Question

Two light beams of intensities in the ratio of 9:4 are allowed to interfere. The ratio of the intensity of maxima and minima will be:

• A. 2:3
• B. 16:81
• C. 25:169
• D. 25:1

Hint:

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 \(I_{\text{min}} = (I_1 + I_2 2 \sqrt{I_1 I_2}) \).

Answer 1

The Correct Option is D

Step 1: Formula for Intensity of Interference Maxima and Minima 
The intensity of interference maxima and minima for two interfering beams is given by the following formulas: 
For maxima: \[ I_{\text{max}} = (I_1 + I_2 + 2 \sqrt{I_1 I_2}) \] 
For minima: \[ I_{\text{min}} = (I_1 + I_2 2 \sqrt{I_1 I_2}) \] Where \( I_1 \) and \( I_2 \) are the intensities of the two interfering beams. 
Step 2: Substitute the Intensities Given in the Question 
The ratio of the intensities is given as 9:4. So, \( I_1 = 9 \) 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 the Ratio of Intensities 
The ratio of the intensity of maxima to minima is: 

\[\frac{I_{\text{max}}}{I_{\text{min}}} = \frac{25}{1} = 25:1\]

 

Final Answer: The ratio of the intensity of maxima and minima is  25:1 .