Reflecting Telescope

Part of Optics

Building a reflecting telescope — using a concave mirror rather than a lens to gather and focus light, eliminating chromatic aberration while enabling larger apertures than refractors.

Why This Matters

Isaac Newton invented the reflecting telescope in 1668 to solve a problem that had plagued refracting telescopes since their invention: chromatic aberration, the rainbow fringing around objects that becomes worse at higher magnifications. A mirror reflects all wavelengths at exactly the same angle, so a concave mirror brings all colors to the same focus without chromatic aberration.

The reflecting telescope has additional advantages that make it particularly suitable for a rebuilding community: large mirrors can be made from cast metal (speculum metal historically, or glass silvered with reduced silver solution), whereas large lenses require casting large, homogeneous glass blanks with very high quality requirements. The grinding of a mirror also has self-testing methods (Foucault knife-edge test) that are more sensitive and easier to apply than equivalent lens tests.

The Newtonian reflector — the original design — is the simplest practical reflecting telescope and remains among the most popular designs for amateur astronomers worldwide. It is buildable by anyone who can grind and polish a parabolic (or spherical for shorter focal lengths) mirror.

Optical Principle

A concave mirror follows the same focal-length behavior as a converging lens. Parallel rays (from a distant star) reflect from the concave surface and converge at the focal point. The focal length of a spherical concave mirror is half its radius of curvature.

f = R/2

For a mirror with 800 mm radius of curvature: f = 400 mm.

Parabolic vs. spherical mirror: A spherical mirror focuses parallel rays from the center of the mirror correctly, but rays reflecting from the edge focus at a slightly different distance — this is spherical aberration. For long focal lengths (f/8 and longer), spherical aberration is small enough to be negligible. For shorter focal lengths (f/4-f/6), a parabolic mirror profile is needed. Parabolizing is an additional step after achieving correct spherical figure.

Newtonian design: The primary mirror at the bottom of the tube focuses light toward a secondary flat mirror at 45° near the top of the tube, which deflects the beam out the side of the tube to an eyepiece. The secondary flat mirror is small and causes minimal light obstruction.

Mirror Materials

Speculum metal: Historical mirror material before silver coating technology. Alloy of approximately 2 parts copper to 1 part tin with minor additions. Hard, brittle, takes a good polish, reflects about 60% of visible light. Cast in molds, ground, and polished. Tarnishes in damp air, requiring periodic repolishing.

Glass mirrors with metal coating: A glass blank is ground and polished (same technique as lenses), then coated with a reflective metal layer. This is the modern standard.

• Silver (chemical deposition): Silver nitrate solution reduced by glucose or formaldehyde deposits a thin silver film on clean glass. Reflectivity 94-96% for visible light. Beautiful but tarnishes in air containing sulfur compounds. Historically achievable with relatively simple chemistry.
• Aluminum (vacuum deposition): Modern standard. Requires vacuum equipment. Not achievable in a rebuilding context initially.

For a rebuilding community, the silvered glass mirror is the most practical. The Tollens’ test (silver mirror reaction) used in chemistry is the same reaction — silver nitrate + reducing sugar + glass = silver mirror.

Building a Newtonian Reflector

Step 1: Choose Mirror Diameter and Focal Length

Diameter determines light gathering (larger = fainter objects visible) and maximum resolution.

Focal length determines the tube length and magnification with a given eyepiece. Longer focal lengths are easier to figure to good quality.

For a first mirror: 150-200 mm (6-8 inch) diameter, f/6-f/8 (focal ratio). This gives:

• 150 mm f/8: focal length 1200 mm, tube ~1300 mm long
• 200 mm f/6: focal length 1200 mm, tube ~1300 mm long

Increasing diameter for same focal ratio extends tube length proportionally.

Step 2: Obtain a Glass Blank

The mirror blank should be:

• At least 25 mm thick for a 150-200 mm diameter mirror (structural support during grinding)
• Borosilicate or pyrex preferred (low thermal expansion — stabilizes quickly to ambient temperature)
• Plate glass (thick window glass) is acceptable and easier to obtain
• Must be bubble-free; inclusions less critical than in a lens (most light bounces off the surface, not through the glass) except large inclusions near the surface

Step 3: Grind and Polish the Mirror

Mirror grinding follows the same abrasive sequence as lens grinding (see grinding-technique article) with one key difference: you are making a concave surface on a flat blank.

