Introduction

This book is about light. Specifically, having fun with light. Tricking light into doing fun and amazing things. Tricking the eye into looking at things in a new way.

We will explore things of all sizes with light, from galaxies to things you can hold in your hand, to things that can live inside you. We will play with time, speeding it up and slowing it to a standstill. We will break light apart and put it back together. And usually, we will do all of this with things you find around the house that won't cost you an arm and a leg.

Here we will show you how to grind your own microscope lens in a half hour. We'll show you how to make scientific instruments out of plumbing parts.  We will use computers to overcome the limits of optics and cameras.

But mostly, we'll have a lot of fun playing around.

Pinhole Cameras

Pinhole cameras used to be a messy business, with negatives and developing and printing. With digital cameras that have interchangeable lenses, it has become much simpler.

You can take a picture without a lens. Just replace the lens with a scrap of aluminum foil that has a tiny pinhole in it. The smaller the pinhole, the better the focus will be. The trade-off is that less light gets to the camera's imaging sensor.

^{_{(Click on any photo for a larger image.)}}

If you look very closely in the center of the aluminum foil, you can see a tiny pinhole, made with a sewing needle. The foil is folded over an extension tube that fits onto the camera like a lens. The tube is 23 millimeters long, so we will take that as our nominal focal length.

Here is a photo of my car, taken using that pinhole. The exposure took 10 seconds at ISO 100.

The photo is quite blurry, but nonetheless, there is a recognizable image there.

A pinhole telescope

Since I have more extension tubes, lets change the focal length to 139 millimeters and see what happens. Again, I used a 10 second exposure at ISO 100.

Taken from the same distance, we can now read my license plate. The ratio of the two focal lengths (139/23) is about 6, and when I count the pixels of my license plate in both photos, I get about the same ratio — 1406 pixels wide in the telephoto shot, and 237 pixels wide in the wide angle shot.

Using my microscope, I took this photo of the pinhole:

Superimposing that photo on top of a photo of my stage micrometer slide, we can measure just how big my pinhole is:

It turns out to be 0.36 millimeters, or 360 microns, in diameter.

Here's a picture of a pot of flowers, taken at ISO 200 for 30 seconds, with the 139 millimeter extension tubes:

The optimum size of the pinhole to use was calculated by Lord Rayleigh in the nineteenth century to be:

where f is the focal length and lambda is the wavelength of the light. Using 550 nanometers as the wavelength, and solving for f, we get:

Since the diameter of our pinhole is 360 microns, we get about 6.5 centimeters for the optimum focal length.

Setting up my extension tubes for 68 millimeters, I got the photo above, using ISO 100 at 30 seconds. The focus is still quite soft compared to even a cheap lens, but this was made using aluminum foil and a rubber band.

Fixing some problems

My next pinhole attempts to fix some of the problems in the quick and simple version. First, I want to reduce the reflections inside the camera from the shiny foil. I am doing this by putting a disk of black paper behind the pinhole, with a small area cut out in the center. This should improve the contrast by keeping the light from the pinhole from bouncing off the image sensor, then back to the foil, then back into the sensor.

Second, I want to try a larger pinhole, on the assumption that any irregularities in it will be diminished on comparison to the aperture.

Third, I will make it a little more robust by using the thin aluminum from a soft drink can instead of aluminum foil, sanding the center down a little to thin just the part I want thin.

My new pinhole is 620 microns in diameter. There are a few rough edges, but it does not look bad overall.

The new focal length is about 193 millimeters. I only have enough extension tubes to make 170 millimeters, so we will get close, but not exactly optimal.

Here's what the pinhole looks like, installed in the body cap of my Canon Xti:

 

Below you can see another picture of my car, this time with the 620 micron pinhole.

The contrast and sharpness have improved, but there is still the soft focus effect pinhole cameras are known for.

A side-by-side comparison of the flowerpot shows less of a difference:

Invisible Light

Exploring invisible light

At either end of the rainbow there is light we can't see. Below the red end is near infrared light, shorter in wavelength than the infrared we feel as heat. Above the violet end of the rainbow is near ultraviolet, longer in wavelength than the ultraviolet light that causes sunburn.

Because these invisible lights are so close to the visible light we can see, they act in many ways just like normal light. They can be focused with lenses, and cameras can see them.

