\(I_{\max }=\left(A_{1}+A_{2}\right)^{2}, I_{\min }=\left(A_{1}-A_{2}\right)^{2}\) where

\(A=\)amplitude

\(=\frac{4 A_{1} A_{2}}{2\left(A_{1}^{2}+A_{2}^{2}\right)}=\frac{2 A_{1} A_{2}}{A_{1}^{2}+A_{2}^{2}}\)

Now, dividing the numerator and denominator by \(A _{1} A _{2}\), we get

\(\frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }}=\frac{2}{\left[\frac{A_{1}}{A_{2}}+\frac{A_{2}}{A_{1}}\right]}=\frac{2}{\left[\sqrt{\alpha}+\frac{1}{\sqrt{\alpha}}\right]}=\frac{2 \sqrt{\alpha}}{(\alpha+1)}\)