Optics
Why This Matters
A lens the size of your thumb can change the course of your community’s future. A magnifying glass lets you start fires without flint. A microscope reveals the bacteria that cause disease — making water testing, wound care, and food safety possible for the first time. A telescope lets you see approaching threats from kilometers away and navigate by the stars with precision. Signal mirrors communicate over distances of 30 km or more with no technology beyond polished metal. Optics is the tier of technology where you stop guessing and start seeing, and it all begins with understanding how light bends when it passes through glass.
What You Need
For lens grinding:
- Clear glass pieces or blanks (see Glassmaking)
- Abrasive powders: coarse sand (initial grinding), fine sand (shaping), wood ash or rottenstone (polishing)
- A concave or convex form (a metal bowl, a rounded stone, or a glass blank ground to the desired curve)
- Pitch (tree resin, beeswax, or pine tar) for polishing laps
- Water for wet grinding
- Patience — lens grinding takes hours to days
For telescope construction:
- Two lenses: one large (objective, 4-8 cm diameter) and one small (eyepiece, 1-2 cm diameter)
- A tube (wood, bamboo, rolled bark, metal pipe) long enough for the focal lengths combined
- Glue, tar, or wax for sealing
- Black paint or soot for the tube interior (to prevent internal reflections)
For microscope construction:
- One or two small, strongly curved lenses (short focal length, 1-3 cm)
- A rigid frame (wood or metal)
- A stage for holding specimens
- A light source (mirror to reflect sunlight or a candle)
For mirrors:
- Flat metal: copper, bronze, or tin sheet
- Polishing compounds: rottenstone, jeweler’s rouge, or fine ash
- A flat reference surface (a thick piece of glass or polished stone)
How Light Bends: The Fundamental Principle
When light passes from one material into another (like from air into glass), it changes speed. This change in speed causes the light to change direction — a phenomenon called refraction.
The key rule: Light slows down when it enters a denser material (like glass) and speeds up when it exits into a less dense material (like air). When it slows down entering at an angle, it bends toward the normal (the perpendicular to the surface). When it speeds up exiting, it bends away from the normal.
A flat piece of glass bends light into the glass and then back out again — the two bends cancel and the light exits parallel to how it entered (just shifted sideways slightly). This is why flat windows do not distort what you see.
A curved piece of glass bends light more on one side than the other, causing the light rays to converge (come together) or diverge (spread apart). This is a lens.
Converging (Convex) Lenses
A lens that is thicker in the middle than at the edges. Parallel light rays entering a convex lens converge to a single point on the other side — the focal point. The distance from the lens center to the focal point is the focal length.
Properties:
- Shorter focal length = more powerful lens = more curvature = thicker at center
- A magnifying glass is a single convex lens
- Held close to an object, it magnifies. Held far from the eye, it projects a real image (like a pinhole camera)
- Used as the objective lens in telescopes and as the eyepiece in microscopes
Diverging (Concave) Lenses
A lens that is thinner in the middle than at the edges. Parallel light rays entering a concave lens spread apart as if they came from a point behind the lens (a virtual focal point).
Properties:
- Used to correct nearsightedness
- Used in some telescope designs (Galilean telescope) as the eyepiece
- Harder to grind than convex lenses (you must grind a hollow into the glass)
The Lensmaker’s Equation (Simplified)
For a simple convex lens ground on one side (the other side flat — called a plano-convex lens):
Focal length (approximate) = Radius of curvature / (n - 1)
Where n is the refractive index of the glass (about 1.5 for common soda-lime glass).
Example: If you grind a lens with a curve that has a 30 cm radius, the focal length is approximately:
f = 30 / (1.5 - 1) = 30 / 0.5 = 60 cm
For a lens curved on both sides (biconvex) with equal curvature:
f = R / (2 x (n - 1))
So the same 30 cm radius of curvature on both sides gives:
f = 30 / (2 x 0.5) = 30 cm
Practical tip: For a magnifying glass, you want a focal length of about 10-25 cm (comfortable hand-held viewing distance). For a telescope objective, 50-150 cm. For a microscope, 1-5 cm (very strongly curved).
Method 1: Grinding a Lens from Glass
Lens grinding is a patience-intensive process, but the technique is straightforward. People have been grinding lenses by hand since the 13th century with no power tools.