Fluorescent light

Seeing in the infrared

A source of near infrared light is as close as your television remote control.

Infrared remote control

Look directly into the front of the remote control and push some buttons. You can't see anything change. But now point the remote at an inexpensive digital camera or video camera and push the buttons. Now, in the camera's screen, you see a brightly flashing beacon of light. You can use it as a flashlight to read by, as long as you look in the camera screen.

Infrared remote control

Digital camera sensors can easily see in the infrared. In fact, they are more sensitive to infrared than they are to normal light. Camera manufacturers try to fix this by adding infrared blocking filters in front of the sensor. In cheap cameras, these are not very effective. In more expensive cameras, such as the digital single-lens reflex camera used to take the shot below, the infrared light is much dimmer than in the pocket camera shots above.

Infrared remote control

Seeing in the ultra-violet

Cheap ultraviolet light sources use a mercury vapor lamp and some dark purple glass that blocks most of the visible light from shining through. Unfortunately, rather a lot of blue and violet light gets through.

A better source is an ultraviolet light emitting diode. While some of the cheap LEDs called "ultraviolet" are actually really just purple LEDs, you can obtain good LEDs whose wavelength is 395 nanometers or below. At the time of this writing, 395 nm LEDs can be had for a few dollars, while a 375 nm LED penlight goes for $25, and a 255 nm LED will set you back $600.00.

It is not advisable to look into an ultraviolet LED, any more than it is to look at the sun. But a quick glance shows that a 395 nm LED looks dimly blue-violet to the human eye. But when we look at it through the camera, we can see that the camera sensor is again rather good at seeing this otherwise mostly invisible light. The light looks blue-white to the camera because the camera and its software interpret ultraviolet as blue, and this light is very bright in the ultraviolet.

Ultraviolet light emitting diodes

Bees can see in the ultraviolet. Flowers take advantage of this, and have ultraviolet pigments that bees can see but humans cannot. But when we take such a flower, in this case a California Poppy, and illuminate it with our 395 nanometer ultraviolet LED, and take a picture, we can see some of these markings.

In the photo below, I took the picture on the left in normal light, and the picture on the right using the UV LED. You can see that the edges of the flower are lighter in color, and the center is darker, except for the stamens, which are very bright.

Poppy in visible and ultraviolet

Invisible ink

Invisible ink has many uses beyond secret communications between spies or criminals. One such use is as an anti-counterfeiting measure in money, as seen by the photo below, where a U.S. twenty dollar bill is lit from behind by one of our ultraviolet LEDs.

Twenty dollar bill in ultraviolet light

In the bright green band of fluorescent ink, you can read the words "USA TWENTY".

How to see invisible ink

What we will need:

1. Invisible ink (either in a vial or in an invisible ink pen).
2. A source of ultraviolet light, such as a UV light emitting diode.
3. (Optional) Blue-blocking sunglasses (yellow goggles).

A kit with an ultraviolet LED, battery, invisible ink pen, and bottles of ultraviolet dye is available in our catalog.

The invisible ink pen is sold as a security marker, so you can invisibly write your name or driver's license on your belongings.

The fluorescent dyes can be used as ink in a fountain pen or a quill pen, or you can just dip a cotton swab into the dye and write with that.

They can also be poured into ink pads and used as hand stamps at dances or events, to permit re-entry without paying again.

To see the ink, put a small button cell lithium battery between the two leads of the ultraviolet LED. If it doesn't light up, turn the battery over (LEDs are diodes, and only light up if the current is flowing in the right direction). You can use two batteries to get a brighter light. Just stack the batteries one on top of the other, and place the LED wires on the top and bottom as if it were one battery.

Ultraviolet LED with two CR2032 batteries

Aim the light at the invisible writing. You may want to do this in a dark place for better readability.

The blue-blocking sunglasses are useful for enhancing the contrast. They block most of the blue and violet light that leaks through the purple glass filters of mercury vapor lamp ultraviolet lights. They are still useful with the ultraviolet LEDs, even though those emit much less visible light.

How to make your own fluorescent dye

You can make your own fluorescent dye easily, after a trip to the kitchen for some powdered turmeric spice, and the bathroom for some rubbing alcohol.

