Q 12-10-102JEE MainJEE Main 2022 (27 Jul, Shift 1)Easy
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 $\dfrac\pi2$ and $\dfrac\pi3$ at points $A$ and $B$ respectively. The difference between the resultant intensities at the two points is $xI$. The value of $x$ will be ______ .
Numerical value type. Enter your answer.
Answer: 2
$$I_R = I_1 + I_2 + 2\sqrt{I_1I_2}\cos\phi = 5I + 4I\cos\phi$$
At $A$: $\cos\dfrac\pi2 = 0$, $I_A = 5I$.
At $B$: $\cos\dfrac\pi3 = \dfrac12$, $I_B = 7I$.
$I_B - I_A = 2I$, so $x = 2$.
Solution by Sreeraj P, M.Sc Physics