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If the ratio of intensities of two waves causing interference be 9:4, then the ratio of maximum and minimum intensities will be
  • a)
    3:2
  • b)
    5:1
  • c)
    9:4
  • d)
    25:1
Correct answer is option 'D'. Can you explain this answer?
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If the ratio of intensities of two waves causing interference be 9:4, ...
Ratio of Intensities
The given ratio of intensities of two interfering waves is 9:4. Let the intensities of the two waves be I1 and I2 respectively. Therefore, we can write:

I1/I2 = 9/4

Ratio of Maximum and Minimum Intensities
The maximum and minimum intensities occur due to constructive and destructive interference respectively. The maximum intensity will occur when the two waves are in phase and the minimum intensity will occur when the two waves are out of phase. Let Imax and Imin be the maximum and minimum intensities respectively. Therefore, we can write:

Imax = I1 + I2 + 2√(I1I2)
Imin = I1 + I2 - 2√(I1I2)

Dividing Imax by Imin, we get:

Imax/Imin = (I1 + I2 + 2√(I1I2))/(I1 + I2 - 2√(I1I2))

Substituting the value of I1/I2, we get:

Imax/Imin = (9 + 4 + 2√(9×4))/(9 + 4 - 2√(9×4))
Imax/Imin = (13 + 12)/(13 - 12)
Imax/Imin = 25:1

Therefore, the ratio of maximum and minimum intensities is 25:1, which is option D.
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If the ratio of intensities of two waves causing interference be 9:4, then the ratio of maximum and minimum intensities will bea)3:2b)5:1c)9:4d)25:1Correct answer is option 'D'. Can you explain this answer?
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