Refracting Telescope

Part of Optics

Building and using a refracting telescope — a lens-based instrument for long-range observation — including simple and achromatic designs, tube construction, and the factors that determine performance.

Why This Matters

The refracting telescope was invented around 1608 (attributed to Hans Lippershey in the Netherlands) and within months Galileo Galilei had made one and pointed it at the sky, triggering a scientific revolution. Within a few years, telescopes had been used to discover Jupiter’s moons, the phases of Venus, craters on the Moon, and sunspots — observations that fundamentally changed humanity’s understanding of the cosmos.

For a rebuilding community, the refracting telescope serves more immediate practical purposes: extending visual range for navigation, military observation, and communication. A 20-30x telescope allows observation of ships, signals, and landmarks at distances that are completely impractical with naked-eye observation. For astronomical applications, even a simple 50 mm refractor shows the Moon’s surface in detail, Jupiter’s moons, and hundreds of deep-sky objects.

The refracting telescope is among the first practical applications of lens-making skills — requiring fewer lenses than a compound microscope and less precision than a high-power microscope objective. It is achievable early in a community’s optical development.

Optical Principle

A refracting telescope consists of two lens elements:

Objective lens: A large-diameter, long-focal-length lens (the “big” lens) that gathers light and forms a real image of the distant object at its focal plane. The objective is the performance-limiting component — its diameter determines how much light is gathered, its quality determines image sharpness.

Eyepiece (ocular): A short-focal-length lens that examines the image formed by the objective, acting as a magnifying glass for that intermediate image.

Magnification: M = f_objective / f_eyepiece

For a 600 mm objective with an 18 mm eyepiece: M = 600/18 = 33x

Angular resolution (minimum angular separation of two resolvable points, in arcseconds): Dawes’ limit = 116 / D(mm)

For a 60 mm objective: resolution ≈ 1.9 arcseconds — adequate for splitting double stars and seeing detail on planets.

The Galilean vs. Keplerian Design

Galilean telescope (original design): Uses a concave (diverging) lens as the eyepiece. Produces an upright image. The eyepiece is placed inside the focal point of the objective — the tube is shorter than the objective focal length. Limitation: narrow field of view, cannot have crosshairs in the image plane, awkward to use at high power.

Keplerian telescope: Uses a convex (converging) eyepiece. Produces an inverted image (upside down, left-right reversed). However: wider field of view, eyepiece can be placed at focus for crosshairs/reticle, better suited for high magnification. Preferred for all precision work.

For terrestrial observation where upright image is desired, a Keplerian telescope requires an erecting system — either an inverting prism (Porro prisms or Amici prism) or an additional erecting lens group. The addition of an erecting prism also folds the optical path, enabling compact binoculars.

Choosing Specifications

Aperture (D): The objective lens diameter. Larger is better — more light, better resolution — but harder to make. For a first instrument, 50-80 mm is practical. A 60 mm objective provides excellent views.

Focal length: Longer focal length reduces chromatic aberration (the chromatic aberration of a single-element objective scales as 1/f). But longer focal length means a longer, heavier tube. Traditional pre-achromatic telescopes were 30-100 feet long to reduce chromatic aberration enough for useful astronomy. The achromatic doublet (1750s) enabled useful astronomy in tubes 3-5 feet long.

For a simple single-element refractor minimizing chromatic aberration: aim for f/15 to f/20 (focal length 15-20 times the aperture). For a 60 mm objective: focal length 900-1200 mm. For an achromatic doublet: f/8-f/12 is acceptable with much shorter tube length.

Eyepiece focal length: Shorter = more magnification = narrower field. For a 600 mm objective:

• 25 mm eyepiece: 24x
• 18 mm eyepiece: 33x
• 12 mm eyepiece: 50x
• 6 mm eyepiece: 100x

High magnifications (above 50x) require good optics, stable atmosphere, and careful polar alignment. Below 30x is useful for wide-field scanning.

