The Gateshead projectFocal ratios for five great telescopes
Parse the list, convert the units, compute one ratio, and look for groups.
The learner copies Byrn's five telescopes into a Python list: where each stood, the year, whether its main optic was a mirror or an object glass (a large lens), its width and its length. Widths come in inches, except the Earl of Rosse's, which Byrn gives as 6 feet. Lengths come in feet, some with fractions like 17¾. The focal ratio is the length divided by the width. The first attempt divides 30 feet by 25 inches for the Newall telescope and gets 1.2, a number that means nothing, because the units never matched.
Our Python focal ratios from Byrn's list of great telescopes, 27 September 2026| Telescope (Byrn) | Main optic | Width and length | Focal ratio |
|---|
| R. S. Newall, Gateshead, 1870 | Object glass | 25 in, tube 30 ft | 14.4 (from tube) |
| US Observatory, Washington, 1873 | Object glass | 26 in, tube 33 ft | 15.2 (from tube) |
| Earl of Rosse, Parsonstown, 1842-45 | Mirror | 6 ft, focal length 54 ft | 9.0 |
| Foucault, Paris, 1862 | Mirror | 31½ in, focal length 17¾ ft | 6.8 |
| A. Ainslie Common, Ealing, 1879 | Mirror | 37½ in, tube 20 ft | 6.4 (from tube) |
Converting everything to inches fixes it: 360 inches of tube over 25 inches of lens gives 14.4 for Newall's telescope. Then the learner notices a second trap. Byrn gives the true focal length for Rosse and Foucault, but only the tube length for the other three. A tube is close to the focal length but not the same, so those three ratios are marked as approximate rather than silently mixed in. Recording which field each number came from is as important as the number.
Sorting by focal ratio reveals the pattern. The two object-glass telescopes, Newall's and Washington's, come out at 14.4 and 15.2. The three mirror telescopes sit between 6.4 and 9.0. In this list the lens telescopes are long and slim, the mirror telescopes short and wide. One computed feature separated five objects into two families that Byrn's raw figures hid. The learner writes a test with an invented telescope given in metres and centimetres to prove the conversion works in any units.
Ages 8 to 11
Measure the length and width of cardboard tubes and work out how many widths fit along each.
Ages 11 to 15
Type the five telescopes into Python, convert to inches and compute focal ratios.
Ages 15 and up
Track which figures are tube lengths, sort, and plot the two families.
Byrn's figures, our ratios
The telescope details come from Edward W. Byrn's The Progress of Invention in the Nineteenth Century on Project Gutenberg. The conversions and ratios are ours.
