Question

Match the following columns and choose the correct options from the codes given below.

Column I		Column II
A	Constructive interference	1	$n \lambda$
B	Destructive interference	2	$(n+1) \lambda / 2$
C	Path difference for constructive interference	3	Waves are in phase at point of interference
D	Path difference for destructive interference	4	Waves are out of phase at point of interference

• A. $A \rightarrow 4, B \rightarrow 1, C \rightarrow 3, D \rightarrow 2$
• B. $A \rightarrow 4, B \rightarrow 3, C \rightarrow 1, D \rightarrow 2$
• C. $A \rightarrow 3, B \rightarrow 4, C \rightarrow 1, D \rightarrow 2$
• D. $A \rightarrow 3, B \rightarrow 4, C \rightarrow 2, D \rightarrow 1$

Answer 1

Answer: (C)

A constructive interference is produced when waves overlaps such that a crest meets a crest and waves are in phase.

For maxima,
$S_{1} P \sim S_{2} P=n \lambda(n=0,1,2,3, \ldots)$
For minima,
$S_{1} P \sim S_{2} P=\left(n+\frac{1}{2}\right) \lambda(n=0,1,2,3, \cdots)$
we will have destructive interference and the resultant intensity will be zero.