Building a Simple Refracting Telescope

Materials

• Objective lens: plano-convex or biconvex, 60-80 mm diameter, 600-1000 mm focal length
• Eyepiece lens: plano-convex, 20-25 mm diameter, 18-25 mm focal length
• Tube: cardboard, thin sheet metal, or turned wood, ~10 mm larger ID than objective

Step 1: Make the Objective

For a single-element objective, a plano-convex lens has minimum spherical aberration when the curved surface faces the incoming light (the star or distant object):

Target: 60 mm diameter, 800 mm focal length (f/13) Glass with n=1.5: R = f × (n-1) = 800 × 0.5 = 400 mm

Grind and polish this lens following standard procedure. A lens with 400 mm radius of curvature is gently curved — the sagitta is only: s = D²/(8R) = 3600/(3200) = 1.125 mm

This gentle curve is easier to grind accurately than the deeper curves needed for microscope lenses.

Step 2: Make the Eyepiece

A simple eyepiece: 20 mm diameter plano-convex lens, 25 mm focal length.

R = f × (n-1) = 25 × 0.5 = 12.5 mm

This is a more deeply curved small lens — more demanding to grind. However, since it is smaller, the total grinding area is less.

For a Ramsden eyepiece (better quality): two identical plano-convex lenses, each with focal length f_e, spaced 2/3 × f_e apart. The combination acts as a 10x eyepiece when f_e = 16 mm, spacing = 10 mm.

Step 3: Build the Tube

The tube length between objective and eyepiece must equal (f_objective + f_eyepiece) for the Keplerian design with focus at infinity target:

Total tube = 800 + 25 = 825 mm (to objective lens position, with eyepiece at far end)

But “focusing” on objects at finite distances requires the eyepiece to slide. Build:

• Main tube: 800 mm long, closed at one end with the objective lens centered in it
• Eyepiece focuser: sliding tube at the other end, carrying the eyepiece, with 40-50 mm travel range
• Focus is achieved by sliding the eyepiece tube in or out until the image is sharp

Step 4: Mount

A simple altazimuth mount for terrestrial use:

• Pivot vertically (altitude) on a horizontal rod
• Pivot horizontally (azimuth) on a vertical rod
• Both pivots should be smooth but firm enough to hold the telescope still after positioning

For astronomical use, a platform that rotates about a polar-aligned axis dramatically simplifies tracking.

Improving a Simple Telescope

Adding crosshairs: Place fine threads (spider silk, human hair) or an etched glass plate at the focal plane of the objective (where the intermediate image forms, before the eyepiece). The threads are imaged by the eyepiece and appear as fine lines crossing the field of view. Used for precise pointing, transit timing (when a star crosses a line), and surveying.

Upgrading the objective to a doublet: Replacing the single-element objective with an achromatic doublet (crown + flint glass pair) eliminates most chromatic aberration, enabling the tube to be shortened to f/8-f/10 while maintaining color correction. See color-correction article.

Better eyepieces: Multi-element eyepiece designs (Kellner, Plössl, Erfle) provide wider apparent field of view and better edge correction than simple singlet or doublet eyepieces. Each additional element adds complexity but improves the observing experience.

Practical Performance Assessment

Test the completed telescope by:

1. Observing a distant terrestrial target (a tree, building, or sign at >200 m) in daytime — checks for chromatic aberration (rainbow fringing on high-contrast edges), field flatness, and image sharpness
2. Observing the Moon at night — the limb (edge) of the Moon shows chromatic aberration clearly; surface detail reveals resolution and figure quality
3. Splitting double stars — confirms resolution limit
4. Observing Jupiter and Saturn — planetary detail reveals overall optical and atmospheric performance

A well-made 60 mm f/13 refractor with a decent eyepiece shows the Moon’s craters in detail, Jupiter’s cloud bands, Saturn’s rings, the four Galilean moons, and a vast number of star clusters and double stars. It is fully capable of all navigation and practical astronomy needed by a rebuilding civilization.