Preparing the Glass Blank
Step 1 — Start with a piece of clear glass at least 10 mm thick and larger than your target lens diameter. The clearest glass you can get matters — bubbles, inclusions, and color tints all degrade the lens quality. If you are making glass from scratch (see Glassmaking), aim for the clearest batch you have.
Step 2 — Cut the glass into a rough circle using a glass-scoring tool (a hard, sharp stone, a piece of quartz, or a steel point) and breaking pliers, or by chipping with careful taps. The circle does not need to be perfect — you will grind the edge later.
Step 3 — Grind the edge round on a flat stone with coarse sand and water until you have a smooth-edged disc. A disc 5-8 cm in diameter is a good size for a first lens (large enough to gather useful light, small enough to grind in a reasonable time).
Rough Grinding (Hogging)
Step 4 — You need a grinding tool (also called a “tool” or “lap”) with the curve you want to create. For a convex lens, the tool should be concave (a bowl shape). For your first lens, use a smooth, rounded rock with approximately the right curvature, or grind a concave depression into a thick piece of glass or hard metal.
To calculate the radius of curvature you need, use the lensmaker’s equation above. For a 20 cm focal length biconvex lens in soda-lime glass: R = f x 2 x (n-1) = 20 x 2 x 0.5 = 20 cm radius of curvature on each side.
Step 5 — Apply coarse abrasive (coarse sand, about 60-80 grit equivalent) mixed with water to the tool surface. Place the glass blank on top of the tool.
Step 6 — Grind using a “W” stroke pattern: push the blank forward while sweeping it to the right, then pull back while sweeping left, tracing a W shape. Rotate the blank and the tool periodically (1/6 turn every few strokes) to ensure even grinding. The glass should always be wet — add water and abrasive frequently.
Step 7 — Continue grinding until the glass blank has developed a uniform curve matching the tool. Check by holding the lens up and looking through it — it should begin to magnify or distort the view. Check the curve by pressing the blank against the tool — there should be uniform contact across the surface, with no rocking or gaps.
This stage takes 30 minutes to 2 hours depending on the lens size and the amount of glass to remove.
Fine Grinding
Step 8 — Switch to progressively finer abrasives. After coarse sand, use fine sand (roughly 200 grit), then very fine sand or crusite/emery (roughly 400-600 grit). Each stage removes the scratches left by the previous stage and refines the curve.
Step 9 — Clean the lens and tool thoroughly between each grit change. A single grain of coarse grit in your fine grinding will scratch the surface and set you back. Wash everything in clean water.
Step 10 — At each stage, grind until the scratches from the previous grit are completely gone (check by holding the lens up to bright light — you should see only the current grit’s finer scratches). Each stage takes 15-30 minutes.
Polishing
Step 11 — Build a polishing lap. Melt pitch (tree resin or beeswax) and pour a thin layer (3-5 mm) onto the tool surface. While the pitch is still warm and soft, press the lens into it to form a matching imprint. Let the pitch cool and harden.
Step 12 — Apply polishing compound to the pitch lap. Options:
- Rottenstone (decomposed limestone) — a traditional optical polishing compound
- Cerium oxide — if available from old glass-polishing supplies
- Very fine wood ash sifted through cloth — a last resort, but it works
- Jeweler’s rouge (iron oxide) — excellent if available
Mix the polishing compound with water to a thin slurry.
Step 13 — Polish using the same W stroke pattern, with rotation. The pitch lap conforms to the lens surface and polishes without changing the curve. Continue until the lens is clear and transparent with no visible scratches. This stage can take 1-3 hours.
Step 14 — Clean the finished lens with clean water and a soft cloth. Hold it up to the light — you should be able to focus sunlight to a bright point (the focal point). The smaller and brighter the point, the better your lens.
Grinding the Second Side
Step 15 — For a biconvex lens (curved on both sides), you need to grind the other side. Mount the finished side onto a support (a thick pad of pitch on a flat block works as a holder — warm the pitch, press the lens finished-side-down into it, let it harden). Then repeat the entire grinding and polishing process on the second side.
Step 16 — For a plano-convex lens (one curved side, one flat), simply polish the flat side smooth. This is easier and works well for many applications, though a biconvex lens gives a shorter focal length for the same curvature.
