I've always found interference effects in light highly entertaining,
but it also seemed disappointing that obvious visual effects due to
interference are so rare.
Of course, they're demonstrated in
high school physics labs, and anyone who's done much astrophotography
has probably seen diffraction patterns from stars, but both of those
take some fairly fancy equipment -- they're certainly not something you
can typically see just walking down the street.
Holograms are, of course, an example of interference effects -- but they're anything but simple
, and the relationship between a simple diffraction pattern and a 3-d photograph is anything but obvious to most of us.
rainbows sometimes show a colorless "diffraction bow" inside the main
bow -- but these are not common (at least where I live), and proving
that the "diffraction bow" is really caused by diffraction, let alone
understanding exactly why it appears where it does, is not an
especially simple or obvious exercise. Similarly, during a total
solar eclipse one may see dark bands on the ground which are apparently
due to diffraction -- but this is extremely
rare, and most of us will never see it.
There's one major reason why we rarely see diffraction or interference patterns: The sun is too fat
It subtends about 1/2 degree in the sky, which means that the
edges of shadows -- the angle between the umbra and penumbra -- spreads
at an angle of 1/2 degree, also. This means shadows cast by the
Sun are too fuzzy to show visible diffraction effects, and when the Sun
shines through closely spaced holes or slits, the "fuzzing" of 1/2
degree again tends to mush out the pattern.
All this can leave
one feeling that diffraction of light is such a subtle effect, and the
dimensions of the waves are so small, that save in certain very unusual
circumstances, one will never see a "gross" diffraction or interference
pattern without using special, precision-made equipment.
I was enormously amused to find that this is not true.
Diffraction from Window Blinds
ago, I worked in a high rise office building down town. There
were venetian blinds in the window of my office. One day, when
the Sun was on the other side of the building (not
shining in my
window), I noticed an annoyingly bright spot shining into my eyes from
a parking lot next door. It was the Sun, reflected from a shiny
chrome bumper (figure 1
closing the blinds to block it out, I happened to glance at the shadows
the blinds were casting on the opposite wall.
Each slat was
casting a sharp, sharp shadow -- far sharper-edged than the shadows
they cast when the Sun shone in directly. Of course, the reason
was that the image of the Sun, reflected on the curved
surface of the bumper, appeared far smaller
than the directly viewed image of the sun would have. From my
office, the Sun's image subtended a tiny angle, much smaller than 1/2
degree. In other words, the sunlight coming in the window was
very "well collimated". And, much to my amazement, I noticed that
the shadow of each slat had a series of dark and light bands
its edge. The sunlight was forming a diffraction pattern on the
wall! It was clearly visible to a casual glance, no special
|Figure 1 -- Placement of sun, bumper, and building:|
Unfortunately I didn't photograph the pattern on the wall, and I no longer work next to a
parking lot, so that situation isn't likely to come up again. But I
recently ran across something nearly as surprising.
few years ago, I was staying in a hotel room, and noticed that the
street lights from the next block looked "funny". They appeared
"broken up", almost like I was seeing multiple images of them. A
little experimenting revealed it was the curtains doing it. The
curtain material was inexpensive, very coarsely woven stuff, made of
some shiny white fabric. Since the dark colored window screens
weren't doing the same thing, my guess at the time was that it was the
effect of reflections from the shiny white threads. I dismissed
it as odd but not very interesting. I was wrong, as I later
More recently, we moved into a different house, and the
former owners left behind some inexpensive coarsely woven curtains
something like the ones at the hotel. One night I happened to
notice the same effect
when I looked at a lamp in front of a
house down the street, and I decided to figure out what really was
causing it -- I was no longer sure it was just reflections from the
threads. And, indeed, it was not!
First test: How
did the image behave as I moved around -- how did it change?
Answer: It didn't change; it didn't depend on where I stood or
how close I was to the curtain. Its size and position remained
fixed relative to the image of the lamp, whether I was close to the
curtain or on the other side of the room. Strange -- if this was
some reflection from the threads, it's not how I would have expected it
Second test: Was it an illusion of some sort? Answer: Nope -- a camera sees the effect, too. Figure 2
shows the lamp photographed "directly", with the curtain pulled to one side.
|Figure 2 -- Lamp (telephoto shot, enlarged):|
shows the same lamp, photographed at the same scale
with the curtain in place. It's a high contrast subject and the
pattern in the photo is far more limited than what I can see with bare
eyes, but none the less it's a striking image.
|Figure 3 -- Lamp shot through curtain (same scale as figure 2):|
Third test: How did the pattern size depend on the spacing of the threads?
If it's really a diffraction (or interference) pattern, then
moving the threads closer together, and thus making the holes
between them smaller, should expand
|Figure 4 -- Curtain Mesh:|
the curtain, so I was looking through it diagonally, thus effectively
shrinking the holes. Sure enough, the pattern "spread out" as I
did so -- it got larger.
At that point I was convinced that this had
be an interference pattern of some sort. But the holes in the
curtain still seemed too large for me to believe it ... perhaps a
measurement was in order. I took a few pictures of the curtain
material with a couple of rulers (see example in figure 4
using a 64th inch steel rule). Counting the holes and comparing
with the ruler, we find the holes appear to be on 0.33 mm centers.
