Introductory Physics Volume Two

150 Wave Optics 7.8
§ 7.7 Interference of Two Sources
Suppose that we have two wave sources that are in phase with each
other.
Detector
r A
r B
Source A
Source B
While the sources are in phase, the waves are not when they reach the
detector because they must travel a different distance: at the detector
the phase difference between the waves will be φ A −φ B = k(r B −r A ) =
k ∆r = 2π ∆r
λ
. The minimum and maximum power occur when this
phase difference is an odd and even multiple of π. That is when
2π ∆r
{ max m is even.
λ = mπ min m is odd
∆r = m λ { max m is even.
2 min m is odd
Theorem: Interference of Two Sources
If you have two wave sources that are in phase with each other,
the minimum and maximum of the power occur at points where
the path difference is and odd (min) or even (max) multiple of half
of the wavelength of the wave.
∆r = m λ { max m is even.
2 min m is odd
⊲ Problem 7.9
Draw two points that are 3 cm apart on a piece of paper.
(a) Find all points on the paper that have ∆r = 0.
(b) Find all points on the paper that have ∆r = 1cm.
(c) Find all points on the paper that have ∆r = 2cm.
(d) If λ = 1.0cm what are the locations of the maximum and minimum
of power?
(e) If λ = 2.0cm what are the locations of the maximum and minimum
of power?