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Students often meet Roger Bacon as a one-line answer: the medieval friar who invented the scientific method. That line is too simple, and believing it hides the useful part of his story. This post sets out what historians can actually say about Bacon, the rainbow measurement he is known for, a worked example you can do with the same geometry, and what his habits mean for the way you study physics.
Who was Roger Bacon?
The Stanford Encyclopedia of Philosophy entry on Roger Bacon dates his life to 1214/1220 to 1292. He was a master of arts at the University of Paris in the 1240s, one of the early teachers of Aristotle's works on nature. He then became an independent scholar who mastered the Greek and Arabic texts on optics available to him, and joined the Franciscan order in 1256 or 1257.
On the instruction of Pope Clement IV, dated 22 June 1266, he quickly wrote the Opus maius, with two related works, the Opus minus and the Opus tertium. The MacTutor biography of Bacon adds that the manuscript reached Rome, but the Pope died before seeing it.
You may read that Bacon was imprisoned by his order around 1278. MacTutor reports this, but the SEP calls it a purported condemnation and says scholars have tended to over-emphasise it. When two good sources disagree, say so rather than pick the dramatic version.
What did Bacon mean by experimental science?
Bacon's term was scientia experimentalis. In the SEP's account, he set out in his Perspectiva (1267) a model for an experimental science based on optics, and he succeeded in getting optics added to the traditional university mathematical subjects of arithmetic, geometry, astronomy and music. His method combined mathematics with careful observation, and its aim was to certify, or verify, conclusions that reasoning alone had reached.
Three cautions keep this honest:
His optics was a synthesis. The historian David Lindberg, summarised in the SEP, points out that Bacon's theories of vision were not his own creation. He drew on Greek and Islamic scholars, especially the Optics of Ibn al-Haytham.
Not every experiment was done. MacTutor notes that he carried out some systematic observations with lenses and mirrors, but many experiments described in his writings were never carried out in practice.
His experimental science included astrology. The SEP lists prediction of the future from the stars as one of its tasks. It also notes that his allowance for revealed intuition is what most clearly separates his practice from modern science.
The SEP also describes a long debate. Historian A. C. Crombie argued that experimental science began at Oxford with Robert Grosseteste and Bacon; critics replied that Crombie read modern method back into medieval texts. Bacon is part of the story of experiment, not its single inventor.
What did Bacon measure about the rainbow?
The rainbow was Bacon's first example of an experimental science. The SEP says his own important contribution was a measured value of 42 degrees for the maximum elevation of the rainbow, probably obtained with an astrolabe. His explanation of how the bow forms was not complete. The SEP credits Theodoric of Freiberg, some forty years later, with the account of a single reflection and two refractions inside each drop.
That account is the one in your NCERT Class 10 chapter The Human Eye and the Colourful World. It explains that a rainbow forms opposite the Sun, and that each droplet refracts and disperses sunlight, reflects it internally, and refracts it again as it leaves.
A worked example with Bacon's 42 degrees
The primary rainbow is a circle of radius about 42 degrees centred on the antisolar point: the point directly opposite the Sun, which lies as far below the horizon as the Sun is above it.
Question. The Sun is 30 degrees above the horizon. How high above the horizon is the top of the rainbow? When can you not see a rainbow from flat ground at all?
The antisolar point is 30 degrees below the horizon.
The top of the bow is 42 degrees above that point: 42 − 30 = 12 degrees above the horizon.
If the Sun is higher than 42 degrees, the top of the bow is below the horizon, so no primary bow is visible from the ground.
This is why rainbows are seen in the early morning or late afternoon, and almost never at noon in an Indian summer, when the Sun is high. A common mistake is to measure the 42 degrees from the horizon or from the Sun. It is measured from the antisolar point, which is roughly where the shadow of your head falls.
What can a student take from Bacon's way of working?
Check reasoning against a measurement. Bacon wanted conclusions certified by experience. After you derive a result in physics, plug in a real number and ask whether it is sensible.
Know your sources. He built openly on Ibn al-Haytham. In your notes, write where each formula comes from: a law, a definition or a derivation.
Be honest about what you have not tested. Bacon described experiments he never did. When you revise, mark which claims you have checked yourself with a problem or an activity.
Expect the explanation to come later. His number came decades before the full account of the rainbow. A correct measurement is worth keeping even when you cannot yet explain it.
Bacon's emphasis on measured quantities connects to another medieval scholar who turned change into geometry; read about him in our post on Nicole Oresme's graphs of motion. If refraction inside a droplet is hard to picture, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Next time the Sun is low after rain, stand with your back to it, estimate its height with your outstretched fist, and predict how high the rainbow should be before you look.
