Question

Three coherent source kept along the same line produce intensity $I_0$ each at point P on this line. When $S_1$ and $S_2$ are switched to simultaneously, intensity at point P is ${2I}_0$ Then

• A. When $S_1$ and $S_3$ are switched on simultaneously, intensity at point P can be $2I_0$
• B. When $S_1$ and $S_3$ are switched on simultaneously, intensity at point P can be 0
• C. When all 3 sources switched on simultaneously intensity at Point P can be $I_0$
• D. When all 3 sources switched on simultaneously, intensity at point P can be $3I_0$

Answer 1

The correct option is C When all 3 sources switched on simultaneously intensity at Point P can be $I_0$

Given,

$S_1=I_0$

$S_2=I_0$

$S_3=I_0$

$S_{12}=2I_0$

We know that

$S_{12}=I_1+I_2+\sqrt{I_1{I}_2}\cos \theta$

$\Rightarrow 2I_0=2I_0+\sqrt{I_0^2}\cos \theta$

$\Rightarrow \cos \theta =0$

$\theta ={90}^{\circ }$

$S_{13}=90+90={180}^{\circ }$

$S_{13}=I_2+I_2+\sqrt{I_1{I}_2}\cos \theta$
$=2I_0-I_0$
$=I_0$

Correct option is C