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

I being the intensity of wave expressed by field strength `E_1 , I alpha E_0^2` (intensity `alpha" (amplitude)"^2` ]
Intensity of wave expressed by` E_2`
`I. alpha (2E_0)^2`
` therefore (I.)/(I) =4, I. = 4I`
Phase difference between the two waves ` = (omegat + pi//4) - (omega t -pi//4) = pi/2`
Resultant intensity is given
`I_R = I + I. + 2 sqrt(II.) cos phi`
`therefore I_R = I + 4I = 2 sqrt(I(4I)) cos pi//2`
`I_R = 5I`
Thus resultant intensity is five times the intensity of wave expressed by `E_1` .