The interference pattern is obtained with two coherent light sources of intensity ratio $$n.$$ In the interference pattern, the ratio $$\frac{{{I_{\max }} - {I_{\min }}}}{{{I_{\max }} + {I_{\min }}}}$$   will be

Solution :
It is given that, $$\frac{{{I_2}}}{{{I_1}}} = n \Rightarrow {I_2} = n{I_1}$$
$$\therefore $$ Ratio of intensities is given by
$$\eqalign{ & \frac{{{I_{\max }} - {I_{\min }}}}{{{I_{\max }} + {I_{\min }}}} = \frac{{{{\left( {\sqrt {{I_2}} + \sqrt {{I_1}} } \right)}^2} - {{\left( {\sqrt {{I_2}} - \sqrt {{I_1}} } \right)}^2}}}{{{{\left( {\sqrt {{I_1}} + \sqrt {{I_2}} } \right)}^2} + \left. {{{\left( {\sqrt {{I_2}} - \sqrt {{I_1}} } \right)}^2}} \right)}} \cr & = \frac{{{{\left( {\sqrt {\frac{{{I_2}}}{{{I_1}}}} + 1} \right)}^2} - {{\left( {\sqrt {\frac{{{I_2}}}{{{I_1}}}} - 1} \right)}^2}}}{{{{\left( {\sqrt {\frac{{{I_2}}}{{{I_1}}}} + 1} \right)}^2} + {{\left( {\sqrt {\frac{{{I_2}}}{{{I_1}}}} - 1} \right)}^2}}} \cr & = \frac{{{{\left( {\sqrt n + 1} \right)}^2} - {{\left( {\sqrt n - 1} \right)}^2}}}{{{{\left( {\sqrt n + 1} \right)}^2} + {{\left( {\sqrt n - 1} \right)}^2}}} \cr & = \frac{{2\sqrt n }}{{n + 1}} \cr} $$