Put a teaspoon of turmeric into a glass, and add a few tablespoons of alcohol. Fold a paper towel into quarters to make a funnel, and filter the liquid into another glass. The photo below shows the liquid in a tiny glass vial, lit by our UV LEDs.

You can use a cotton swab to write things with your new ink. It will appear yellow on the paper, and bright yellow-green when lit with ultraviolet light.

Tiny vial of turmeric dye

How does it do that?

A typical fluorescent dye (several are shown below) has manyconjugated bonds, where double bonds and single bonds alternate in the molecule.

Curcumin molecule

What is actually going on in the molecule is more complicated than the simple diagrams suggest, because the electrons that form those bonds aren't pinned down in one place, but tend to wander or smear out along the whole molecule. The electrons have many possible energy states. The lowest energy state (the ground state) is one where the electrons are closest to the nucleus of the atom, and are paired up, with each electron in the pair spinning in the opposite direction. We say that one electron is spin up, and the other is spin down.

Ethidium bromide molecule

At room temperature, the electrons have enough heat energy to bounce around and bump one another between energy levels at random. But most of the electrons will be in the lower energy levels at any given time.

Fluorescein molecule

The electrons in the molecule have energy levels of different types. The basic energy levels are the electronic states (the ground state, the excited ground states, and the exited triplet state). But layered on top of these are vibrational and rotational energy states.

Propidium iodide molecule

These extra vibrational states allow the electron to absorb photons of different energies that raise the energy of the electron to different levels. Since the energy of a photon is related to its wavelength (the color of the light), many slightly different colors of light can be absorbed by the electron to push it into higher energy states.

Sulforhodamine B molecule

Once an electron has absorbed a photon and has jumped into a higher energy state, it can lose some of the energy easily by releasing the vibrational energy as heat. The electron then settles into the lowest vibrational energy level at that excited electonic state.

The three electronic states are diagrammed below. In the ground state, electrons are paired, one with spin up, and one with spin down. In the excited state, one of the electrons has a higher energy, but still has the opposite spin. In the third (triplet) state, one of the electrons has flipped its spin, so both electrons have the same spin.

Electron states

All of these energy levels and states come together in what is called the Jablonski diagram, which is used to show what is happening during fluorescence.

Jablonski diagram for fluorescence

The diagram shows an electron in the ground state absorbing a photon and rising to the second excited singlet state (S₂). This transition is shown in purple. Because the photon had more energy than was necessary to achieve the second electronic excited state, the electron is sitting at one of the vibrational energy levels in that electronic state. As time goes by, the electron loses energy as heat and settles into the bottom vibrational level of the second excited singlet state. It can lose more energy as heat and move down to the bottom of the excited singlet state 1, either in one step or in many small steps, stopping at various vibrational energy levels. These energy drops are shown in red in the diagram.

It is possible for the electron to lose energy further, either by emitting a photon of light, or by what are called non-radiative means, where the energy ends up as heat. When a photon is emitted, we say the molecule has fluoresced. This is shown in yellow in the diagram.

Jablonski diagram for phosphorescence

Sometimes the electron will lose energy by flipping its spin, and jump to the excited triplet state. It can then jump back and fluoresce like before, in which case it is called delayed fluorescence. Or it can flip again, and jump to one of the vibrational energy levels just above the singlet ground state. We call this phosphorescence. Flipping electron spins is statistically unfavorable, and this causes a delay in releasing the energy as a photon. Phosphorescent materials glow for a while after the exiting light is removed (glow in the dark paints are phosphorescent).

Adding heat energy makes it more likely that electrons will shake loose from their current states and fall down into lower states. Heating a glow in the dark toy will make it appear brighter, but the glow will fade way faster.

Kryptonite

Most glow in the dark products are made from zinc sulfide doped with tiny amounts of copper. This compound is inexpensive, but the glow does not last long.

A very long lasting phosphorescent material has recently been discovered. It glows bright green for over 12 hours (all night long) after charging in the afternoon sun for an hour or two. It lasts so long, and glows so brightly, it has been named Kryptonite, after the glowing green mineral in the Superman comics and movies.

Kryptonite in the light

You can charge this stuff up by setting it next to a lamp for a while, then turn off the lamp and have a free night-light, or read Superman comics with it under the covers.

