Two waves have intensities in the ratio 1 : 9. If these waves produce interference, then ratio of maximum and minimum intensities is
Two waves have intensities in the ratio 1 : 9. If these waves produce interference, then ratio of maximum and minimum intensities is
A ) 3 : 1
B ) 4 : 1
C ) 9 : 1
D ) 16 : 1
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The correct option is (B) 4 : 1.
I1 = 1
I2 = 9
Imax = (√I2 + √I1)2
Imin = (√I2 - √I1)2
\(\frac{I_{max}}{I_{min}}=\frac{(\sqrt{I_2}+\sqrt{I_1})^2}{(\sqrt I_2-\sqrt I_1)^2}\)
\(\frac{I_{max}}{I_{min}}=\frac{(\sqrt{9}+\sqrt{1})^2}{(\sqrt 9-\sqrt 1)^2}\)
\(\frac{I_{max}}{I_{min}}=\frac{(3+1)^2}{(3-1)^2}\)
\(\frac{I_{max}}{I_{min}}=\frac{(4)^2}{(2)^2}\)
\(\frac{I_{max}}{I_{min}}=\frac{16}{4}\)
\(\frac{I_{max}}{I_{min}}=\frac4{1}\)
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