Question

If we have two coherent sources S₁ and S₂ vibrating in phase, then for an arbitrary point P destructive interference is observed whenever the path difference is ______.

Options

• ${\displaystyle (\text{n}+\frac{1}{2})\lambda }$, where n = 0, 1, 2, 3,...

• ${\displaystyle (\text{n}+\frac{1}{3})\lambda }$, where n = 0, 1, 2, 3,...

• ${\displaystyle \text{n}\lambda }$, where n = 0, 1, 2, 3,...

• ${\displaystyle (\text{2n}+\frac{1}{2})\lambda }$, where n = 0, 1, 2, 3,...

Answer 1

If we have two coherent sources S₁ and S₂ vibrating in phase, then for an arbitrary point P destructive interference is observed whenever the path difference is ${\displaystyle \underline{(\text{n}+\frac{1}{2})\lambda }}$, where n = 0, 1, 2, 3,....

Explanation:

If the point P is such that the path difference,

S₂ P ~ S₁P = ${\displaystyle (\text{n}+\frac{1}{2})\lambda }$, (where n = 0, 1, 2, 3,...), we will have destructive interference and the resultant intensity will be zero.