Q131 / 180 · KCET 2009 · Physics

For the constructive interference the path difference between the two interfering waves must be equal to

  • A
    $(2 \mathrm{n}+1) \lambda$
  • B
    $2 \mathrm{n} \pi$
  • Correct answer
    C
    $\mathrm{n} \lambda$
  • D
    $(2 \mathrm{n}+1) \frac{\lambda}{2}$

Solution

Phase difference, $\Delta \phi=\frac{2 \pi}{\lambda} \Delta \mathrm{x}$ In a constructive interference, $\begin{array}{cc} \Delta \phi=2 \mathrm{n} \pi & \text { where } \mathrm{n}=0,1,2,3, \ldots \\ \therefore \quad 2 \mathrm{n} \pi=\frac{2 \pi}{\lambda} \Delta \mathrm{x} \\ \text { or } \quad & \Delta \mathrm{x}=\mathrm{n} \lambda \end{array}$

Hence, the correct answer is option: 'C'.

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