Question
Write down the conditions for constructive and destructive interference in terms of path difference.
✓
Answer
• Constructive Interference :
→If we have two coherent sources $S _1$ and $S _2$ vibrating in phase, then for an arbitrary point $P$, whenever the path difference,
$S _1 P \sim S _2 P =n \lambda \quad(n=0,1,2,3, \ldots)$
we will have maximum intensity $\left( I =4 I _0\right.$ ) at the given point, which means we will have constructive interference.
[The sign $\sim$ between $S _1 P$ and $S _2 P$ represents the difference between $S _1 P$ and $S _2 P$.]
• Destructive interference :
→When two coherent sources $\left( S _1\right.$ and $\left.S _2\right)$ are vibrating in phase, and if the point P is such that the path difference
$S _1 P \sim S _2 P =\left(n+\frac{1}{2}\right) \lambda$
$\begin{array}{l}\left( OR S _1 P \sim S _2 P =(2 n+1) \frac{\lambda}{2}\right) \\ \text { (where, } n=0,1,2,3 \ldots \text { ) }\end{array}$
We will have destructive interference and the resultant intensity will be zero.
→If we have two coherent sources $S _1$ and $S _2$ vibrating in phase, then for an arbitrary point $P$, whenever the path difference,
$S _1 P \sim S _2 P =n \lambda \quad(n=0,1,2,3, \ldots)$
we will have maximum intensity $\left( I =4 I _0\right.$ ) at the given point, which means we will have constructive interference.
[The sign $\sim$ between $S _1 P$ and $S _2 P$ represents the difference between $S _1 P$ and $S _2 P$.]
• Destructive interference :
→When two coherent sources $\left( S _1\right.$ and $\left.S _2\right)$ are vibrating in phase, and if the point P is such that the path difference
$S _1 P \sim S _2 P =\left(n+\frac{1}{2}\right) \lambda$
$\begin{array}{l}\left( OR S _1 P \sim S _2 P =(2 n+1) \frac{\lambda}{2}\right) \\ \text { (where, } n=0,1,2,3 \ldots \text { ) }\end{array}$
We will have destructive interference and the resultant intensity will be zero.
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