To my eyes, looking at a blowup of the photo, it looks like the
threads are about 1/2 the width of the holes, which makes the
holes about 0.22 mm square.
With the camera placed about 5 feet from the window, the angle subtended by one hole
would be about 0.22/1524 = 0.000144 radians. The angular
separation of two holes would be about 0.33/1124 = 0.000217 radians.
I could go much farther, I also needed to know how "big" the image of
the lightbulb really was -- that is, I needed to know what angle it
subtended. In principle I could determine that from the photos
I'd taken, but I don't know off hand what the angular width of an image
is on this camera, and I'd need to run some careful tests to find out.
So, I took the direct approach instead. I went out the next
morning and paced off the distance from the window to the lamp post; it
was about 60 paces, or about 150 feet. The bulb is roughly 2
inches in diameter. Dividing out, the angular diameter of the
bulb, viewed from the window, is about 0.00111 radians. The
lightbulb's image is about five times as large as the separation
between two holes -- i.e., if we could see the fabric of the curtain in
figure 3, we would see five threads running each way across the central
bright area of the picture where the lightbulb should be. (And,
not incidentally, the apparent diameter of the bulb is about 1/8 the
apparent diameter of the Sun -- consequently, it's likely to produce
far sharper, more visible diffraction and interference patterns than
direct sunlight would.)
The next question which came up is
whether the light passing through one hole in the curtain would
actually spread enough to form an interference pattern with the light
from the neighboring holes. It would spread due to diffraction --
but how much?
From here on I'll be treating the holes as slits
, and assuming that what I've got is two "crossed" grids of slits. The slits are 0.22 mm wide, on 0.33 mm centers.
|Figure 5 -- First null in diffraction pattern:|
want to know the angle at which the first null in the diffraction
pattern cast by a single slit occurs, as this will tell me how wide a
cone the light will spread into after passing through a hole in the
curtain. The first null in the pattern will be the point at which
the light from the middle of the slit exactly cancels the light from
one edge; as we continue on across the slit, each portion cancels the
light from one "half-slit" to the left. This implies that, in figure 5
the path length from the observer to the right edge of the slit must be
exactly 1 wavelength longer than the path to the left edge of the slit.
angles are grossly exaggerated in the figure. In fact, θ is very
small, so the slit width and the separation of the left and right edges
of the "outgoing light" beam can be taken as identical. Let's
define some things:
The first null will therefore be at
the angle subtended by the central maximum in the diffraction pattern
from one hole will be 0.0055 radians, or about five times the apparent
size of the lightbulb. That's more than enough "spread" to allow
for the interference pattern we're seeing.
Now, what should an
interference pattern from the curtain look like? A grid of bright
spots seems right: it will be the intersection of two patterns of
lines, one vertical and one horizontal. We can presumably figure
out the spacing of the lines by treating the curtain as a grid of slits
rather than an array of holes.
Let's just consider two slits.
In fact, let's be sloppy about it and just consider two "line
sources", separated by distance Δ
. There's a maximum in
the center of the pattern, of course. The next maximum will be
where the two sources are once again in phase; that will be at the
angle λ/Δ. Amusingly, the diagram shown in figure 5 describes
this case nicely as well, if we just eliminate all the "middle" arrows
in the "Incoming Light" rays!
Our holes are on 0.33 mm centers, so we have Δ = 0.33 mm, and the first maximum in the pattern will be at
A little fiddling with diagrams of multiple slits seems to show that adding more slits increases the sharpness
of the central maximum but won't change the locations of the first side
lobes in the pattern. So, we can reasonably use this angle for
our estimate of where the lobes on either side of the central bright
spot should fall.
|Figure 6 -- Figure 3 again, with guides:|
We know the bulb diameter is 0.0011 radians, and we can measure the size of its image in figure 2
From that, we can determine how large each of the features we've
been discussing should appear in the photographs -- and that, after
all, is the whole point of this exercise! In figure 6, we've
superimposed a diagram of our "predicted" features on a copy of figure 3
. The blue ring shows the size of the lightbulb as measured in figure 2
(which is thoroughly obscured by the interference pattern!). The
yellow square shows the location of our computed "lobes" in the
interference pattern, and the magenta circle shows the boundary of the
central maximum of the light shining through one hole in the curtain.
features agree quite well with the observed pattern, particularly
considering the rather imprecise measurements which went into them.
From this I conclude that it is, indeed, an interference pattern
caused by the mesh curtain.
Finally, we show two more photos of
the lamp, taken during the afternoon with the sun reflecting from the
curved surface of the lamp, making a small but intense bright spot
something like the bright spot on the car bumper I described earlier.
These are shown at the same scale as the other images. Figure 7
shows the lamp with with the curtain pulled to one side, and figure 8
shows the lamp photographed through the curtain; the bright spot of
sunlight reflected from the lamp is responsible for the
intense pattern of nine bright spots. In the photo as a
whole, a number of light-colored features appear "doubled" or
"ghosted"; before doing this exercise, I never would have realized that
was caused by interference as a result of the light passing through the
fine mesh of the weave.
|Figure 7 -- Lamp in the afternoon:||Figure 8 -- Through the curtain:|
Page created on 7 Sep 2007