coherence, interference, and thin films
TRANSCRIPT
COHERENCE, INTERFERENCE,
AND THIN FILMS
Purdue University – Physics 241 – Lecture 26 Brendan Sullivan
Overview
Wave superposition
Constructive vs. deconstructive interference
Wave phases
(Optical) Path length difference
Reflection Boundary Conditions
Thin film interference
Young’s double slit experiment
Wave superposition is merely the
addition of waves
-3
-2
-1
0
1
2
3
0 1 2 3 4 5 6 7
Constructive (in-phase) interference –
blue+orange = green
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7
Deconstructive (out of phase) interference
– blue+orange = green
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 2 4 6 8
Arbitrary wave addition (superposition) -
blue+orange = green
0GreenBlue
180GreenBlue
Path length difference leads to a
difference in phase for waves
Consider two waves that
start at the same phase,
but have to travel
different distances
While the wave is
moving, its “current
phase” is changing
If the waves travel
different distances, then
their phases have
changed relative to
eachother
2360rr
Light reflecting of optically denser
material picks up 180° phase change
If n2>n1 we pick up 180°
phase change
Comes from boundary
conditions of wave equation
Similar to a guitar string
reflecting off bridge
This plays a role in
determining if waves will
constructively or
deconstructively interfere
n=1
n>1
180° phase change
No 180° phase change
Thin film interference
“Thin”: A couple of wavelengths
of light
Condition for maximum (bright
fringe): The two reflected
waves interfere constructively
Minimum: deconstructively
Example: Air, soap, air bright
fringes
mt2Maxima:
Minima: )2
1(2 mtn
air
Thin films exhibit either our answer or
the opposite
We had n2>n1 and n2>n3. If we have an intermediate index of refraction (e.g. n1>n2 and n3>n2) then the 180° phase change gives us the opposite answer
The equations fail for some of the following situations. Which one(s)?
Glass wedges act like thin films of
varying thickness
Two pieces of glass
ramped (like at right) act
like a thin film
We’ll do an example
Newton’s Rings: the air
between the glass plates
acts like a thin film
Newton’s Rings
• Since the thickness of the film changes over the radius of the
plates, alternating bright and dark fringes form, when the
plates are illuminated. Because of the curvature of the upper
piece, the film thickness varies more rapidly at larger radius.
Thus the fringe separation is smaller toward the outside.
The double slit pattern is a result of
constructive interference
Double slit experiment: two small
slits act as point light sources
We observe their interference
pattern on a screen a distance L
away
Bright fringes: constructive
interference
Dark fringes: deconstructive
interference
md )sin(
)2
1()sin( md
Determining the intensity of fringes
For two coherent EM waves:
The overall field thus is:
We showed that intensity is
proportional to E2:
1 0
2 0
sin
sin( )
E E t
E E t
1 2
0
0
sin sin( )
2 cos sin2 2
E E E
E t t
E t
2
0 0
2
024 cos
2
m II E
I EI
2)sin(d
This is the phase
difference between the
two rays