> Q. Two coherent light beams of intensity $ I$ and $4,I$ are superposed. The maximum and minimum possible intensities in the resulting beam are – LIVE ANSWER TODAY

Q. Two coherent light beams of intensity $ I$ and $4,I$ are superposed. The maximum and minimum possible intensities in the resulting beam are

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Two coherent light beams of intensity $ I$ and $4,I$ are superposed. The maximum and minimum possible intensities in the resulting beam are

Solution:

As $I propto a^{2}$ or $a propto sqrt{I}$

$ therefore , frac{a_{1}}{a_{2}} =sqrt{frac{I}{4 I}} $

$ Rightarrow , frac{a_{1}}{a_{2}} =frac{1}{2}$

$ frac{I_{max }}{I_{min }} =left(frac{a_{1}+a_{2}}{a_{1}-a_{2}}right)^{2} $

$=left(frac{1+2}{1-2}right)^{2}=frac{9}{1}$

$ therefore I_{max }=9 I, I_{min } =I$

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