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 $\pi /2$ at point $A$ and $\pi$ at point $B$. Then the difference between the resultant intensities at $A$ and $B$ is

• A. $2I$
• B. $4I$
• C. $5I$
• D. $7I$

Answer 1

Answer: (B)

Here, $I_1=I,I_2=4I,{\varphi }_1=\frac{\pi }{2},{\varphi }_2=\pi$
$I_A=I_1+I_2+2\sqrt{I_1{I}_2}cos{\varphi }_1$
$=I+4I+2\sqrt{I\times 4I}cos\frac{\pi }{2}=5I$
$I_B=I_1+I_2+2\sqrt{I_1{I}_2}cos{\varphi }_2$
$=I+4I+2\sqrt{I\times 4I}cos\pi$
$=5I-4I=I$
$\therefore I_A-I_B=5I-I=4I$