Question

Two coherent sources of intensity ratio 9:4 produce interference. What is the ratio between maxima and minima in the interference pattern produced?

• A. 3 : 2
• B. 25 : 1
• C. 13 : 5
• D. 5 : 1

Hint:

\(\dfrac{I_{max}}{I_{min}} = \left(\dfrac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)^2\). Use the square root of the intensity ratio directly.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
\(I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2\), \(I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2\).
Step 2: Detailed Explanation:
\(\sqrt{I_1/I_2} = \sqrt{9/4} = 3/2\)
\[ \frac{I_{max}}{I_{min}} = \left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)^2 = \left(\frac{3+2}{3-2}\right)^2 = \left(\frac{5}{1}\right)^2 = 25 : 1 \]
Step 3: Final Answer:
Ratio of maxima to minima \(= \mathbf{25 : 1}\).