Tip
Your first lens will not be perfect. Expect distortion at the edges, some residual scratches, and imperfect curvature. For a magnifying glass, this is acceptable. For a telescope objective, you will need to practice and improve your technique over several attempts. The good news is that the process is forgiving — if you make a mistake, you can go back to a coarser grit and regrind.
Method 2: Building a Refracting Telescope
A refracting telescope uses two lenses to magnify distant objects. The large lens at the front (objective) gathers light and focuses it. The small lens at the back (eyepiece) magnifies the focused image for your eye.
Understanding Magnification
Magnification = Focal length of objective / Focal length of eyepiece
Example: An objective with a 100 cm focal length and an eyepiece with a 5 cm focal length gives 100/5 = 20x magnification.
The total tube length equals the sum of the two focal lengths: 100 + 5 = 105 cm.
Choosing Your Lenses
Step 1 — For the objective lens, grind a biconvex or plano-convex lens with a long focal length (50-150 cm) and the largest diameter you can manage (4-8 cm). A larger objective gathers more light, making the image brighter. A longer focal length gives less distortion (aberration).
Step 2 — For the eyepiece, grind a small biconvex lens with a short focal length (2-5 cm). This can be as small as 1-2 cm in diameter — only your pupil looks through it, so it does not need to be large.
Step 3 — Test each lens individually before assembly. Hold the objective up and project an image of a distant bright object (like a sunlit building across a field) onto a white surface behind the lens. The distance from the lens to the sharp image is the focal length. Repeat for the eyepiece.
Building the Tube
Step 4 — Build a tube from whatever material is available: rolled bark sealed with pitch, bamboo sections, split wood assembled into a square or hexagonal tube, or metal pipe. The tube must be rigid, straight, and the right length (sum of both focal lengths).
Step 5 — The tube internal diameter should be slightly larger than the objective lens. Paint or coat the inside of the tube flat black (soot mixed with glue or resin works well). This prevents internal reflections, which would wash out the image.
Step 6 — Mount the objective lens at the front of the tube. Cut a ring or disc with a hole slightly smaller than the lens diameter, sandwich the lens between this disc and the tube end, and seal with pitch or wax. The lens must be perpendicular to the tube axis — any tilt degrades the image.
Step 7 — Mount the eyepiece in a smaller tube that slides inside the main tube (for focusing). The inner tube should be a snug sliding fit — tight enough to stay put, loose enough to slide for focusing. Mount the eyepiece at the end of this inner tube the same way as the objective.
Using the Telescope
Step 8 — Point the objective end at a distant object. Look through the eyepiece. Slide the inner tube in and out until the image snaps into sharp focus. You should see a magnified, inverted image (upside-down and mirror-reversed).
Step 9 — The inverted image is normal for astronomical telescopes. For terrestrial use (watching for approaching people, scouting), the inverted image is confusing. You can add a third lens (an erecting lens, another convex lens with the same focal length as the eyepiece, mounted between the objective and eyepiece) to flip the image right-side-up, but this makes the tube longer and adds more glass to lose light through.
Performance Expectations
A first homemade telescope with a 5 cm objective and 20x magnification will let you:
- See the craters on the Moon clearly
- See the four largest moons of Jupiter as points of light
- Spot people at 3-5 km distance
- Read a sign at 500 meters that is invisible to the naked eye
- Identify ships or settlements across a lake
The main limitations will be chromatic aberration (colored fringes around bright objects, caused by different wavelengths of light focusing at slightly different points). This is a fundamental problem with single-element lenses. Reducing it requires either a very long focal length (which reduces the aberration relative to the image size) or an achromatic doublet (two lenses of different glass types cemented together — this is advanced work requiring two types of glass with different refractive properties).
Tip
Galileo’s first telescope in 1609 was only about 8x magnification with a 2-3 cm objective, and he discovered the moons of Jupiter with it. Even a crude homemade telescope is transformative.
Method 3: Building a Simple Microscope
A simple microscope is just a very strong magnifying glass — a single lens with a very short focal length (1-5 cm) that magnifies objects placed very close to it. Anton van Leeuwenhoek used single-lens microscopes to discover bacteria, blood cells, and sperm cells in the 1670s. You do not need a compound microscope for most practical purposes.
Building the Leeuwenhoek Microscope
Step 1 — Grind a tiny, strongly curved biconvex lens, about 3-5 mm in diameter. The shorter the focal length, the higher the magnification. A 3 mm focal length lens gives approximately 80x magnification — enough to see large bacteria and individual cells.
