Refracting telescope

Two lenses in a tube: a 1-metre objective and a 25 mm eyepiece give 40×, enough to see Jupiter's moons and the phases of Venus.

Build Tier 3 · Medieval to early modern Knowledge Moderate with ready-made lenses; hard if you grind the objective 1–2 days with ready-made lenses; 1–2 weeks more to grind and polish the objective by hand Crew 1

Home: Science and measurement, Level 3 · Mill, level 1 of 3 in its track. Serves 2 steps across 2 subjects.

Every build on this site has hazards that injure or kill — quicklime, carbon monoxide, molten metal, collapsing ground. Read the safety notice before starting, and read this build's own failure modes below.

**Galileo's two surviving telescopes, 1609–10, Museo Galileo, Florence: long thin tubes, because a single-lens objective only gives a sharp image at a long focal length and a small aperture.** Galileo galilei, telescopi del 1609-10 ca. · 2013-12-28 12:53:05 · Sailko · CC BY-SA 3.0 · Commons ↗

What it is and why this shape

A telescope turns the sky into an instrument: better star positions for the calendar and for finding latitude, and evidence that settled what moves around what. Galileo ground his own lenses and in 1609–10 built instruments magnifying about 30 times, with which he saw the moons of Jupiter and the phases of Venus (Bell, The Telescope).

This is Kepler's design, two convex lenses. The objective forms an image at its focal length; the eyepiece magnifies that image. Magnification = objective focal length ÷ eyepiece focal length, and the tube is the sum of the two. The image is upside down, which does not matter in the sky.

A single lens brings colours to focus at different distances: for crown glass the red and blue foci are about f ÷ 59 apart, 17 mm for a 1-metre lens. Without special glass the only cure is a long focal length and a small aperture, which is why early telescopes are long, thin tubes.

Section along the tube Fig 1

TimberMetalGlass

Light from a distant object comes to a focus one objective focal length behind the objective; the eyepiece sits one eyepiece focal length beyond that focus. With a 1,000 mm objective and a 25 mm eyepiece the tube is 1,025 mm long at infinity focus and the magnification is 40×. Not to scale: the tube is shortened.

Grinding the objective Fig 2

TimberMetalGravel / aggregateGlass

Two discs ground together with wet grit take matching curves: stroked across the lower disc, the upper disc wears concave and the lower convex, the rule telescope makers use (Draper). So the lens blank goes underneath. For a plano-convex objective of 1,000 mm focal length the curve is R = 500 mm, and on a 50 mm blank it is only 0.63 mm deep at the centre (sagitta = r² ÷ 2R). The curve here is exaggerated.

Keyed parts

1	Objective lens	Focal length 1,000 mm (+1.0 dioptre), 40–50 mm across. A +1.0 spectacle or reading-glass lens works, or grind one as below.
2	Aperture stop	A ring of card or metal in front of the objective with a 25–30 mm hole. It cuts the colour fringes and blur from the lens's edge.
3	Main tube	Rolled card, paper and glue, or thin wood, about 1 m long and 50–55 mm inside, blackened inside.
4	Baffles	Blackened rings inside the tube that stop light bouncing off its walls. Each hole is just larger than the cone of light at that point.
5	Draw tube	Slides inside the main tube for focusing, with about 60 mm of travel.
6	Eyepiece lens	Focal length 25–50 mm (+40 to +20 dioptres): a strong magnifying glass, 15–25 mm across.
7	Eye cap	A cap with a 5 mm hole that holds the eye on the axis at the right distance.

Specifications

Magnification	Objective ÷ eyepiece focal length	1,000 ÷ 25 = 40×; 1,000 ÷ 50 = 20×
Tube length at infinity focus	Objective + eyepiece focal length	1,025–1,050 mm
Aperture	25–30 mm	f/33 to f/40: longer focus and a smaller hole mean less colour fringing
Colour spread of a single lens	≈ focal length ÷ 59	17 mm between the red and blue foci at 1,000 mm, for crown glass
Focus travel	≈ 60 mm	An object 20 m away focuses 53 mm behind the infinity position (1/v = 1/f − 1/d)
Exit pupil	Aperture ÷ magnification	30 ÷ 40 = 0.75 mm
Objective curve	Plano-convex R = 500 mm; equi-convex R = 1,000 mm each side	From 1/f = (n − 1)(1/R₁ − 1/R₂) with n ≈ 1.5
Depth of curve (sagitta)	r² ÷ 2R	0.63 mm on a 50 mm blank at R = 500 mm

Bill of materials

Material	Quantity	Notes and substitutes
Objective lens	1, 40–50 mm	+1.0 dioptre spectacle or reading-glass lens. Or a disc of clear, bubble-free glass 50 mm across and 5–6 mm thick, to grind.
Eyepiece lens	1, 15–25 mm	+40 dioptre (25 mm) or +20 dioptre (50 mm) magnifier.
Card or paper and glue	About 0.5 m² of card	Rolled round a former into two tubes that slide one inside the other. Substitute: thin wooden staves glued round a former.
Matt black	A little	Soot mixed into glue, or black paint, for the inside of the tube and the baffles.
Abrasive grits, if grinding	About 100 g of each grade	Coarse sand or carborundum to shape the curve, then three or four finer grades; emery washed and settled in water gives the fine grades (Draper describes the washing).
Polish and pitch, if grinding	50 g polish, 200 g pitch	Iron oxide (rouge) or cerium oxide; pine pitch or tar for the polishing lap.
Grinding tool, if grinding	1 disc, 50 mm	Cast iron, a flat stone, or thick glass, the same size as the blank.

