Light waves from two coherent sources having intensities I and 2I cross each other at a point with a phase difference of `60^(@)`. The intensity at the point will be

Options

A. `4.414 I`
B. `5.455 I`
C. `4I`
D. `6.441I`

Answer

A

Explanation

Here, `I_(1)=I, I_(2)=2I and phi =60^(@)`
We know that, the amplitude A of resultant wave is
`A=sqrt(A_(1)^(2)+A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cos phi)`
`A^(2)=A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cos phi`
We also know that, `I prop A^(2)`
`therefore` Required intensity, `I=I_(1)+I_(2)+2sqrt(I_(1)I_(2))cos phi`
`=I+2I+2sqrt(I xx 2I) cos 60^(@)`
`=4.414I`