Coding classes in Slough

A telescope mirror is a light bucket. Double its diameter and its area, and so the light it gathers, goes up four times. The learner converts all three openings to millimetres: Herschel's four-foot mirror is 1,219 millimetres, Caroline's six and an eighth inches is about 156, and a dark-adapted human pupil is typically about 7, a textbook figure rather than a measurement. Squaring the ratio of diameters gives the ratio of light collected. Then comes the astronomer's scale: every factor of 100 in brightness is 5 steps of magnitude, so the gain in magnitudes is 5 times the logarithm of the diameter ratio.

So the 40-foot telescope collected about thirty thousand times as much light as an eye, enough in principle to show objects more than eleven magnitudes fainter. Caroline's smaller instrument already gathered nearly five hundred times as much as an eye, which is one reason a patient observer with a modest telescope could find comets. The magnitudes also add up neatly: 6.7 plus 4.5 is 11.2, because logarithms turn multiplying into adding, and the learner's code checks that the two routes agree.

The slip is forgetting the square. Compare widths instead of areas and the 40-foot telescope seems only 174 times better, worth 5.6 magnitudes instead of 11.2. Learners test that doubling the width must quadruple the light. Our sums also ignore losses: metal mirrors, eyepieces and the air all waste some light, so real gains were smaller, and seeing fine detail is a separate matter of resolution. The record facts come from the Science Museum Group; the arithmetic is ours.

Spotting a missing square in a confident answer is a habit a Slough teenager builds by writing code in 2026. The longer argument is in why teenagers should still learn to code in 2026.