Please solve this problem.

Dear Student,

As we know that

$I = I_{1} + I_{2} + 2 \sqrt{I_{1}} \sqrt{I_{2}} \sqrt{\cos ϕ}$

It is given that intensity of the both sources are same,

If Ø =0 , cos(0)=1

Maximum intensity = Io+Io+2Io = 4Io

If, Ø=180,

then cos(180)=-1,

Intensity = Io+Io-2Io=0
Hence, intensity will be minimum which is equal to zero.

If Ø=90, so , cos(90)=0
Intensity = Io+Io+0 = 2Io
Hence, Average intensity will be 2Io

Hence option A is the correct answer.

Regards