Question

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

• A. 9:1
• B. 16:1
• C. 8:1
• D. 4:1

Hint:

In interference, maximum and minimum intensities depend on the constructive and destructive interference between the waves.

Answer 1

The Correct Option is B

In interference, the intensity at a point is given by: \[ I = I_1 + I_2 + 2 \sqrt{I_1 I_2} \cos(\delta) \] Where \( I_1 \) and \( I_2 \) are the intensities of the two coherent sources, and \( \delta \) is the phase difference. For maximum intensity, \( \cos(\delta) = 1 \), so: \[ I_{\text{max}} = I_1 + I_2 + 2 \sqrt{I_1 I_2} \] For minimum intensity, \( \cos(\delta) = -1 \), so: \[ I_{\text{min}} = I_1 + I_2 - 2 \sqrt{I_1 I_2} \] If the ratio of the intensities is 1:9, then: \[ I_1 = I, \quad I_2 = 9I \] The maximum intensity is: \[ I_{\text{max}} = I + 9I + 2 \sqrt{I \cdot 9I} = 10I + 6I = 16I \] The minimum intensity is: \[ I_{\text{min}} = I + 9I - 2 \sqrt{I \cdot 9I} = 10I - 6I = 4I \] Thus, the ratio of the maximum to the minimum intensities is: \[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{16I}{4I} = 4:1 \] Therefore, the correct answer is \( 4:1 \).