Light waves from two coherent sources having intensities `I and 2 I` cross each other at a point with a phase diff. of `60^(@)`. What is the resultant intensity at the point ? If the sources were incoherent, what would be the resultant intensity ?

Light waves from two coherent sources having intensities `I and 2 I` c

1.	Light waves from two coherent sources having intensities `I and 2 I` cross each other at a point with a phase diff. of `60^(@)`. What is the resultant intensity at the point ? If the sources were incoherent, what would be the resultant intensity ?
Answer» Here, `I_(1) = I and I_(2) = 2 I, phi = 60^(@)` When sources are coherent Amplitude `R` of resultant wave is `R = sqrt(a^(2) + b^(2) + 2 ab cos phi)` `R^(2) = a^(2) + b^(2) + 2 ab cos phi` As intensity `prop ("amplitude")^(2)` `:.` Resultant intensity, `I_(R ) = I_(1) + I_(2) + 2sqrt(I_(1)I_(2)) cos phi = I + 2 I + 2 sqrt(I xx 2I) xx cos 60^(@)` `= 3 I + I sqrt(2) = I(3 + sqrt(2)) = 4.414 I` If the sources are incoherent, `I_(R ) = I_(1) + I_(2) = I + 2 I = 3 I`

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Light waves from two coherent sources having intensities `I and 2 I` cross each other at a point with a phase diff. of `60^(@)`. What is the resultant intensity at the point ? If the sources were incoherent, what would be the resultant intensity ?

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