Kryptonite in the dark

The material is made of strontium magnesium aluminate, doped with the rare earth lanthanides europium and dysprosium. No evil genius should be without a vial of this in his pocket!

Imagine sprinkling sand made from Kryptonite onto sidewalks before the concrete hardens. Now you won't need street lights. How many other uses can you think of?

Time-lapse Photography

 

Time Lapse Photography

I carry my digicam with me everywhere. It is an old Canon SD850IS. There are newer models available, with more features and more pixels, but this camera has been just fine for recording interesting things I see on my walks through the woods, and I have more professional DSLR cameras for studio work.

But I recently came across some very nice free software called CHDK (the Canon Hack Development Kit) that I can load directly into my camera, that takes over its firmware and adds a lot of very nice features, such as ultra-long shutter speeds, ultra-fast shutter speeds, RAW mode, shutter priority, aperture priority, shutter, aperture, and ISO overrides, high speed bursts, shutter bracketing, aperture bracketing, ISO exposure bracketing, focus bracketing, high speed flash sync, motion detection, USB cable remote shutter release, and scripting in BASIC.

It is that last feature that allows some amazing control of the camera. When you can write programs that run on the camera itself, and operate all of its controls and features, you can do some wonderful things.

One of the things I have been playing with is time lapse photography.

Because the camera can take 10 megapixel photos, the video can be very sharp. I reduced the size of the photos to 1920 by 1536 pixels, and then YouTube compressed them quite a bit in the videos shown on this page, but they still look pretty good. The originals played on my 30 inch monitor look stunning.

The CHDK software loads onto the memory card that goes into the camera. If the write lock switch on the memory card is not locked, then the camera does not load it, and operates normally. If the write lock switch is on, the CHDK software takes over, and you get a much bigger menu of things you can do with your camera.

To take time lapse movies, we use an included script called an intervalometer. This is a tiny little BASIC program that takes a picture, waits some number of seconds (you set that number), and then loops back to the start to take another picture. You set the number of pictures you want to take, or set the number to a very high value and let the memory card fill up.

Once you have a bunch of photos captured, you can use another free software program Slide Show Movie Maker to convert all of the photos into a video. Then upload the video to YouTube for sharing.

Both of the free programs have manuals that show how to use them, so I won't duplicate that here. Instead, I will show some more results.

 

High Speed Photography

High Speed Photography

In my page about time-lapse photography, I described the softwarefree software called CHDK (the Canon Hack Development Kit) that I can load directly into my camera, that takes over its firmware and adds a lot of very nice features.

One of the nice features is the extended shutter speed control. Not only can you take very long exposures, but you can take extremely short exposures as well, shorter than most cameras, even those that cost many thousands of dollars.

The following photos were taken at a CCD electronic shutter speed of 1/64,000th of a second. Any blur that you see is not motion blur, it is simply focus blur caused by using a fairly wide open aperture to capture more light. This has the effect of making things that are too close or too far away be a little out of focus (an effect called limited depth of field that is often used for artistic effect, or to make the subject stand out against a blurred background).

Click on any photo to get a larger version.

When shooting water, it helps to have a corner of paper to focus on.

The flash duration can be controlled as well as the shutter duration. In these photos the flash was set to its maximum to provide as much light as possible. But if you need even faster speeds, the flash can be set lower, so the subject is illuminated for less than 1/60,000th of a second.

Long Exposures

Gigapixels

Macrophotography

Microphotography

Stacking

 

Stacking photos for greater depth

In my page about time-lapse photography, I described the free software called CHDK (the Canon Hack Development Kit) that I can load directly into my camera, that takes over its firmware and adds a lot of very nice features.

One of the nice features is focus bracketing. This allows you to take a series of shots with one button press, and have each shot focus a little bit farther away each time.

While this can be nice by itself to ensure that one of the photos has the focus you really wanted when focusing can be difficult, where it really shines is when you use software that combines all of the photos into one shot where everything is in focus.

This is called focus stacking, and there are several free programs that do this for you. The one I use is CombineZP.

In the camera you can control how many millimeters the focus changes for each shot, and in which direction (forward or back, or both). And if that isn't enough control, all of the features in the camera can be controlled in the camera by user-written BASIC programs, to give you all the flexibility you want.

