Question

The interference pattern is obtained with two coherent light sources of intensity ratio \( 9 : 1 \). The ratio of \( \frac{I_{MAX}+I_{MIN}}{I_{MAX}-I_{MIN}} \) is \( \frac{\alpha}{\beta} \). The values of \( \alpha \) and \( \beta \) are:

• A. 5 and 3
• B. 3 and 1
• C. 1 and 9
• D. 9 and 1

Hint:

In interference, use \( I_{max}=(\sqrt{I_1}+\sqrt{I_2})^2 \) and \( I_{min}=(\sqrt{I_1}-\sqrt{I_2})^2 \) directly to save time.

Answer 1

The Correct Option is A

Step 1: Use intensity relations.
For two coherent sources:
\[ I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2 \]
\[ I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2 \]

Step 2: Substitute given ratio.
Given:
\[ I_1 : I_2 = 9 : 1 \Rightarrow \sqrt{I_1} = 3,\; \sqrt{I_2} = 1 \]

Step 3: Calculate \( I_{max} \) and \( I_{min} \).
\[ I_{max} = (3+1)^2 = 16 \]
\[ I_{min} = (3-1)^2 = 4 \]

Step 4: Find required ratio.
\[ \frac{I_{max}+I_{min}}{I_{max}-I_{min}} = \frac{16+4}{16-4} = \frac{20}{12} \]
\[ = \frac{5}{3} \]

Step 5: Conclusion.
\[ \alpha = 5,\quad \beta = 3 \]
\[ \boxed{5 \text{ and } 3} \]