INTERFERENCE
Phase Shift
Phase shift due to reflections at
a interface
Changes in phase due to the passage through thin film
Phase difference between two wavefronts of the same
wave
Changes in phase due to reflections at a interface
Interface
Phase difference between two wavefronts of the
same wave
wavefront B
wavefront A
For illustrative purposes, here we have chosen the locations of point A
and B very conveniently. Indeed, such selection allow us to guess the
phase difference between the two wavefronts.
The next two figures show two examples where the phase difference
between two wavefronts can be guessed.
X
n=1
n>1
n=1
In general, it is not obvious to guess what is the difference between 2 arbitrary
wavefronts A and B.
Phase difference between two
wavefronts separated by a
distance L
wavefront B
For a wave
travelling in a
medium of
index of
refraction n
wavefront A
λ is the wavelength in
vacuum
n is the index of
refraction of the medium
Phase shift between two waves, each travelling
through a different material
wave
n1
n1
n1
A
B
X
wave'
n1
n2
n1
Example: Consider a harmonic wave whose wavelength in vacuum is
equal to λ=550 nm. The wave will pass through a plastic film of
thickness L= 2.6 μm and index of refraction n = 1.6. Calculate the
phase shift that the wave will undergo after passing the plastic film.
Phasors Method
Wave-1
Wave-2
At x=xB:
At x=xB and t=0 :
φB = k xB + δ
phasor plane
xB
At x=xB and t=t0 :φB = k xB - ωto + δ
These two phasors are rotating
in phase. The same value of φ
for both waves
xB
At a fixed value of time t = to, it occurs the following:
A
n1 = 1
B
xB
B'
n2 = 1.6
xB
xA
X
A'
xA
X
At a fixed value of time t = to, it occurs the following:
B
A
B'
A'
A'
A
B
B'