Question

Two beams of having intensities $I$ and $4I$ interfere to produce interference pattern. The phase difference between the waves is $\pi /2$ at point $A$ and $\pi$ at point $B$. Then the difference between the resultant intensities at $A$ and $B$ is.

• A. $2I$
• B. $5I$
• C. $I$
• D. $4I$

Answer 1

Answer: (B), (D)

The correct options are
B $5I$
D $4I$

Resultant intensity at any point, $I_R=I_1+I_2+2\sqrt{I_1{I}_2}cos\delta$

where $\delta$ is the phase difference at that point.

Given: ${\delta }_A=\frac{\pi }{2}{\delta }_B=\pi$

Resultant intensity at A, $I_A=I+4I+2\sqrt{I\times \left(4I\right)}cos\frac{\pi }{2}$

$⟹I_A=5I$

Resultant intensity at B, $I_B=I+4I+2\sqrt{I\times \left(4I\right)}cos\pi$

$⟹I_B=I$

Thus $I_A-I_B=5I-I=4I$