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Two coherent sources of different intensities send waves that interfere. The ratio of maximum to minimum intensity is 2 5 . The intensity ratio of the sources is

Two coherent sources of different intensities send waves that interfere. The ratio of maximum to minimum intensity is 25. The intensity ratio of the sources is

 
 
 

Grade:12

1 Answers

Govind Sharma
167 Points
3 years ago
Let a1a1 and a2a2 be amplitudes of the two waves. For maximum intensity
Imax=(a2+a2)2Imax=(a2+a2)^2
For minimum intensity
Imin=(a2−a2)2Imin=(a2−a2)^2
Given, ImaxImin=251=((a1+a2)2)(a1−a2)2Imax/Imin=25/1=((a1+a2)^2)/(a1−a2)^2
⇒a1+a2a1−a2=51⇒a1a2=32⇒a1+a2/a1−a2=5/1
                                                           ⇒a1/a2=3/2
I1/I2 = a1^2/a2^2 = 9/4
∴I1I2=a21a22=(32)4=94

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