The photo below shows the first and last of a series of shots at different focus points.

Notice that in the left photo, the closer parts of the flower are in focus, but the stem is not. In the photo on the right, the stem is in focus, but the front of the flower is blurred. Also, the flower looks larger in the photo on the right, since the focus has shifted closer. The software takes this into account when it combines the pictures into one.

The photo below is the result of stacking those in CombineZP:

You can see that the entire flower is in focus, from the stamens in front to the end of the stem in the back. Even the wood grain in the table is always in focus.

Here are some more examples:

I generally use from 6 to 20 shots for each take. CombineZP has several different methods of combining the photos, and for each series, some work better than others. So I run them all (there is a single-click menu item for that) and select the one that works the best.

With the closeup of the quarter, isn't it nice to be able to read all of the letters?

Click on any photo to get a larger version.

Astrophotography

Optical Trickery

Rainbows and spectra

 

A high resolution spectrograph

Building a home-brew recording spectrograph used to mean dealing with microcontrollers and stepper motors moving diffraction gratings past a light sensor, and although many were planned, few were actually built.

Modern digital cameras and the Internet have combined to make building a laboratory quality high resolution spectrograph a task that can be done in fifteen minutes at your kitchen table, with a few plumbing parts.

...and a digital camera and Internet access, but you probably have access to both of those already.

For the spectrograph you will need:

1. A 15 inch long black ABS plastic tube, 2 inches in diameter. These pipes are common plumbing items found at any hardware store, and they will usually cut the pipe to the length you want right there in the store.
2. A rubber cap for the tube, with a hose clamp. These are found in the same section in the hardware store. The rubber cap is easy to cut with an Xacto® knife or razor blade.
3. A 22½ degree 2 inch diameter ABS angled pipe coupling. In a pinch you could use a 45 degree angle, but the 22½ is perfect.
4. A 2 inch diameter circle of 1000 line-per-millimeter holographic diffraction grating. We carry this item in our catalog.
5. Some cardboard from the back of a writing pad or a shoe box.
6. Some glue.
7. An 8½ by 11 inch sheet of black construction paper. We will roll this up and insert it into the tube to eliminate reflections.

Click on the photo for a larger image.

The first thing we do is cut a slit into the center of the rubber cap.

Click on the photo for a larger image.

We hold the slit open with little pieces of thick paper.

You could use slivers of cardboard cut from a cereal box, but I found the cardboard cover of the razor blade I was using to cut the slit was just perfect. The slit is now as wide as the paper. A wider slit will let in more light, but will make broader lines in the spectrum, giving you less resolution. You can experiment with the spacing to get a slit that suits your needs.

You can also decide to use a longer tube, together with a wider slit, or a shorter tube and a narrower slit. The longer tube will make a fat slit look thinner.

Roll up the black construction paper so that it fits neatly against the inside of the tube, and slide it all the way in. Now put the rubber cap with the slit in it on the end of the tube.

Next we cut a two inch circle out of cardboard from the back of a tablet, or a shoe box. Cut a circle out of the inside to form a ring. We glue the diffraction grating to the cardboard ring, and then trim off the excess diffraction grating film once the glue has dried completely.

Click on the photo for a larger image.

Next we insert the diffraction grating ring into the end of the angle fitting, and press the tube in after it. This keeps it in place, but allows the film to be removed for cleaning, and to be rotated easily to line up with the slit.

Click on the photo for a larger image.

Hold the slit up to the light and look into the angle fitting to see the spectrum. Rotate the rubber cap until the slit and the grating are aligned, and the spectrum is a neat rectangle, instead of a parallelogram. You can rotate the grating instead if that is more convenient.

Rotate the pipe clamp so the screw part is perpendicular to the slit. This will act as a stand that keeps the slit vertical by preventing the tube from rolling.

Click on the photo for a larger image.

That's it! We're done!

Using the high resolution spectrograph

You can use the tube as it is, and just look at the spectra. In this mode, it is a spectroscope. A spectrograph is something that records and analyzes the spectrum. For that, we need the camera and the Internet.

Click on the photo for a larger image.

Use the zoom lens on the camera to make the spectrum fill the viewfinder as much as possible. This will get you the highest resolution. The more pixels your camera has, the better the result will be, but inexpensive cameras will work pretty well.

