Two sources of microwaves P and Q produce coherent waves with a phase difference of 180°.

Question 24

Two sources of microwaves P and Q produce coherent waves with a phase difference of 180°.

The waves have the same wavelength λ.

At the point S there is a minimum in the interference pattern produced by waves from the two sources. The distance (QS – PS) is called the path difference.

In the expressions shown, n is an integer.

Which expression represents the path difference?

A nλ                             B ½ nλ                        C (n + ½) λ                             D (2n + ½) λ

Reference: Past Exam Paper – November 2018 Paper 12 Q29

Solution:

Answer: A.

When 2 sources of waves that are in phase interfere:

Constructive interference (maxima): path difference = nλ     where n is an integer

Destructive interference (minima): path difference = (n+1) λ / 2

However, if the sources has a phase difference of 180°, the above conditions no longer hold for constructive and destructive interference. The conditions are reversed.

Constructive interference (maxima): path difference = (n+1) λ / 2

Destructive interference (minima): path difference = nλ

A minima is produced at S, indicating that destructive interference occurs.  So, path difference = nλ.