Q 12-10-072JEE MainJEE Main 2024 (31 Jan, Shift 1)Medium
Two waves of intensity ratio $1:9$ cross each other at a point. The resultant intensities at the point, when (a) the waves are incoherent is $I_1$, and (b) the waves are coherent and differ in phase by $60^\circ$ is $I_2$. If $\dfrac{I_1}{I_2} = \dfrac{10}{x}$, then $x = $ ______.
Numerical value type. Enter your answer.
Answer: 13
Let the intensities be $I$ and $9I$.
(a) Incoherent: $I_1 = I + 9I = 10I$.
(b) Coherent: $I_2 = I + 9I + 2\sqrt{I\cdot9I}\cos60^\circ = 10I + 3I = 13I$.
$\dfrac{I_1}{I_2} = \dfrac{10}{13}$, so $x = 13$.
Solution by Sreeraj P, M.Sc Physics