Question

Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are π/2 and π/3 at points A and B, respectively. The difference between the resultant intensities at the two points is xI. The value of x will be ___.

Answer 1

The correct answer is 2
$I_{R_1}=I_1+I_2+2\sqrt{I_1I_2}\cos⁡\phi$
$I_A=I+4I+2\sqrt{I⋅4I}\cos⁡90^∘=5I$
$I_B=I+4I+2\sqrt{I⋅4I}\cos⁡60^∘=7I$
$I_B–I_A=2I$
$\therefore$ value of x is 2