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Put a clear calcite crystal on a printed page and every letter appears twice. Turn the crystal and one copy swings around the other. Erasmus Bartholin described this in 1669 and showed it was a new kind of refraction. This post covers who he was, how he ruled out the easy explanations, and a short calculation that explains one of his observations.
Who was Erasmus Bartholin?
The MacTutor biography from the University of St Andrews gives the outline. Bartholin was born on 13 August 1625 in Roskilde, Denmark, and died on 4 November 1698 in Copenhagen. He studied at Copenhagen and Leiden and took a medical degree at Padua in 1654. From 1656 he was professor of geometry at Copenhagen, then of medicine, and in 1667 he became Royal Mathematician. With Ole Rømer he prepared Tycho Brahe's observations for publication.
He wrote mostly on mathematics, but MacTutor notes that he is remembered for one discovery: double refraction in crystals of Iceland spar gathered on an expedition to Iceland in 1668.
What did Bartholin see?
He published a book in 1669, and the Royal Society printed an English summary, An accompt of sundry experiments... upon a Chrystal-like Body, sent to him out of Island, in Philosophical Transactions. With it came his covering letter from Copenhagen, sending a piece of the stone to London so others could try the experiments.
The summary says the crystal was dug mainly from a mountain near a bay at about 65 degrees north. Among the observations it lists:
Objects seen through the crystal often appear double.
The two images are farther apart in a bigger piece and almost merge in a thin one.
In one position there is only a single image.
When the crystal is turned, one image stays still and the other moves around it.
How did he rule out the obvious explanations?
A double image could come from reflection off two faces. Bartholin tested this. He dulled the side faces so they could not reflect well, and the image stayed double. He broke a large crystal into small pieces, and every piece still doubled the object. Reflection could not explain either result, so he concluded there must be two refractions. He called them the usual refraction, which gives the fixed image, and the unusual refraction, which gives the moving one.
His sharpest test used light at right angles to the surface. The rules of optics say a ray falling perpendicularly on a surface passes through without bending. Looking straight down, Bartholin found that the fixed image obeyed this rule. The second image did not: it appeared some distance away even though his eye was directly above the object. The unusual refraction broke a rule every optics book of his time accepted.
A worked example: why does the gap grow with thickness?
Inside the crystal the unusual ray travels at a small angle θ to the ordinary ray. After a thickness t, the two rays are a distance s apart:
s = t tan θ
Take these sample numbers: θ = 6°, so tan θ ≈ 0.105.
For t = 1 cm: s = 1 × 0.105 = 0.105 cm, about 1 mm.
For t = 3 cm: s = 3 × 0.105 = 0.32 cm, about 3 mm.
For t = 1 mm: s ≈ 0.1 mm, too small to notice easily.
The gap is proportional to thickness, which is exactly Bartholin's note that thin pieces barely double the image.
Common mistakes to avoid:
Saying double refraction means light bends twice. It means one ray splits into two that refract differently.
Assuming one image comes from reflection. Bartholin's dulled-face and broken-piece tests rule that out.
Crediting Bartholin with polarisation. He did not explain the effect; MacTutor notes the crystal splits light into two plane-polarised beams, which was understood only later.
What came after Bartholin?
Christiaan Huygens took up the puzzle. The NCERT Class 12 chapter on wave optics notes in its box on Huygens that his Treatise on Light "brilliantly explained the double refraction shown by the mineral calcite". Our post on Huygens and the wave theory of light covers his method.
More than a century later Étienne-Louis Malus, looking at reflected light through Iceland spar, discovered polarisation by reflection. Read Malus and polarisation for that story. In the current NCERT book, section 10.7 on polarisation covers polaroids and Malus's law; double refraction itself appears only in the Huygens box, so treat it as background rather than an exam topic.
What can a student take from Bartholin's way of working?
Bartholin listed the simple explanations and tested each one before accepting a strange result. He also sent a sample abroad so others could check his claims. Both habits help in a lab practical: when a reading looks wrong, change one thing at a time to find out why, and let someone repeat it.
If polarisation and wavefronts are hard to picture, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Next step: work out s for a 2 cm crystal with θ = 6°, then write one sentence on why a thin flake of calcite barely doubles an image.
