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Mirror Tile Parabola

4 min read

Gluing flat mirror tiles onto a dish approximates a parabola, but each flat tile throws a patch as wide as itself plus about 0.0093 times its distance to the focus, so the tile size sets the smallest spot: 3 cm tiles on a 0.6 m focal length give a spot about 3.6 cm across. Each tile must also be aimed to within about half a degree, because a tile tilted by an angle sends its light off by twice that angle.

Part of Building Reflectors from Salvage

A mirror-tile parabola is a bowl surfaced with many small flat mirrors, each angled to aim its reflection at the same focal spot.

The Tile Sets The Spot

A flat mirror cannot focus. It sends back an image of the sun the same width as itself, widened by the sun’s own angular size, which is about 0.0093 radians (0.53°): the sun’s image at distance L has width 0.0093 × L. So each tile of width s throws a patch of width about s + 0.0093 × L at the focus.

Inputs, assumed: tiles 3 cm square; distance from tiles to focus L = 0.6 m (a 1.5 m dish with focal length 0.6 m; rim tiles are farther, the centre ones nearer).

  1. Sun-width term = 0.0093 × 0.6 = 0.0056 m = 0.56 cm.
  2. Spot width = 3 + 0.56 = 3.56 cm, about 3.6 cm.
  3. Spot area = π × (0.0178)² = 9.9 × 10⁻⁴ m².
  4. Mirror area with a fill of 85% (gaps between tiles) = 1.77 × 0.85 = 1.50 m².
  5. Concentration = 1.50 ÷ 9.9 × 10⁻⁴ = about 1,500.

Smaller tiles give a smaller spot but need more tiles and more aiming work. The parent page’s 200-500x for a 1.5 m dish corresponds to a spot of 6.7-10.6 cm across (area 1.77 ÷ C, then diameter); its “2-5 cm” spot implies 900-5,600x. These are not contradictions if the 2-5 cm is the bright core carrying part of the power and the rest spreads wider; measure your own (Accuracy & Focus Testing).

Aiming Tolerance Per Tile

A tile tilted by ε sends its patch off by 2ε radians, landing 2ε × L away from where it should.

Inputs: allowed wander of the patch 1 cm; L = 0.6 m.

  • ε = 0.01 ÷ (2 × 0.6) = 0.0083 rad = 0.48°.
  • A 5° error moves the patch by 0.6 × tan(10°) = 10.6 cm, completely off a spot a few centimetres wide, as the parent page says.

So each tile needs aiming to about half a degree, which means a bed of adhesive that stays soft while you adjust.

What You Need

  • A dish or bowl as the base
  • Mirror tiles 2-5 cm square (parent page), cut with a glass cutter
  • High-temperature RTV silicone or epoxy rated for 200°C or more (parent page)
  • Cardboard to cover tiles
  • A target card at the focus on a stick
  • Gloves and eye protection

Method: Lay And Aim The Tiles

Step 1: Cover the whole dish with cardboard. Mark the focus with a card on a stick.

Step 2: Work ring by ring from the centre outward. For each tile: spread a thin bed of adhesive, press the tile down, and while the adhesive is soft, tilt it until its patch lands on the card’s centre.

Step 3: To see one tile’s patch only, uncover that tile and keep the rest covered. One tile throws the sun’s brightness (about 1,000 W/m² times its reflectance), not a concentrated beam, but its image on the card is blinding to look at: look at the card, never into the tile, and wear eye protection.

Step 4: Leave the adhesive to cure with the dish parked off the sun, then uncover and check the combined spot.

Step 5: Seal the tile edges against moisture, which attacks the silvering.

Common Mistakes

  • Large tiles. The spot is as big as the tile.
  • Aiming all tiles to the same point on the card by eye. Use the sun’s patch itself and check at the real working time.
  • Tiles creeping as the adhesive cures. Re-check after an hour.

Safety

A half-tiled dish is a partial concentrator

Uncovered tiles already combine into a beam that can ignite tinder at the focus and burn skin. Look only at the target card, wear eye protection, keep the rest of the dish covered while you work, and cover the whole dish before you walk away. Broken mirror edges cut; tempered glass bursts when scored, so use plain mirror (Glass Salvage & Handling).

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