Tools: Sheet-metal radius gauge, cut to R · String compass for laying out the radius · Magnifying glass for inspecting the surface · Knife, saw and glue for the tube · Measuring tape

Construction

Cut a radius gauge

With a string 500 mm long as a compass, scribe an arc on thin sheet metal. Cut along it and file both edges true, giving a concave gauge and a convex one.

✓ Check: The two halves fit together edge to edge with no light between them.

Rough-grind the curve

Fix the glass blank face-up on a post. Wet it, sprinkle on coarse grit, and stroke the tool across it, each stroke about a third of the diameter through the centre, turning the tool a little each time and walking slowly round the post. The lower disc becomes convex. Always grind wet: dry glass and grit dust damages the lungs.

✓ Check: The concave gauge sits on the blank touching at the centre and the edge with no gap, and the centre stands 0.6 mm above the edge.

Fine-grind in stages

Wash the blank, the tool, your hands and the bench, then repeat with each finer grade. Move on only when every pit left by the previous grade has gone. One coarse grain in a fine stage scratches the whole surface, so keep grits in covered jars.

✓ Check: Under a magnifying glass the surface is an even, fine grey with no larger pits, at the centre and the edge alike.

Polish

Pour warm pitch onto the tool to make a layer 3–5 mm thick, press it against the wetted blank while warm so it takes the curve, and cut a grid of channels in it. Polish with rouge or cerium oxide in water using the same strokes, for hours, until the surface is fully clear.

✓ Check: In a bright light at a low angle, no grey pits remain anywhere, including the edge.

Grind the back flat

For a plano-convex lens, grind and polish the back against a flat plate the same way, checking with a straightedge.

✓ Check: A straightedge across the back shows no light under it in any direction.

Measure the focal length

In a darkened room, form the image of a distant window or a street lamp on a white card, and measure from the lens to the sharp image.

✓ Check: 1,000 mm ± 20 mm. If it is shorter, the curve is too deep; if longer, too shallow.

Build the tube

Roll card round a former to make a main tube 1 m long and 50–55 mm inside, and a draw tube that slides snugly inside it with 60 mm of travel. Blacken the insides. Glue in three or four baffle rings, each hole just larger than the cone of light where it sits.

✓ Check: Looking down the empty tube at a bright sky, the walls look black, not grey.

Assemble and focus

Mount the objective at the front with the stop in front of it, and the eyepiece and eye cap at the back of the draw tube, both centred on the axis. Focus on something far away by day, then on the Moon at night. Never point it at the Sun.

✓ Check: Distant detail is sharp across the middle of the field, and the edge of the Moon is crisp.

Tolerances that matter

Dimension	Target	Why it matters
Focal length	± 2%	The tube length and the draw-tube travel are set from it.
Surface finish	No pits visible under a magnifier	Every pit scatters light into a haze over the whole image.
Centring	Lenses on one axis within about 1 mm	An off-axis lens gives coloured, doubled edges.

How this fails

Looking at the Sun through it. Instant, permanent blindness. The only safe way to see the Sun is to project it: point the telescope at the Sun without looking through it and hold a white card 20–30 cm behind the eyepiece. Never leave it pointing at the Sun: the focused light can set the tube on fire.

Grinding dry. Glass and grit dust damages the lungs. Keep everything wet and clean up wet.

A coarse grain in a fine stage. One grain drags scratches across the whole surface. Wash everything between grades.

No aperture stop. The full lens shows colour fringes and a soft image; the stop costs brightness and buys sharpness.

A shiny tube. Light bouncing off the walls lays a grey fog over the image. Blacken everything inside and fit the baffles.

How you know it worked

VerificationOn a clear night Jupiter shows up to four small points of light in a line on either side of it, which change position from night to night, and the craters along the Moon's day–night line are sharp.

Scaling and variants

Upright image: Galileo's design uses a concave eyepiece placed inside the focus. The tube is the objective focal length minus the eyepiece's, the image is upright, and the field is narrow: good for use on land.

More power: a shorter eyepiece raises the magnification but dims the image and shrinks the exit pupil; below about 0.5 mm, floaters in your own eye get in the way.

Better colour: an achromatic objective pairs two lenses of different glass. Or change principle: a curved mirror has no colour error at all, and Draper's method for grinding and silvering one is in the sources.

The same thing, built

**Grinding a large optical disc by hand on a turntable: the tool turns with abrasive and water while the maker strokes across it. Small lenses are ground the same way in a tool cut to the curve wanted.** Lens grinding machine · 2013-05-18 12:05:13 · Totallyhaywire2 · CC BY-SA 3.0 · Commons ↗