Q 12-10-111JEE MainJEE Main 2021 (25 Feb, Shift 1)Medium
Two coherent light sources having intensity in the ratio $2x$ produce an interference pattern. The ratio $\dfrac{I_{max} - I_{min}}{I_{max} + I_{min}}$ will be
Answer: (C) $\frac{2\sqrt{2x}}{2x+1}$
Let $I_1 = 2xI_2$. $I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2$ and $I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2$, so
$$\frac{I_{max} - I_{min}}{I_{max} + I_{min}} = \frac{4\sqrt{I_1I_2}}{2(I_1 + I_2)} = \frac{2\sqrt{2x}\,I_2}{(2x + 1)I_2} = \frac{2\sqrt{2x}}{2x+1}$$
Solution by Sreeraj P, M.Sc Physics