Air-Water (n=1.3)-Air film (soap film)
Normal incidence
Can we make a
device with greater
contrast in
transmission?
T
Dd/l
Air-Diamond (n=2.4)-Air film
r
10
r
2.4  1
2.4  1
T
F = 0.88
Dd/l
1 2

Air- Kryptonite? (n=10) -Air
r
10
r
1 2

10  1
10  1
T
F = 18
Dd/l
Interference ideas for why increasing r makes these peaks so sharp?
Multiple reflection view of T at low angle
r
r’ t’
t
Eo

1  x  x  x  ...   x 
2
3
n
n 0
ik z d
i 2kz d



tt e r r e
ik z d
tt e
1
1 x
As long as |x| < 1, this will converge
But for |x| 1, the dependence on phase is very fast!
r
Eo
t
r’ t’
ik z d
i 2kz d



tt e r r e
ik z d
tt e
If |r|,|r’| approach 1, many reflections contribute to the
interference for R and T. Many phasors of nearly equal
size give much more contrast in magnitude and much
sharper features than just a few of very different size.
Very important concept in many contexts of interference
Multiple reflection view of T
Suppose R = rr = 0.1. The relative strength of the first
three transmitted fields are 1, 0.1, 0.01… etc .
If added in phase (0 shift) you get ____
If added out of phase (p shift) , you get ____
Max/min fields______
Max/min T’s _______
Multiple reflection view of T
Suppose R = rr = 0.75 The relative strengths of the
transmitted fields are 1, 0.75, 0.752 …. etc . Now we
must add many more fields to get the transmission.
Multiple reflection view of T
Sketch with phasors the addition of the fields 1, 0.75,
0.752 …. etc in phase
This adds up to something close to
a) 2
b) 4
c) 6
d) 8
e) 10
Multiple reflection view of T
Sketch with phasors the addition of the fields 1, 0.75,
0.752 …. Out of phase (p shift)
This adds up to something close to
a) 0.1
b) 0.2
c) 0.4
d) 0.6
e) 1
Max/min fields______
Max/min T’s _______
Multiple reflection view of T
Sketch with phasors the addition of the fields 1, 0.75,
0.752 …. at p/4 shift
This adds up to something close to
a)
b)
c)
d)
e)
0.2
0.4
0.6
1
2
Do the same for 1, 0.1, 0.01
In a relative sense, which is most sensitive to
phase?
General feature of wave interference: if you want sharp
features you have to add lots of waves with varying
phase. (e.g. Fourier)
If I want to make an instrument that distinguishes
wavelengths, I can get sharp transmission by
increasing n to increasing R.
But it’s hard to obtain and work with kryptonite.
Fabry-Perot Etalon/Interferometer
F 

4 R10 R12
1  R10 R12
)
2
High R due to large k in in metal
coating.
Fabry-Perot Etalon/interferometer for low R:
Fabry-Perot Etalon/interferometer for high R, same d
Red: l = 1.00
Blue: l = 1.01
Is the device most sensitive to l changes for small or large d?
lmin  lFWHM 
2
lvac
p n1d o cos 1 F
Free spectral range:
At a given d, how much can l change before it confuses
us by “lapping” its original peak near d?
lFSR 
2
lvac
2n1d o cos 1
Given a choice, is it better to increase d or increase
R to make lmin as small as possible?
a) increase d
b) increase R
lmin  lFWHM 
lFSR 
2
lvac
2
lvac
p n1d o cos 1 F
2n1do cos 1
Multiple reflection view of T
Solar corona taken
with the LASCO C1
coronagraph which
employed a tunable
Fabry-Pérot
interferometer near
an iron atom
emission line at
530.8 nm. Color
coded image of the
doppler shift of the
line, after
subtracting solar
rotation.
What you see on a screen for any interferometer
There is always some angular divergence
Phase shift k 2d o cos 1
Two close sodium emission lines are
visible
Experiment on video