Click on the photo for a larger image.

Avoid the temptation to take a colorful rainbow picture like the one above. This one is overexposed for our purposes, and the lines are all smeared out.

Click on the photo for a larger image.

A properly exposed image will be very dark, with only four or maybe six of the mercury lines from the fluorescent light being visible.

Take the picture. In fact, take several, using different exposure times and aperture settings if your camera has those abilities. Load the photos onto your computer, and crop them so that just the spectrum is visible.

The box below has a form that will let you upload your spectra to the analysis program.

If you simply upload your spectrum photo without clicking on either of the checkboxes, you will get a spectrum plot like the one below.

Click on the photo for a larger image.

You can see four peaks in the graph, corresponding to four of the bright lines in the spectrum of mercury vapor. The brighter the lines, the taller the peaks.

But we can do even more with our spectrograph. If you place a sample of some transparent material or liquid between the light and the bottom half of the slit, you will get a spectrum where the top half is the fluorescent light, and the bottom half is the same light, but filtered through the material.

Click on the photo for a larger image.

The analysis results in two graphs. The top graph is the calibration graph, and is the same graph we just looked at. The bottom graph is the spectrum of the light that passed through the sample.

In this particular sample, instead of letting the fluorescent light pass through my sample (which was a bit of transparent green plastic), I had a second light source (a white LED) shining through the sample. This produced a continuous spectrum, so the peaks of the mercury vapor did not interfere with the analysis. A bit of aluminum foil kept the calibration light and the sample light separate, dividing the slit into two parts, a top half and a bottom half.

How does it do that?

The diffraction grating is a transparent plastic with dark lines on it spaced 1/500th of a millimeter (2 microns) apart. Light waves go through the spaces between the lines (we call those spaces slits, since they are similar to the slit we made with the razor blade in the rubber cap). Waves that go through one slit interfere with waves going through the next slit, and produce bands of light and dark, where the waves interfere constructively to form bright bands and destructively to form dark bands.

The light bands form where the waves from one slit and from the next slit are both an integer number of wavelengths from the diffraction grating. Since this depends on the wavelength, different colors will form bright bands in different places. In this way, the colors become separated into the rainbow we call the spectrum.

The mercury vapor in the fluorescent light does not produce all colors. It produces only a few colors — the ones we see as bright lines in our spectrum, plus some in the infrared and ultraviolet which the camera cannot capture. The white light comes from phosphors painted on the inside of the glass that glow when the blue and ultraviolet light from the mercury vapor hits them. These phosphors do not emit as much light as the mercury vapor, so we can easily see the bright lines in the spectrum, especially if we set the camera to record less light.

The computer program looks at each column of pixels in the photo, and adds them up to get a value for how much light of that color entered the camera. It then plots this value for each column, forming the graph.

Making lenses

Many years ago, I built the replica of Antony van Leeuwenhoek's microscope you see above. (You can open any of these images in a new browser window to get the full size photo for closer examination.)

Although I used brass instead of the silver he used, I made the long screws and the special tapped block they fit into (on the back side, see the photo below) by hand.  But I did not make my own lens, using instead a lens from a microscope objective.

The microscope has a small hole for putting a drop of pond water to observe.  There is a small lever with a ball on the end that rotates the drop left and right, and the screw at the bottom raises and lowers the specimen.  To move it left or right, you simply rotate the lens on the screw by which it is attached to the focus mechanism.  To focus, you turn the screw that faces out of the picture, to change the distance between the lens and the drop of water.

As a replica of the original focus mechanism, the model served its purpose.  But it was far too time consuming and difficult to build to end up as a project in one of my books.

The version in this chapter is much more slap-dash in appearance, and a little more clumsy in operation, but it can be built in an afternoon, and that includes making your own lens, which turned out to be much higher in magnification than the one I used in the replica.

Van Leeuwenhoek was not very forthcoming when asked how he made his lenses, scoffing that it was done "in the usual way" or words to that effect.  So the method I will describe here is most likely different from the method used in 1668.

Although compound microscopes had been invented in 1595, they were only good at magnifying objects by twenty or thirty times.  Van Leeuwenhoek's microscopes, with their one simple lens, were capable of magnifying 200 times.

