Question

Choose the Correct answer from alternative given.
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 $\pi$ at point B. Then the difference between resultant intensities at A and B is

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

Answer 1

The correct option is B $4I$

Here,$I_t=I,I_2=4I,{\varphi }_1=\frac{\pi }{2},{\varphi }_2=\pi$

$I_A=I_1+I_2+2\sqrt{I_1{I}_2}cos{\varphi }_1$

$I_A=I+4I+2\sqrt{I\times 4I}cos\frac{\pi }{2}=5I$

$I_B=I_1+I_2+2\sqrt{I_1{I}_2}cos{\varphi }_2$
$=I+4I+2\sqrt{I\times 4I}cos\pi$
$=5I-4I$
$I_B=I$

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