Alternative shortcut: Instead of grinding, melt the tip of a thin glass rod in a flame until a small bead of glass forms. The surface tension of molten glass naturally creates a nearly perfect sphere. Let it cool. A glass bead 2-3 mm in diameter makes an excellent microscope lens with 100-200x magnification. This is actually how Leeuwenhoek made his famous lenses.
Step 2 — Build a mounting plate from a small piece of brass, copper, or hardwood — about 3 cm x 8 cm. Drill or punch a tiny hole (slightly smaller than the lens) near the center.
Step 3 — Mount the lens in the hole. If using a glass bead, sandwich it between two thin metal plates with aligned holes and rivet or screw them together. The lens must be firmly held and centered in the aperture.
Step 4 — Mount a specimen pin or stage on the other side of the plate. This is a pointed metal pin that holds the specimen (a drop of water, a thin slice of plant, a smear of blood) directly in front of the lens. The pin should be adjustable — a small screw mechanism that moves the pin closer to or farther from the lens allows focusing.
The simplest focusing mechanism: thread a small bolt through the plate near the lens hole. Mount the specimen on the bolt tip. Turning the bolt moves the specimen toward or away from the lens.
Using the Microscope
Step 5 — Hold the lens side up to your eye, with the specimen side toward a bright light source (direct sunlight works best, or reflected sunlight from a mirror). Bring the lens very close to your eye — almost touching.
Step 6 — Adjust the specimen distance by turning the focusing screw until the image snaps into focus. You should see the specimen enormously magnified.
Step 7 — For transparent specimens (water drops, thin tissue slices), the light must pass through the specimen. For opaque specimens (insect parts, metal surfaces), angle the light to reflect off the specimen surface.
What You Can See at Different Magnifications
| Magnification | What You Can See | Practical Value |
|---|---|---|
| 10x | Fabric weave, insect anatomy, pollen grains | Inspecting materials, identifying plants |
| 30x | Cells in plant tissue, crystal structure of minerals | Agriculture, geology |
| 80x | Human blood cells (red and white), large bacteria, yeast | Medical diagnosis, fermentation control |
| 200x | Individual bacteria (rod and sphere shapes), fine cell detail | Water quality testing, wound infection diagnosis |
Building a Compound Microscope (Higher Magnification)
For magnifications over 100x, a compound microscope (two lenses) gives a better image than a single lens.
Step 1 — Mount a short-focal-length objective lens (3-10 mm focal length) at the bottom of a tube, pointed at the specimen. This lens creates a magnified real image inside the tube.
Step 2 — Mount an eyepiece lens (2-5 cm focal length) at the top of the tube. This lens magnifies the real image created by the objective, like using a magnifying glass to look at a photograph.
Step 3 — Total magnification = objective magnification x eyepiece magnification. A 20x objective and a 10x eyepiece gives 200x total.
Step 4 — The tube length between the lenses matters — typically 15-25 cm for standard microscope designs. The exact distance depends on the focal lengths. Adjust by sliding the eyepiece tube until the image is sharp.
Step 5 — Build a stage (a flat platform with a hole for light) below the objective lens. Mount the specimen on a glass slide (a thin, flat piece of clear glass) placed on the stage. Illuminate from below using a mirror that reflects sunlight or candlelight upward through the specimen.
Mirrors: Polished Metal Optics
Before glass lenses were common, mirrors were the primary optical tool. A polished metal mirror reflects light with high efficiency and can serve many purposes.
Making a Flat Mirror
Step 1 — Start with a piece of flat metal: copper, bronze, or tin. Thickness should be at least 2-3 mm to prevent flexing. Flatten it as much as possible by hammering on an anvil.
Step 2 — Polish one face by rubbing with progressively finer abrasives. Start with fine sand on a flat surface, then switch to rottenstone or jeweler’s rouge. The polishing surface must be flat — use a thick piece of glass or a flat stone.
Step 3 — Continue polishing until you can see a clear reflection. A well-polished copper or bronze mirror reflects about 60-70% of light (compared to about 90-95% for a modern silvered glass mirror), which is adequate for most purposes.
Signal Mirror
A flat mirror 8-15 cm across can be seen reflecting sunlight from over 30 km away on a clear day. Signal mirrors were used by navies, explorers, and militaries well into the 20th century.
