Let the intensities of the two coherent light sources be $I_1$ and $I_2$. We are given that $\frac{I_1}{I_2} = n$. The maximum intensity in the interference pattern is given by $I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2 = I_1 + I_2 + 2\sqrt{I_1 I_2}$. The minimum intensity is given by $I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2 = I_1 + I_2 - 2\sqrt{I_1 I_2}$. We need to find the ratio $\frac{I_{max} - I_{min}}{I_{max} + I_{min}}$. First, calculate the numerator: $I_{max} - I_{min} = (I_1 + I_2 + 2\sqrt{I_1 I_2}) - (I_1 + I_2 - 2\sqrt{I_1 I_2}) = 4\sqrt{I_1 I_2}$ Next, calculate the denominator: $I_{max} + I_{min} = (I_1 + I_2 + 2\sqrt{I_1 I_2}) + (I_1 + I_2 - 2\sqrt{I_1 I_2}) = 2(I_1 + I_2)$ Now, find the ratio: $\text{Ratio} = \frac{4\sqrt{I_1 I_2}}{2(I_1 + I_2)} = \frac{2\sqrt{I_1 I_2}}{I_1 + I_2}$ Divide both the numerator and the denominator by $I_2$: $\text{Ratio} = \frac{2\sqrt{\frac{I_1}{I_2}}}{\frac{I_1}{I_2} + 1}$ Substitute $\frac{I_1}{I_2} = n$ into the equation: $\text{Ratio} = \frac{2\sqrt{n}}{n+1}$