Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of the maximum to minimum is

Two light beams have intensities in the ratio $$I_1 : I_2 = 1 : 9$$. Let $$I_1 = I$$ and $$I_2 = 9I$$.

The maximum intensity is $$I_{max} = \left(\sqrt{I_1} + \sqrt{I_2}\right)^2 = \left(\sqrt{I} + 3\sqrt{I}\right)^2 = 16I$$

The minimum intensity is $$I_{min} = \left(\sqrt{I_1} - \sqrt{I_2}\right)^2 = \left(\sqrt{I} - 3\sqrt{I}\right)^2 = 4I$$

The ratio is $$\dfrac{I_{max}}{I_{min}} = \dfrac{16I}{4I} = \dfrac{4}{1}$$

Hence, the correct answer is Option D.