Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is (π ÷ 2) at point A and π at point B on the screen, respectively. The difference between the resultant intensities at A and B is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4 I
When two coherent beams interfere, the resultant intensity depends on their phase difference \( \phi \).
\( \displaystyle I_R = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi \)
\( \displaystyle \sqrt{I_1 I_2} = \sqrt{I \times 4I} = 2I \)
At A, \( \phi = \pi/2 \) and \( \cos\phi = 0 \):
\( \displaystyle I_A = I + 4I + 2(2I)\cos\frac{\pi}{2} = 5I \)
At B, \( \phi = \pi \) and \( \cos\phi = -1 \):
\( \displaystyle I_B = I + 4I + 2(2I)\cos\pi = 5I - 4I = I \)
\( \displaystyle I_A - I_B = 5I - I = 4I \)