Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is _______.

\(\mathrm{I} \propto\) width \(\quad\quad \mathrm{I}_{\max }=\left(\sqrt{\mathrm{I}_1}+\sqrt{\mathrm{I}_2}\right)^2\)
\(\therefore \mathrm{I}_1=\mathrm{I}_0, \mathrm{I}_2=2 \mathrm{I}_0 \quad\quad \mathrm{I}_{\min }=\left(\sqrt{\mathrm{I}_1}-\sqrt{\mathrm{I}_2}\right)^2\)
\(\frac{I_{\max }}{I_{\min }}=\frac{(\sqrt{2}+1)^2}{(\sqrt{2}-1)^2} \Rightarrow \frac{3+2 \sqrt{2}}{3-2 \sqrt{2}}\)