Two coherent sources of intensity ratio $\alpha$ interfere. The value of $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$ is :

Given $\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}=\mathrm{\alpha }\Rightarrow {\mathrm{I}}_1={\mathrm{\alpha I}}_2$

$\begin{array}{l}{\mathrm{I}}_{\max }={\left(\sqrt{{\mathrm{I}}_1}+\sqrt{{\mathrm{I}}_2}\right)}^2={\left(\sqrt{\mathrm{\alpha }}+1\right)}^2{\mathrm{I}}_2\\ {\mathrm{I}}_{\min }={\left(\sqrt{{\mathrm{I}}_1}\text{\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}\hspace{0.17em}}\sqrt{{\mathrm{I}}_2}\right)}^2={\left(\sqrt{\mathrm{\alpha }}-1\right)}^2{\mathrm{I}}_2\\ \frac{{\mathrm{I}}_{\max }-{\mathrm{I}}_{\min }}{{\mathrm{I}}_{\max }+{\mathrm{I}}_{\min }}=\frac{2\sqrt{\mathrm{\alpha }}}{1+\mathrm{\alpha }}\end{array}$