The interference pattern is obtained with two coherent light sources of intensity ratio $$4:1$$. And the ratio $$\frac{I_{max} + I_{min}}{I_{max} - I_{min}}$$ is $$\frac{5}{x}$$. Then, the value of $$x$$ will be equal to :

Given the intensity ratio of two coherent sources is $$4:1$$.

Let $$I_1 = 4I$$ and $$I_2 = I$$.

The amplitudes are proportional to the square root of intensities:

$$A_1 = 2\sqrt{I}, \quad A_2 = \sqrt{I}$$

Maximum intensity (constructive interference):

$$I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2 = (2\sqrt{I} + \sqrt{I})^2 = 9I$$

Minimum intensity (destructive interference):

$$I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2 = (2\sqrt{I} - \sqrt{I})^2 = I$$

Now computing the required ratio:

$$\frac{I_{max} + I_{min}}{I_{max} - I_{min}} = \frac{9I + I}{9I - I} = \frac{10I}{8I} = \frac{10}{8} = \frac{5}{4}$$

Comparing with $$\frac{5}{x}$$, we get $$x = 4$$.

Hence, the correct answer is Option B.