What we will need:

• A glass rod or tube
• A propane torch
• A small piece of wood, such as a shim or a paint stirrer
• Some Duco Cement or other fast drying glue
• 2 pieces of copper sheet, about 1 inch by 2 inches or slightly larger
• 3 binder clips
• Sandpaper (carborundum or silicon carbide) in 220, 320, 400, 600, 1500, 2000, and 2500 grits.
• Drill and 3/32 inch drill bit (or a bit that is slightly smaller than your sphere)
• A round toothpick.

We'll start by making the lens.

Take a glass tube or rod, holding it by both ends, and heat it in the middle until a good inch of glass is soft and glowing orange.  Then remove it from the flame, and pull the ends apart to make a glass thread several inches long.

Break off the large part at one end, and hold the thread in the flame so that a small glass sphere forms on the end of the thread.  My sphere was a hair over an eighth of an inch in diameter.  With a thicker thread, you can make a larger sphere, but we actually want a small sphere, since it will have a higher magnification.

Now we glue the glass sphere onto the small piece of wood, so that we can hold it easily while grinding the glass.

Go ahead and use a lot of glue.  We want the whole sphere to be covered.

When the glue has dried, break off the glass thread.

Lay the 220 grit sandpaper on the table, and rest the wood on the sandpaper, with the glass sphere facing the grit, and the other end of the wood flat against the table.  This will keep the surface flat as we grind it.  Move the wood back and forth on the sandpaper, grinding the glass down until there is a flat surface.  We want to grind away about a quarter of the diameter.

Next, we use the 320 grit.  At each stage, we want to remove all the larger scratches from the previous grinding, leaving only the new smaller scratches.  You can carefully examine the surface with a strong magnifying glass, or you can just sand away for three or four minutes one each grit to make sure the big scratches are gone.

Above you can see the effects halfway through the 2500 grit stage.  There are still a few scratches, and they may actually be from several stages ago, due to carelessness.  Don't worry, just spend a few extra minutes on this last stage to grind them all out.

Leave the sphere embedded in the glue while we make the rest of the microscope.  The little sphere rolls and bounces easily, and is really hard to find if you drop it.

The next step is to make a holder for the sphere.  We use two sheets of copper or brass.  Hold them together neatly, and drill a hole in one end, equidistant from the sides and top.  Sand the pieces to remove burrs and sharp edges.  I stopped at the 220 grit, but you can polish yours to a mirror shine if you like, using the finer grits in sequence, just like we did with the sphere.

Using a knife, carefully dig the sphere out of the glue.  The glue will not stick perfectly to the glass, and the sphere should come out fairly easily, needing no cleaning or solvents.  But be careful not to lose it.  Working on a black felt surface might be a good idea.

Place the sphere in the hole in one of the copper sheets, with the flat face up.  You can lay the second copper sheet on the flat face to make it line up flat with the copper, before centering the hole in the top copper sheet over the lens.  Now hold the two sheets tightly together, and clip the three binder clips onto the end of the sheets away from the lens.

That's it.  You're done.

To use the microscope, we attach a microscope slide to the side with the flat part of the lens, using a rubber band.

We insert the toothpick between the slide and the copper, so it can act as a wedge, moving the slide away from the lens or closer to the lens to adjust the focus.

Look into the rounded part of the lens, holding the microscope very close to your eye.

The photo above is an onion skin, stained with methylene blue dye to make the nuclei show up better.  It was taken using our own homemade lens.  You can see that the lens suffers from severe spherical aberration, with the center in focus, and the edges definitely out of focus.  The lens also suffers from chromatic aberration, where different colors of light focus at different lengths.  But these problems are the same ones Antony van Leeuwenhoek had, and he discovered microorganisms.  The lens easily resolves protozoans like Paramecium and Vorticella, and many diatoms and algaes.

Above is a photo of a micrometer scale taken using a commercial microscope at 40x magnification.

This is the same scale, shown using our homemade lens.  The fine lines are 10 micron apart.  We are resolving details close to a thousandth of a millimeter, with a microscope we made in an afternoon.

In the stained paramecium shown above, we can see tiny organelles inside the organism.

And if you are feeling particularly handy, by all means make you own more accurate and elegant replica of van Leeuwenhoek's microscope.