Question

Two light beams of intensities $4I$ and 9I interfere on a screen. The phase difference between these beams on the screen at point $A$ is zero and at point $B$ is $\pi$. The difference of resultant intensities, at the point A and B, will be___ $I$

Answer 1

Answer: 24

$I_{net}=I_1+I_2+2\sqrt{I_1}\sqrt{I_2}\cos \varphi$
$I_{\max }\text{ for }\varphi =0\&I_{\min }\text{ for }\varphi =\pi$
$I_{\max }={\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2=(\sqrt{9I}+\sqrt{4I}{)}^2=25I$
$I_{\min }={\left(\sqrt{I_1}-\sqrt{I_2}\right)}^2=(\sqrt{9I}-\sqrt{4I}{)}^2=I$
$I_{\max }-I_{\min }=25I-I=24I$