Question

If two light waves of intensities \( I \) and \( 4I \) superimpose at a point with a phase difference of \( \frac{\pi}{2} \), then the resultant intensity at that point is

• A. 5I
• B. 7I
• C. 6I
• D. 8I

Hint:

When light waves interfere with a phase difference of \( \frac{\pi}{2} \), the cross-term vanishes due to \( \cos\left( \frac{\pi}{2} \right) = 0 \).

Answer 1

The Correct Option is A

Let the amplitudes be \( A_1 = \sqrt{I}, A_2 = \sqrt{4I} = 2\sqrt{I} \) When two waves with a phase difference \( \phi \) interfere: \[ I = A_1^2 + A_2^2 + 2A_1A_2 \cos\phi \] Substitute \( \phi = \frac{\pi}{2} \Rightarrow \cos\left( \frac{\pi}{2} \right) = 0 \) \[ I = I + 4I + 0 = 5I \]