Two identical coherent waves, each of intensity I, are producing … - Vidyadip

Question

Two identical coherent waves, each of intensity I, are producing an interference pattern. Find the value of the resultant intensity at a point of:

Constructive interference.
Destructive interference.

✓

Answer

Resultant intensity at any point having a phase difference $\varphi$ is
$\text{I}_\text{R}=\text{I}_1+\text{I}_2+2\sqrt{\text{I}_1\text{I}_2}\cos\phi$
Here, $\text{I}_1=\text{I}_2=\text{I}$
$\therefore\text{I}_\text{R}=\text{I}_1+\text{I}_2+2\sqrt{\text{I}.\text{I}.}\cos\varphi=2\text{I}+2\text{I}\cos\varphi$

At a point of constructive interference:

$\varphi=2\text{n}\pi(\text{n}=0,1,2,\dots)\Rightarrow\cos\varphi=1$

$\therefore\text{I}_\max=2\text{I}+2\text{I}=4\text{I}$

At a point of denstructive interference:

$\Rightarrow\cos\varphi=0 $

$\therefore \text { I}_\min=\text{2I}-\text{2I}=0$

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