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 depends on the amplitudes of the sources. The relationship between the maximum and minimum intensities can be found using the formula for the intensity of interference: \[ I_{\text{max}} = (A_1 + A_2)^2 \quad \text{and} \quad I_{\text{min}} = (A_1 - A_2)^2 \] Where \(A_1\) and \(A_2\) are the amplitudes of the two coherent sources. The ratio of intensities is proportional to the square of the amplitudes. Let the ratio of the amplitudes \( \frac{A_1}{A_2} \) be \( \sqrt{\frac{1}{9}} = \frac{1}{3} \), as the ratio of intensities is 1:9. Now, we can calculate the ratio of the maximum and minimum intensities: \[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{(A_1 + A_2)^2}{(A_1 - A_2)^2} \] Substituting the values of \(A_1\) and \(A_2\), we get: \[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{(1 + 3)^2}{(1 - 3)^2} = \frac{16}{4} = 4 \] Thus, the ratio of the maximum to the minimum intensities is 4:1.