Q 12-10-103JEE MainJEE Main 2022 (27 Jul, Shift 2)Medium
Two coherent sources of light interfere. The intensity ratio of two sources is $1 : 4$. For this interference pattern if the value of $\dfrac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}}$ is equal to $\dfrac{2\alpha + 1}{\beta + 3}$, then $\dfrac\alpha\beta$ will be
Answer: (B) $2$
With $I_1 : I_2 = 1 : 4$, the amplitudes are in the ratio $1 : 2$:
$$I_{\max} \propto (1 + 2)^2 = 9, \qquad I_{\min} \propto (2 - 1)^2 = 1$$
$$\frac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}} = \frac{10}{8} = \frac54$$
Matching $\dfrac{2\alpha + 1}{\beta + 3} = \dfrac54$ term by term: $2\alpha + 1 = 5$ and $\beta + 3 = 4$, so $\alpha = 2$, $\beta = 1$ and $\dfrac\alpha\beta = 2$.
Solution by Sreeraj P, M.Sc Physics