Question

The ratio of intensities of two coherent sources is 1:9. The ratio of the maximum to the minimum intensities is:

Hint:

In problems involving interference, remember that the intensity ratio depends on the square of the amplitude ratio of the sources.

Answer 1

The intensity of interference patterns is determined by the amplitudes of the sources. The maximum and minimum intensities are related by the interference intensity formulas:\[I_{\text{max}} = (A_1 + A_2)^2 \quad \text{and} \quad I_{\text{min}} = (A_1 - A_2)^2\]Here, \(A_1\) and \(A_2\) represent the amplitudes of the two coherent sources. The ratio of intensities is proportional to the square of the amplitudes. Given an intensity ratio of 1:9, the ratio of amplitudes \( \frac{A_1}{A_2} \) is \( \sqrt{\frac{1}{9}} = \frac{1}{3} \).We can now compute the ratio of maximum to minimum intensities:\[\frac{I_{\text{max}}}{I_{\text{min}}} = \frac{(A_1 + A_2)^2}{(A_1 - A_2)^2}\]Substituting the amplitude values yields:\[\frac{I_{\text{max}}}{I_{\text{min}}} = \frac{(1 + 3)^2}{(1 - 3)^2} = \frac{16}{4} = 4\]Therefore, the ratio of maximum to minimum intensities is 4:1.