Question
Derive the condition of Constructive and destructive interference in terms of the phase difference.
✓
Answer
→The formula to find out the intensity of resultant wave generated due to super position of waves emanated from two coherent sources is, $I =4 I _0 \cos ^2\left(\frac{\phi}{2}\right)$ (where, $\phi$ - phase difference)
• Constructive Interference :
→If the phase difference at the point of super position is
$\phi=0, \pm 2 \pi, \pm 4 \pi \ldots$ we will have constructive interference leading to maximum intensity.
→Condition : phase difference $= \pm 2 n \pi$
$(n=0,1,2,3 \ldots)$
• Destructive Interference :
→If the phase difference at the point of super position is
$\phi= \pm \pi, \pm 3 \pi, \pm 5 \pi \ldots$ we will have destructive interference leading to zero intensity.
→Condition : phase difference $= \pm(2 n+1) \pi$
$(n=0,1,2,3 \ldots .)$
• Constructive Interference :
→If the phase difference at the point of super position is
$\phi=0, \pm 2 \pi, \pm 4 \pi \ldots$ we will have constructive interference leading to maximum intensity.
→Condition : phase difference $= \pm 2 n \pi$
$(n=0,1,2,3 \ldots)$
• Destructive Interference :
→If the phase difference at the point of super position is
$\phi= \pm \pi, \pm 3 \pi, \pm 5 \pi \ldots$ we will have destructive interference leading to zero intensity.
→Condition : phase difference $= \pm(2 n+1) \pi$
$(n=0,1,2,3 \ldots .)$
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