For interference of light, the intensity at maxima is given by \( I_{\text{max}} = (I_1 + I_2 + 2 \sqrt{I_1 I_2}) \), and the intensity at minima is \(I_{\text{min}} = (I_1 + I_2 2 \sqrt{I_1 I_2}) \).
Step 1: Interference Intensity Formulas
The intensity of interference maxima and minima for two interfering beams is calculated using the following formulas:
For maxima: \[ I_{\text{max}} = (I_1 + I_2 + 2 \sqrt{I_1 I_2}) \]
For minima: \[ I_{\text{min}} = (I_1 + I_2 2 \sqrt{I_1 I_2}) \] Here, \( I_1 \) and \( I_2 \) represent the intensities of the two interfering beams.
Step 2: Substitute Given Intensities
The question provides an intensity ratio of 9:4. Therefore, we set \( I_1 = 9 \) and \( I_2 = 4 \).
For maxima: \[ I_{\text{max}} = (9 + 4 + 2 \sqrt{9 \times 4}) = 13 + 2 \times 6 = 13 + 12 = 25 \]
For minima: \[ I_{\text{min}} = (9 + 4 2 \sqrt{9 \times 4}) = 13 12 = 1 \]
Step 3: Calculate Intensity Ratio
The ratio of the intensity of maxima to minima is computed as follows:
Final Answer: The ratio of the intensity of maxima to minima is 25:1 .