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  • I need help with Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio: 

  • Option 1)

    16 : 9

  • Option 2)

    25 : 9

     

  • Option 3)

    4 : 1

     

  • Option 4)

    5 : 3

Answers (1)

best_answer

 

Resultant Intensity of two wave -

I= I_{1}+I_{2}+2\sqrt{I_{1}I_{2}}\cos \theta

- wherein

I_{1}= Intencity of wave 1

I_{2}= Intencity of wave 2

\theta = Phase difference

Let intensities be I1, I2 and amplitudes A1,A2

\frac{I_{max}}{I_{min}} = \left ( \frac{A_{max}}{A_{min}} \right )^{2}

\Rightarrow \frac{A_{max}}{A_{min}} =4

Amax = A1 + A2

Amin = A1 - A2

\frac{4}{1} = \frac{A_{1}+ A_{2}}{A_{1}- A_{2}}

\frac{4 + 1}{4 -1} = \frac{(A_{1}+ A_{2}) +(A_{1}- A_{2}) }{(A_{1}+ A_{2})-(A_{1}- A_{2})}

\Rightarrow \frac{A_{1}}{A_{2}} = \frac{5}{3}

\therefore \frac{I_{1}}{I_{2}} = (\frac{5}{3}) ^{2} = \frac{25}{9}

 

 


Option 1)

16 : 9

Option 2)

25 : 9

 

Option 3)

4 : 1

 

Option 4)

5 : 3

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