Use a convex tool (grinding post) with the same radius of curvature as the desired mirror radius (R = 2f):

For a 150 mm f/8 mirror: f = 1200 mm, R = 2400 mm

This is a very shallow curve. The sagitta (depth of the curved surface below the flat): s = R - √(R² - (D/2)²) ≈ D²/(8R) = 150²/(8×2400) = 1.17 mm

So the center of the mirror is only 1.17 mm lower than the edge. This small sag means precise grinding is needed; even a fraction of a millimeter error significantly affects the focal length.

Procedure:

1. Work the glass blank (tool on top, glass on bottom) — the opposite of lens grinding; with tool on top, the center of the glass is ground faster, creating a concave surface
2. Progress through abrasive grades same as lens grinding
3. Polish to a mirror finish with pitch lap and rouge

Step 4: Figure Testing — The Foucault Test

The Foucault knife-edge test is the most sensitive practical test for mirror surface quality. Setup:

1. Mount the mirror on a wall
2. Place a point light source at approximately the radius of curvature distance in front (for 150 mm f/8: about 2400 mm away)
3. Hold a knife edge (razor blade) at the same distance, just to the side of the source
4. Look past the knife edge at the mirror; slowly move the knife into the reflected beam

For a perfect sphere: all parts of the mirror go dark simultaneously as the knife cuts in. Any zones that go dark before others indicate surface errors.

The Foucault test detects surface errors as small as 30 nanometers — far more sensitive than any test available to lens makers without interferometry. This is one reason amateur mirror making is more common than lens making; the Foucault test enables reliable quality control.

Step 5: Parabolizing (if needed)

For f/8 or longer focal lengths, a sphere is adequate. For shorter focal lengths (f/6 and below), the mirror needs to be parabolized:

Work the center of the mirror slightly more than the edges to change the profile from spherical to parabolic. The Foucault test reveals when the parabola is achieved — the shadow pattern changes from the “all-dark-simultaneously” of a sphere to a specific asymmetric pattern called the “donut” pattern.

Step 6: Silver the Mirror

Chemical silvering procedure (Brashear process):

1. Clean the mirror surface thoroughly — glass must be scrupulously clean for silver to adhere
2. Prepare silvering solution: dissolve silver nitrate in distilled water; add ammonium hydroxide until the brown precipitate just redissolves
3. Separately prepare a reducing solution: dissolve tartaric acid or glucose in water
4. Mix and immediately pour over the horizontal mirror surface
5. Allow to react for 10-20 minutes at room temperature; a silver film deposits
6. Rinse carefully with distilled water
7. Allow to dry completely before handling

The resulting silver film is delicate — do not wipe it. It tarnishes over months to years. Reapplication restores reflectivity.

Step 7: Build the Tube and Mount

The tube:

• Inner diameter 20-30 mm larger than mirror diameter
• Length equals focal length plus clearance for the focuser (total about f + 50 mm)
• Black interior (flat black paint or black felt lining eliminates internal reflections)
• Materials: cardboard tube, wooden staves, thin sheet metal

The Newtonian secondary holder:

• A flat elliptical mirror (minor axis = about 0.15 × D for low magnification use)
• Held by a “spider” (thin metal vanes crossing the tube) in the center of the tube
• Angled 45° to deflect light out the focuser hole

The focuser:

• A sliding tube mechanism allowing the eyepiece to move in and out for focus
• Must move smoothly without wobble
• Rack-and-pinion focuser is ideal; sliding friction fit is functional

The mount:

• Altazimuth: Simplest. Two axes, one vertical (azimuth), one horizontal (altitude). Easy to build; awkward for tracking stars.
• Equatorial: One axis parallel to Earth’s polar axis; rotating this axis at the right rate tracks stars across the sky. More complex to build but far more useful for extended observation.

Performance Expectations

Aperture	Magnification (25 mm ep)	Limiting Magnitude	Resolution
150 mm f/8 (1200 mm)	48x	~13.0	0.8 arcsec
200 mm f/6 (1200 mm)	48x	~13.5	0.6 arcsec
250 mm f/6 (1500 mm)	60x	~14.0	0.5 arcsec

A 150 mm Newtonian shows Jupiter’s cloud bands, Saturn’s rings, thousands of star clusters, nebulae, and thousands of galaxies. For a rebuilding community, it provides all the astronomical capability needed for navigation, calendar keeping, and the foundations of scientific astronomy.