Two beams of light having intensities I and 4I interfere to produce...

Given here, phase difference at point $A$ and $B$ are ${ϕ}_{A} = \dfrac{\pi}{2}$and ${ϕ}_{B} = \dfrac{\pi}{3}$.

Resultant intensity at point $A$,

${I}_{A} = I + 4I + 2\sqrt{I}\sqrt{4I}\cos \left(\dfrac{\pi}{2}\right)$

$⇒ {I}_{A} = 5I + 4I\left(0\right) = 5I$

Resultant intensity at point $B$,

${I}_{B} = I + 4I + 2\sqrt{I}\sqrt{4I}\cos \left(60 °\right)$= 5I + 4I \times \dfrac{1}{2} = 7I$</p><p>Difference in intensities is${I}_{B} - {I}_{A} = 7I - 5I = 2I$.</p><p>Thus, value of$x = 2.