Question

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 $\frac{\pi}{2}$ at point A and π at point B. Then the difference between the resultant intensities at A and B is

• A. 2I
• B. 4I
• C. 5I
• D. 7I

Answer 1

Answer: (B)

4I

Answer 2

By using $I = I_{1} + I_{2} + 2\sqrt{I_{1}I_{2}}\cos\varphi$

At point A : Resultant intensity

$I_{A} = I + 4I + 2\sqrt{I \times 4I}\cos\frac{\pi}{2} = 5I$ At point B : Resultant intensity $I_{B} = I + 4I + 2\sqrt{I \times 4I}\cos\pi = I$.

Hence the difference $= I_{A} - I_{B} = 4I$