Question

The two coherent sources produce interference with intensity ratio ' \(b\) '. In the interference pattern, the ratio \(\frac{I_{\text {max }}+I_{\text {min }}}{I_{\text {max }}-I_{\text {min }}}\) will be

• A. \(\frac{1+b}{\sqrt{b}}\)
• B. \(\frac{1+b}{2\sqrt{b}}\)
• C. \(\frac{2\sqrt{b}}{1+b}\)
• D. \(\frac{2\sqrt{b}}{(1+b)^{2}}\)

Hint:

Express the maximum and minimum intensities in terms of the amplitudes and use the intensity ratio b.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For intensities \(I_1,I_2\): \(I_{\max}=(\sqrt{I_1}+\sqrt{I_2})^{2}\) and \(I_{\min}=(\sqrt{I_1}-\sqrt{I_2})^{2}\).

Step 2: Sum and difference
\(I_{\max}+I_{\min}=2(I_1+I_2)\) and \(I_{\max}-I_{\min}=4\sqrt{I_1I_2}\).

Step 3: Calculation
\(\dfrac{I_{\max}+I_{\min}}{I_{\max}-I_{\min}}=\dfrac{I_1+I_2}{2\sqrt{I_1I_2}}\). With \(\dfrac{I_1}{I_2}=b\): \(\dfrac{b+1}{2\sqrt{b}}\).

Final Answer:
The ratio is \(\frac{1+b}{2\sqrt{b}}\). \[ \boxed{\text{(B) }\dfrac{1+b}{2\sqrt{b}}} \]