Interference Of Light Waves And Young S Experiment

To solve this problem, we need to consider the principle of superposition and interference of coherent light waves. Two coherent light waves of amplitude ‘a’ are interfering with each other. The intensity

I

resulting from interference of waves is given by the equation:

I = I

₁+I₂+2√I₁I₂cosϕ

where

I_1

and

I_2

are the intensities of the individual waves, and

%CF%95

is the phase difference between the two waves. The intensity of a wave is proportional to the square of its amplitude:

I = a^{2}

For each of the waves, we have

I_1%20%3D%20a%5E2

and

I_2%20%3D%20a%5E2

. Substituting these into the interference intensity equation gives:

I = a^{2} + a^{2} +2 a a cos ϕ

which simplifies to:

I = 2 a^{2} + 2 a^{2} cos ϕ

The intensity varies depending on the value of

cos%CF%95

, which ranges between -1 and 1. Thus, the minimum intensity

I_%7Bmin%7D

occurs when

cos%CF%95%20%3D%20-1

I

_min=2a2-2a2=0

The maximum intensity

I_%7Bmax%7D

occurs when

cos%CF%95%20%3D%201

I

_max=2a2+2a2=4a2

Therefore, the intensity of light varies between 0 and

4a%5E2

. The correct answer is:

0 and

4a%5E2

The resultant intensity in an interference pattern is given by: $I%20%3D%20I_1%20%2B%20I_2%20%2B%202%20%5Csqrt%7BI_1%20I_2%7D%20%5Ccos%20%5Cdelta$ Since $I_1%20%3D%20I_2%20%3D%20I_0$ , we get: $I%20%3D%202%20I_0%20(1%20%2B%20%5Ccos%20%5Cdelta)$ The phase difference $%5Cdelta$ is related to the path difference by: $%5Cdelta%20%3D%20%5Cfrac%7B2%5Cpi%7D%7B%5Clambda%7D%20%5Ctimes%20%5Cfrac%7B%5Clambda%7D%7B8%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B4%7D$ Substituting this into the intensity formula: $I%20%3D%202%20I_0%20%5Cleft(1%20%2B%20%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%5Cright)$ Since $%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D$ , we obtain: $I%20%3D%20I_0%20%5Cleft(%201%20%2B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%20%5Cright)$ Thus, the intensity at this point is $I_0%20%5Cleft(%201%20%2B%20%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%5Cright)$ .

About Interference Of Light Waves And Young S Experiment - CBSE-CLASS-XII

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Interference Of Light Waves And Young S Experiment

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About Interference Of Light Waves And Young S Experiment - CBSE-CLASS-XII

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Chapter Questions
3 MCQs