1: Things you need
2: What to do with these items:
3: What you get:
4: The math behind it:
5: A javascript example:
6: Epilogue: One more test.
7: One more try: This time with my 200LPI encoder disk.
8: Just for kicks: Double slit & the sun (White Light)
9: Contact
Most pictures are clickable and will yield a high resolution image (6MP).
Jesse's super-simple double-slit experiment:
How to demonstrate the wave property of light at home.
1: Things you need
Above:A standard issue cheap laser pointer.
Above: Some good hardcover books,
Above: By sticking small objects under the cover, the book can be used as a tilt table.
Above: You will also need a first-surface optical mirror.
Above: I got mine from an old fax machine or flatbed image scanner. Mirrors are fun to photograph.
Above: A trusty pocket knife or other sharp tool to scribe your two "slits".
Above: Styrofoam to use in the fabrication of small vblocks for holding the laser and the mirror.
2: What to do with these items:
Above: Very carefully cut some scratches in the thin reflective plating on the mirror.
Make them as narrow, close together, and parallel as possible.
You can see it took me several tries!
Red arrow indicates the pair I used for this experiment.
Above: Under a high power macro fixed focus lens, my best pair looked like this.
(I superimposed a scale of 200 lines per inch for comparison.)
So my slits are about 2/200ths, or 1/100th of an inch (0.01 inch) apart centers.
Click the above image for a full resolution version of it, and here for a full resolution
version of a photo (with the same fixed focus lens) of my digital calipers set to 1mm.
Using these methods, the images are at 444pix/mm, and since the the slits are about 100 pixels apart,
they calculate to be about (1/444)*100=0.225 mm, or about 0.0089 inches.
Above: My ruler is actually a disk for an optical rotary encoder, taken from an old inkjet printer.
it says on it "200LPI" as you can mostly see (the field of view on my macro lens wasn't wide enough.)
It also says "1800CT" and it measures about 2.85 inches in diameter at the average diameter of the lines.
(1800/(2.85*3.141592654)=201.0378228266)
Above: Now stack up your hardcover books to form an adjustable platform.
Notice how the elevation and tilt in both directions can be adjusted by sliding objects under the cover.
By moving the object in further or out, reasonably fine adjusting can be performed.
Above: Using the Styrofoam v-blocks, set up your laser and mirror so that the laser shoots right through your best slit.
Above: As you can see here, my first experiment was actually rather uncivilized, but it worked well.
Above: Use a rubber band or tape to keep the laser turned on.
Above: Set up some more books to form a target. A white flat non-shiny surface is good.
For my first experiment, I just used the white edge of a book (left) but it would probably
be better to actually use white paper (right) or perhaps graph paper so it was easy to determine the interference pattern size.
3: What you get:
Above: And here is the pattern I got! My slits were about 8.5 feet (2.6meter) from my target.
My interference bands were about 0.26 inches ( 0.006604 meter) apart.
Notice how my interference bands are not parallel - but remember that my slits aren't either!
4: The math behind it:
To recap, here are our dimensions:
| Spacing between the slits: | 0.00022522522 meters. |
| Distance between the slits and target target: | 2.6 meters. |
| Wavelength: | 0.00000065 (650nM) |
| Distance between interference bands: | 0.006604 meters |
Now trust me, I'm no math wiz to be sure. I grew up on a farm, milking cows and feeding chickens. (And taking things apart, reading science books, etc. But all of my education was meager and happened there - I never went to school. To the degree that I was schooled, I was homeschooled. And I don't regret a bit of it!)
But I found this interesting:
If we multiple the (target_distance/slit_spacing) ratio and the wavelength, we get:
(2.6/0.00022522522)*0.00000065=0.0075036001
meter.
That is very close, considering my very sloppy method, to the measured distance between the interference
bands!
Furthermore, using the script simulator below, and setting the span to 2 and the y-step to 0.001 (to give it greater precision, since it is just an iterating simulator) it gave a band to band centers distance of 7.503600mm! (Of course it took a long time to run.)
However, I tried it again with a y-step of 0.0001 which took half an hour, but it gave 7.50367000 which is a little higher then I would have expected. So my simplistic formula above probably isn't perfect.
5: A javascript example:
Well, so I wanted to do the experiment another way, so I threw together this little javascript (Yeah, yeah, I know, javascript is evil..)
to simulate the scenerio.
The diagram is a simplified double-slit experiment setup. It is not to scale, except the Y-axis for the interference
bands on the right is to scale and life size, assuming you have the correct DPI for your monitor keyed into the form below.
My monitor is 100DPI vertically. You can check yours by holding a ruler up to the two vertical bars on the
right top side - one of those is 5CM and the other is 1 inch.
Anyway, this script uses simple geometry to determine the distance between each slit and each vertical point along
the projection screen. Then it calculates the partial wavelength of the two paths, then subtracts
the one phase from the other's phase, then takes the cosine thereof, shifts it up to yield 0-2.0 instead of -1 to +1, then divides it down and sets the alpha level therewith.
