Two coherent sources emit light waves which superimpose at a point where these can be expressed as
`E_(1) = E_(0) sin(omega t + pi//4)`
`E_(2) = 2E_(0) sin(omega t - pi//4)`
Here, `E_(1) and E_(2)` are the electric field strenghts of the two waves at the given point.
If I is the intensity of wave expressed by field strenght `E_(1)`, find the resultant intensity

Explanation

Intensity of wave expressed by field strenght `E_(1), I prop E_(0)^(2)`
[intensity `prop ("amplitude")^(2)`]
Intensity of wave expressed by `E_(2), I' prop (2E_(0))^(2)`
`(I')/(I) = 4` or `I' = 4I`
phase diffenence between the two waves is
`(omega t + pi//4) - (omega t - pi//4) = (pi)/(2)`
Resultant intensity is given by
`I_(R) = I + I' + 2sqrt(II)' cos phi`
`[I_(R) = I_(1) + I_(2) + 2sqrt (I_(1) I_(2)) cos phi]`
`I_(R) = I + 4I + 2sqrt (I(4I)) cos pi//2 rArr I_(R) = 5I`
Thus, resultant intensity is five times the intersity of wave expressed by `E_(1)`.