

If both wave reaching at point R is having a phase difference out of phase they will produce destructive interference. The point R will be dark when 
Phase difference is π , 3π, 5π-------(2n-1)π .
Path difference is  λ /2  ,  3λ /2  ,5λ /2  ,-----------(2n-1)λ /2  
i.e odd multiple of λ /2  

Condition for Obtaining sharp Interference Pattern

The conditions required for steady interference pattern​ are as follows:

There should be two source of light and that should be:

  1. Coherent, i.e, light wave should have no phase difference. Both the source should be obtained from a single source.
  2. Monochromatic light is necessary, i.e  light should have same frequency , colour of light should be same.
  3. Equal amplitudes .i.e light  wave should have same amplitide of vibrations
  4. Narrow sources. Point sources of light in the form of illuminated slits can be used.
  5. distance between both slit should be as close as possible.
  6. The distance from source to screen should be large. should be close to each other.
  7. Should emit waves in nearly the same direction.

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