Thus, it should reasonably well simulate the interference patterns of light as waves.
Do note that if you set too many iterations it can take a long time to finish. It may seem like your browser
has locked up if you fiddle with the parameters but it's probably just really taking a long time. (Of course if you
set the stepsize to 0, it will take forever.)
The vertical green scale are just markers at peaks (actually they are markers between zero crossings.) and the vertical
blue scale is 1cm marks.
Incidentally, it may not run on Internet Explorer, since it uses <CANVAS>. If it doesn't run, you can see a screen
shot of it here.
(Also note that this script runs WAY slower on internet explorer. I suggest using firefox, mozilla, opera, etc.)
6: Epilogue: One more test.
As it turned out, I wanted to do the test again with a greater distance between the target and the slits.
And since I was so better set up now, I did just that. This time, everything was level and square for the
most part, and it was good and dark so I was able to get some reasonable photos.
Above: This time I set up using the Styrofoam blocks - this works way better!
Above: A close-up test shows a small pattern alright.
Above: I got an even fancier pattern this time. You can see where I marked off the distances with a pencil. They are about 19.1mm spaced, centers.
Above: Here I turned out the lights to get just the pattern. You can still see my pencil marks. This second experiment had a distance of about 20 feet.
Specifications and results for this experiment:
| Spacing between the slits: | 0.00022522522 meters. |
| Distance between the slits and target target: | 6.096 meters. |
| Wavelength: | 0.00000065 meters (650nM) (6.5e-7m) |
| Distance between interference bands: | about 0.0191 meters |
So let's try the formula of (Distance/SlitSpacing)*Wavelength and see if it is close:
(6.096/0.00022522522)*0.00000065=0.01759290
It's still not too close. I suspect that the spacing between my slits is my weak point, since they are not parallel
it's hard to accurately measure them.
Above: As a free bonus, I noticed that a few feet below my main pattern, there was another more random looking pattern. This must have had something to do with the fact that I was using a little glass first-surface optical mirror with two almost-parallel scratches in it, as my slits.
7: One more try: This time with my 200LPI encoder disk.
I decided to try something with a known spacing, so I tried my 200LPI optical encoder disk. (The same one which
I used as a "Ruler" in earlier photos.)
Now I realize that it's more of a grating then a double-slit, but it seems to work on the same principles, and, by the way, it works much better - the interference patterns are much much brighter. As a matter of fact, it doesn't really look like interference patterns but rather it looks like multiple dots - as if it just splits the beam into several beams. But the distance between the beams is the same as it would be for a double-slit with the same dimensions, so I'm going to consider that it's working on the same principle.
Above:
The laser pen shining through the 200LPI grating.
Above: The resulting pattern, in the dark.
Above: Same pattern, but with enough light to see the graph paper behind it.
Specifications and results for this experiment:
| Spacing between the slits: | 0.000127 meters. |
| Distance between the slits and target target: | 6.02615 meters. |
| Wavelength: | 0.00000065 meters (650nM) (6.5e-7m) |
| Distance between interference bands: | about 0.0312 meters (+/- 1mm or maybe 0.5mm I'd say) |
Let's try the formula on this one:
(6.02615/0.000127)*0.00000065=0.0308425000
Well, 30.8mm is pretty close to 31.2mm! Still not perfect, but well within a beam's width.
8: Just for kicks: Double slit & the sun (White Light)
Just when I thought I was done, I thought another experiment might be fun. So I rigged up a single slit
followed by a double slit using again first-surface optical mirrors salvaged from old junk
(Polaroid cameras have them too!) then using aluminum foil tape (From the hardware store - it is for ducts
I think, but it makes a great light blocker) to tape the two slit sets onto my telescope-camera adapter.
As you can see, this setup allowed me to rotate the first slit to line up with the second slits.
I was very pleased with the colors I got!
Above: Front(single) slit (left) and rear(double) slit (right)
Above: The whole slit assembly attached to my camera (Canon EOS 300D)(left) and one
of the best patterns I got(right)
Above: 1:1 crop of the above interference band pattern. Notice how the different colors form band
patterns of different spacings, all superimposed on eachother!
Now to demonstrate how each of the present wavelengths are making its own interference pattern, I wrote another
javascript (which is really a crude hack) which takes the RGB levels of a cross-section of the above
color interference pattern, and plots each color separately and then all together. As you can see,
each of Red, Green, and Blue are indeed forming about the same interference patterns, only the longer wavelength
colors are forming larger patterns.
And with that, I must sign off. This is day number two of getting nothing boring done.
Jesse 6-28-2008
9: Contact
Errors? Comments? Feel free to send me a note using the contact form below.
All fields optional, but, of course, if you want a response, I'll need an email address or some way to get back to you.
