Soap Bubble Interference Model
Interference colors in a soap film
Introduction
Here is a model of wave addition which will guide you in exploring
the colors of light reflected by soap bubbles.
Material
3x5 cards at least 24
4x6 or 5x7 cards
masking tape and transparent tape
marking pens, blue and red
optional, acetate transparencies
Assembly
Use a blue pen to draw a single sinewave on twenty-four 3x5 cards.
The wave should start at the left center of the card and go up to a
maximum.
Flip the cards over top-to-bottom and draw a wave on the back which
starts down from the center of the left edge. (If you hold the card
up to a light the wave on the front and the wave on the back will
coincide.)
Use a red pen to draw similar waves on the larger cards.
Tape the cards together in rows of 8 cards.
Optional Acetate waves:
Cut the acetate sheets into 4 long strips (11 inches long and 2.1
inches wide)
Draw two red sinewaves along the 11 inch length of 8 acetate
strips.
Draw 4 blue sinewaves along the 11 inch length of 8 acetate
strips.
Use the transparent tape to tape the strips together.
Tape 4 strips together so that their waves match up into one long
wave.
To Do and Notice
The colors of soap bubbles.
Start using the smaller, blue cards.
Make two parallel lines with masking tape on the floor.
Make the lines one blue wavelength apart,(For index cards 5 inches or
12.5 cm, for acetate strips 2.75 inches or 6.5 cm)
Start two waves, together on the left of the soap film.
Adjust their position so that they strike the soap film surfaces at
the maximum of each wave.
The reflection from the back of the soap film can be found by simply
folding the wave back on itself along the line representing the back
of the bubble. The drawing on the back of the index cards then
accurately shows the reflected wave. When you do this the outgoing
and incoming wave lay exactly on top of each other. (The exact
alignment of incoming and outgoing waves is only true when you
position the maximum or a minimum at the reflecting surface.)
When a light wave reflects as it goes from a high speed of light
material (air) to a lower speed of light material (soap) the wave
flips over. To make the beam of light reflected by the first surface
flip over, flip the wave about a horizontal axis (top-to-bottom) so
that the maximum becomes a minimum, then fold the wave back on itself
along the line representing the front surface of the soap film.
The reflected waves from the two surfaces are out of phase when they
combine and so cancel.
Whats Going On?
There are two contributions to the phase of the reflected waves from
the two surfaces of soap films: the wave flips over as it is
reflected off the front surface, that is, as light goes from air to
soap, and the extra path length traveled by the wave which goes into
the soap then reflects off the back surface and returns to the front.
When the soap film is thin, there is little contribution from the
extra path length and so the waves add out-of-phase and cancel. There
is no reflection from such a thin bubble. Since the colors of bubbles
are usually viewed against a black background, this thin bubble with
no reflection is called black even though it is actually
transparent.
Its more complicated than that.
The wavelength of the light actually changes when it enters the soap
film. In our model we have not added this additional complication.
Think of the thickness of the soap film in terms of the number of
wavelengths measured in the soap film. Since the index of refraction
of soap is a little higher than that of water, for soap use n = 1.4,
then the wavelength of light in soap is the wavelength in air divided
by 1.4.
To Do and Notice
Explore what happens when the soap films are very close together. One
of the waves flips over, and there is no additional phase shift
because there is no extra path length. the waves cancel.
To Do and Notice
Explore what happens when the soap films are 1/2 wavelength apart so
that the front surface is at a wave maximum while the back is at a
minimum. The extra pathlength is one full wave, so the waves
cancel.
So far, it looks like light is never reflected from soap films.
However, try a soap film thickness of 1/4 wavelength. Align the front
of the soap film with the maximum of the waves the the back will then
be at a zero crossing. Flip over the wave reflected from the front.
Fold back on itself the wave from the back. This reflected wave will
add with the reflection from the front surface in-phase and make a
stronger reflection.
Whats Going On?
The reflection from the front surface is flipped over, the reflection
from the back travels a half wavelength extra so it arrives at the
front surface with the same phase and so adds to the front surface
reflection.
To Do and Notice
Explore soap films which are 1/4 and 1/2 of a blue wavelength in
thickness a second time using red light. Notice that where the soap
film reflections cancel for blue light they add for red light and
vice versa.
Further Explorations
To Do and Notice
To explore any thickness of soap film use the following recipe.
Always arrange the incoming light so that a maximum of each wave is
at the front surface of the soap film.
Flip over top to bottom one of the waves to represent inversion when
it reflects off the front surface.
Fold the wave that hits the back surface back on itself.
Add the two waves together as they exit the film.
What's Going On?
When the wave reflects off the back surface without inversion what
reflects off is what has just hit the surface. If a downward portion
of the sinewave has just hit the surface then a downward portion
should be what is reflected. This is simply accomplished by folding
the wave back on itself.
Etc
Soap bubbles have two different stable thicknesses which look
black. The thicker of these is called the common black film, it is 30
nm thick &emdash; about 300 atoms thick or 10 soap molecules or 1/20
the wavelength of light. The thinner film is called the Newton black
film, it is about 6 nm thick,1/100 the wavelength of light, or two
soap molecules, and is much more transparent, i.e. much
blacker.
Math Root
One complete sine wave has a phase associated with it of 2p
radians.
The phase difference between two waves which are in-phase is 0, 2p,
or any even multiple of p radians.
Waves which completely cancel have a phase difference of p, 3p, or
any odd multiple of p radians.
Waves with in-between phase differences add together with amplitudes
between those of completely in-phase and completely out-of-phase.
Reflections from the surfaces of bubbles which are thin compared to a
wavelength of light have a phase difference of p from the flipping
over of the reflection from the front surface, there is little phase
difference from the extra path length.
Reflections from bubbles one half-wavelength thick have a total phase
difference of 3p; one p from the flipping over at the front surface,
and two more from the extra path length which is two half waves or
one complete wave.
Reflections from bubbles which are 1/4 wavelength thick have a total
phase difference of 2p, one p from the flipping over at the front
surface, the second from the extra half wave the other reflection
travels through the film and back.
Math Root 2
The fraction of the energy of the light reflected at the first
surface is 4% of the incoming beam (when the light comes into the
soap film nearly perpendicular). We can measure this reflection from
single surface of soap, such as occur at the top of vats of soap.
The energy reflected is the square of the amplitude of the light
wave. So if the light wave has an amplitude of 1.0 then the reflected
light has an amplitude of 0.2. The intensity of the reflected light
is the amplitude squared or 0.22 =
0.04.
To find the intensity of the reflected light we must add the
amplitudes of the waves we have been modeling and then square the
results. So when the light reflects in phase from two surfaces we add
the two amplitudes, 0.2 + 0.2 = 0.4 and then square to find that 0.16
or 16% of the incident light is reflected by a two surface soap film
which is 1/4 wavelength thick.
Many people expect that a two surface soap film will reflect twice as
much as a single soap film or 8%, when the reflected waves have a
constant phase difference, this expectation is incorrect. (The
constant phase difference comes about when the soap film is
illuminated with coherent laser light.)
First you add the reflected amplitudes and then you square the result
to find the resulting intensity of the scattered light.
# Soap Bubble Interference Scientific Exploration by Paul Doherty 4/21/99