Lecture 27B - UCSD Department of Physics

Physics 1C
Lecture 27B
“Think left and think right and think low and
think high. Oh, the thinks you can think up if
only you try!
Dr. Seuss
http://www.microscopyuk.org.uk/mag/indexmag.html?http://www.microscopyuk.org.uk/mag/artmay08/mm-bubbles.html
Quiz 3 Info
Next Wednesday
It will be a Scantron test that covers Chapters
24, 25, and 26.
A list of equations, constants, and
conversions will be provided on the quiz.
Outline
Last Time
Interference, double slit, thin
films
Today
CD/DVD
Thin film interference
Single slit diffraction
Resolution
Compact Disk
(CD)
y = Ll/d = (1 m)(6.6 x 10-7 m)/(1.6 x 10-6 m)
y = 0.42 m
Clicker Question 27B-1
What is the approximate spacing between DVD
tracks if the distance between the DVD and
screen needs to be adjusted to approximately
one-half to match the first order peaks position?
A. The same
B. Approximately half
C. Approximately double
D. Approximately one-quarter
E. Approximately quadruple
DVD
y = Ll/d
If LDVD ~ 0.4 x LCD for the same y, what is d ??
d = 0.65 mm = (0.65 x 10-6 m)
But how is a CD read?
Diffraction can
separate Colors
Interference and Reading
CDs
Optical Engineering
Interference in Thin Films
Interference in soap bubbles.
The colors are due to
interference between light
rays reflected from the
front and back surfaces of
the thin film of soap making
the bubble.
The color depends on the
thickness of the film.
Black appears where the
film is thinnest.
Red appears where the film is thickest.
Interference in Thin Films
A light wave will undergo a phase change of 180o
upon reflection from a medium of higher index of
refraction than the one in which it was traveling.
So, an electromagnetic wave traveling
in air will undergo a
180o phase shift if it
reflects off an oil
surface.
This is similar to the reflection of a transverse wave
that we observed earlier off of a rigid surface.
Interference in Thin Films
A light wave will not undergo a phase change upon
reflection from a medium of lower index of refraction
than the one in which it was traveling.
So, a light wave
traveling in oil will
not undergo a
phase shift if it
reflects off an air
boundary.
This is similar to the reflection of a transverse wave
that we observed earlier off of a free surface.
Interference in Thin Films
With light incident on a thin film we have to examine
two light rays that follow the same path:
Ray 1 (in air) reflects off
the film surface and
undergoes a phase
change of 180o compared
to the incident ray.
Ray 2 (in air) refracts at the
film surface and then
reflects off of Surface B
(film to air) with no phase
change compared to the
incident wave.
Interference in Thin Films
In addition, Ray 2 travels a distance t down and and
a distance t up (for a total distance 2t).
Since the extra distance
that Ray 2 travels is in the
film medium, its
wavelength will be
different then in air.
The wavelength of light, λn,
in a medium with index of
refraction n is:
l
ln 
where λ is wavelength of
light in a vacuum (air?).
n
Interference in Thin Films
In order for constructive interference to occur,
the two rays must be in phase.
This means that the difference in path length
and phase must combine to m(λ / n), where
m = 0, ±1, ±2...
The difference in path is: 2t
and the difference in phase is:
 
1 l
2 n
Combining all of these gives us:
1l
l
2t 
m
2n
n

2nt  m 
l


1
2
Constructive
Interference for 1
phase change.
Interference in Thin Films
With light incident on a thin film with another thin film
of higher index of refraction below the first:
Ray 1 (in air) reflects off
the film surface and
undergoes a phase
change of 180o compared
to the incident ray.
Ray 2 (in 1st film) reflects
off the film surface and
undergoes a phase
change of 180o compared
to the incident ray.
Thin Film Interference
To solve thin film interference problems you have
to know how many phase reversals there are.
Then you know which equation to use:
Equation
1 phase
reversal
0 or 2 phase
reversals
2nt = (m+1/2)λ
constructive
destructive
2nt = mλ
destructive
constructive
Thin Film Interference
Thin Film Interference Problem Solving
Strategy:
1) Identify the thin film causing the interference.
2) Determine the indices of refraction in the film
and the media on either side of it.
3) Determine the number of phase reversals:
zero, one or two.
4) If the interference is constructive with 0 or 2
phase reversal then use a path length difference
of integral multiples of λ (use odd half multiple of λ
for 1 phase reversal).
Clicker Question 27B-2
Upon reflection, light undergoes a 180o phase
change:
A) If the incident medium has the
lower index of refraction
B) Never
C) Whenever the incident angle
is less than the critical angle
D) Always
E) If the incident medium has the
higher index of refraction
(N.B.: Incident medium is the medium where both incident
and reflected waves are propagating)
Thin Film Interference
5) If the interference is destructive with 0 or 2
phase reversal then use a path length difference
of odd half multiples of λ (use integral multiple of λ
for 1 phase reversal).
Thin film interference is used by Morpho
butterflies to intensify the colors reflected:
.
structural color or iridescence
Thin
Film
Interference
Can be observed in a more continuous manner in
Mellon jelleyfish
Cilia beat in pulses to propel the jellyfish through
the water.
The cilia are so close together that they cause
interference
The varying
distances between the cilia
during pulsing
producing a
range of colors
Bio-Layer Interferometry (BLI)
•
•
•
Much studied physical principle commonly use in surface profiling,
semiconductor industry, astrophysics
Optical layer reflects simple white light; second reflection from tip of
biosensor, both reach detector
Analyte binding changes thickness of bio-layer, which is measured at
detector
Diffraction Patterns
The diffraction pattern that
appears on a screen when
light passes through a
narrow vertical slit.
The pattern consists of a
broad, intense central band
and a series of less intense
and narrower side bands.
A diffraction pattern is
actually a misnomer. In
reality it is another
interference pattern.
Diffraction Patterns
Diffraction pattern of a penny, taken with the penny
midway between screen and source.
The shadow of a penny displays bright and dark rings
of a diffraction pattern.
The bright center spot is called
the Arago bright spot.
The bright spot is explained by
the wave theory of light.
Waves that diffract on the edges
of the penny all travel the same
distance to the center.
The center is a point of
constructive interference
Single Slit Experiment
A single slit of a finite width
placed between a distant light
source and a screen produces a
diffraction pattern (similar to a
double slit experiment).
It will have a broad, intense
central band.
The central band will be flanked
by a series of narrower, less
intense secondary bands
(secondary maxima) that form
the diffraction pattern.
Single Slit Experiment
The bright central band of the pattern will also be
flanked by a series of dark bands (minima).
In general, destructive interference occurs for a
single slit of width, a, when:
ml
sin 
a
where m is ±1, ±2, ±3...
You can observe the
 at the
first minimum
angle:
 
l
  sin  
1
a 
Action figure
Single Slit Experiment
The cause of single slit interference is path length
difference (just like double slit interference).
In the single slit case, each portion of the slit acts as
a source of waves.
The light from one portion
of the slit can interfere
with light from another
portion of the slit.
You can again use the
approximation:
y
sin 
L
For Next Time (FNT)
Finish reading Chapter 27
Continue working on homework for
Chapter 27