Question

Two coherent sources of intensities \( I_1 \) and \( I_2 \) produce an interference pattern on screen. The maximum intensity in the interference pattern is

• A. \( \left(\sqrt{I_1} + \sqrt{I_2}\right)^2 \)
• B. \( I_1 + I_2 \)
• C. \( (I_1 + I_2)^2 \)
• D. \( I_1^2 + I_2^2 \)

Hint:

In interference, always add amplitudes first, not intensities.

Answer 1

The Correct Option is A

Step 1: Relation between intensity and amplitude.
Intensity is proportional to square of amplitude: \[ I \propto A^2 \]
Step 2: Write amplitudes of two waves.
\[ A_1 = \sqrt{I_1}, \quad A_2 = \sqrt{I_2} \]
Step 3: Maximum intensity condition.
For constructive interference, amplitudes add: \[ A = A_1 + A_2 \]
Step 4: Find maximum intensity.
\[ I_{\max} = (A_1 + A_2)^2 = \left(\sqrt{I_1} + \sqrt{I_2}\right)^2 \]
Step 5: Conclusion.
The maximum intensity is \( \left(\sqrt{I_1} + \sqrt{I_2}\right)^2 \).