How to aim a signal mirror:
- Face the sun and hold the mirror near your face
- Extend your other hand toward the target with two fingers in a V shape
- Tilt the mirror so the reflected sunlight falls on your extended hand
- Adjust until the bright reflected spot sits right between your V fingers, aimed at the target
- Flash the mirror in a pattern (3 flashes for distress, for example)
Concave Mirror (Focusing)
A concave mirror (bowl-shaped, polished on the inside) focuses light to a point, just like a convex lens. It can be used to:
- Concentrate sunlight to start fires (a concave mirror 20-30 cm in diameter can ignite tinder almost instantly)
- Act as a reflector behind a lamp to direct light in one direction (a crude spotlight or lantern reflector)
- Build a reflecting telescope (as Isaac Newton did in 1668)
To make a concave mirror: Polish the inside of a metal bowl, or hammer a flat disc into a concave shape over a form and polish the concave surface.
Common Mistakes
| Mistake | Why It’s Dangerous | What to Do Instead |
|---|---|---|
| Grinding with contaminated abrasive | A single grain of coarse grit in your fine polishing stage scratches the entire surface, ruining hours of work | Clean everything thoroughly between grit stages; use separate tools for each grit |
| Trying to rush the grinding process | Pressing too hard or moving too fast creates an uneven curve, heat-cracks the glass, or produces a lens with zones of different focal length | Use consistent, moderate pressure; keep the glass wet at all times |
| Making the lens too small | A tiny lens gathers very little light, producing a dim image (especially important for telescopes) | Make the objective as large as your skill allows; 4-8 cm diameter minimum for a useful telescope |
| Mounting lenses off-axis in a telescope | Even a small tilt in the objective creates a blurry, distorted image | Ensure the lens is perpendicular to the tube axis; test by rotating the tube and checking for image wobble |
| Focusing sunlight through a lens without care | A lens that focuses sunlight can start fires and cause severe eye burns in fractions of a second | Never look at the sun through a lens or telescope; never leave a lens where it could focus sunlight onto flammable material |
| Using glass with too many bubbles or inclusions | Bubbles scatter light inside the lens, creating a hazy, low-contrast image | Select the clearest glass available; reject pieces with visible flaws |
| Polishing on a hard lap instead of pitch | A hard lap digs into the glass unevenly, creating zones and scratches | Always use a pitch or wax lap for final polishing — it conforms to the lens surface |
| Not blackening the inside of telescope tubes | Light bouncing off bright tube walls washes out the image | Coat the interior with soot, charcoal, or flat black paint |
What’s Next
With optics knowledge and lens-making skills, you can advance to:
- Surgery — use microscopes to examine wounds, identify infections, and guide precise medical procedures
- Telegraph — signal mirrors and optical signaling systems for long-distance communication
- Glassmaking — improve your glass quality for better lenses
- Navigation — use telescopes for celestial navigation and surveying
Quick Reference Card
Optics — At a Glance
Lens types:
- Convex (thicker in middle): converges light, magnifies. Used for magnifying glasses, telescope objectives, microscopes.
- Concave (thinner in middle): diverges light. Used for correcting nearsightedness, Galilean telescope eyepieces.
Key formulas:
- Focal length (plano-convex): f = R / (n - 1), where n = 1.5 for common glass
- Telescope magnification: M = f(objective) / f(eyepiece)
- Telescope tube length: L = f(objective) + f(eyepiece)
Lens grinding sequence:
- Coarse sand (shape the curve) — 30-120 min
- Fine sand (remove coarse scratches) — 15-30 min
- Very fine abrasive (remove fine scratches) — 15-30 min
- Pitch lap + polishing compound (optical clarity) — 60-180 min
Quick lens shortcut: Melt the tip of a thin glass rod to form a bead. A 2-3 mm glass bead = 100-200x microscope lens.
What you can see:
Tool Magnification Sees Magnifying glass 2-10x Fine detail, small text, splinters Simple microscope 30-200x Bacteria, blood cells, yeast Telescope (20x) 20x distance Moon craters, Jupiter’s moons, people at 5 km Signal mirror N/A Visible 30+ km on clear day Safety: NEVER look at the sun through any lens or telescope. NEVER leave a convex lens in direct sunlight unattended — it will start fires.