In a Young's double-slit experiment, the ratio of the slit's width...

Intensity∝widthofslit$<br />$\dfrac{{I}_{1}}{{I}_{2}} = \dfrac{4}{1}$.<br />$\dfrac{{I}_\max}{{I}_\min} = {\left(\dfrac{\sqrt{{I}_{1}} + \sqrt{{I}_{2}}}{\sqrt{{I}_{1}} - \sqrt{{I}_{2}}}\right)}^{2} = {\left(\dfrac{\sqrt{\dfrac{{I}_{1}}{{I}_{2}}} + 1}{\sqrt{\dfrac{{I}_{1}}{{I}_{2}}} - 1}\right)}^{2}$<br />$= {\left(\dfrac{\sqrt{4} + 1}{\sqrt{4} - 1}\right)}^{2} = {\left(\dfrac{3}{1}\right)}^{2} = \dfrac{9}{1}$<br />${I}_\max: {I}_\min = 9: 1