Two monochromatic light waves of amplitudes 3A and 2A interfering at a point have a phase difference of `60^(@)` .The intensity at that point will be proportional to

Options

A. `5A^(2)`
B. `13A^(2)`
C. `7A^(2)`
D. `19A^(2)`

Answer

D

Explanation

Here ,`A_(1)=3A,A_(2)=2A`
`phi=60^(@)`
The resultant amplitude at a point is
`R=sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cosphi)`
`=sqrt((3A)^(2)+(2A)^(2))+2xx3Axx2Axxcos60^(@)`
`=sqrt(9A^(2)+4A^(2)+6A^(2))=Asqrt(19)`
As Intensity `oo(Amplitude)^(2)`
Therefore,intensity at the same point is I`oo19A^(2)`