Two coherent light sources having intensity in the ratio 2x produce...

Given that, $\dfrac{{I}_{1}}{{I}_{2}} = 2x$.

We know,

{I}_\max = {\left(\sqrt{{I}_{1}} + \sqrt{{I}_{2}}\right)}^{2} \text{ and } {I}_\min = {\left(\sqrt{{I}_{1}} - \sqrt{{I}_{2}}\right)}^{2}

∴ \dfrac{{I}_\max - {I}_\min}{{I}_\max + {I}_\min} = \dfrac{2\sqrt{{I}_{1}{I}_{2}}}{{I}_{1} + {I}_{2}} = \dfrac{2\sqrt{{I}_{1} / {I}_{2}}}{\dfrac{{I}_{1}}{{I}_{2}} + 1} = \dfrac{2\sqrt{2x}}{2x + 1}