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Look through a cheap magnifying glass at a bright window and you will see coloured edges. A single lens bends violet light more than red, so the colours focus at different points. In the 1750s many believed this could never be cured in a telescope lens. John Dollond, a London optician, showed in 1758 that it could. This post covers what his experiments showed, who else has a claim to the idea, and how to design a colour-free lens pair yourself.
Why did lenses give coloured images?
The NCERT Class 12 chapter on ray optics puts it simply: thick lenses give coloured images due to dispersion. The Linda Hall Library's profile of Dollond explains that Isaac Newton and many others thought this chromatic aberration could not be removed, so most telescope makers of the 1750s concentrated on reflecting telescopes, which use mirrors. Our post on microscopes and telescopes explains why mirrors avoid the problem.
What did Dollond's experiments show?
Dollond's paper, An account of some experiments concerning the different refrangibility of light, was read to the Royal Society on 8 June 1758, with a covering letter from the telescope maker James Short, who said he had tested telescopes made this way and found them free from colours.
Dollond starts with the accepted view: two equal and opposite refractions cancel each other's colours as well as their bending, whatever the materials. He tested it. He made a wedge-shaped vessel from glass plates, put a glass prism inside pointing the other way, and filled the gap with water. He adjusted the vessel until an object seen through it was neither raised nor lowered, so the bending cancelled. The object still showed strong prismatic colours. The prism spread the colours almost twice as much as the water did. Dollond noted that this was the same experiment Newton describes in the *Opticks*, with a different result, and said he kept the apparatus to show anyone who asked.
He first tried lenses with water between two glasses, early in 1757, but the curves had to be so steep that other errors spoiled the image. Late in the year he compared kinds of glass. Venice glass and English crown spread colours least, plate glass more, and white flint the most. Grinding wedges of crown and flint, he found a pair that cancelled each other's colours when the flint's bending was to the crown's nearly as 2 to 3.
That told him the design: a convex lens of crown glass, which does most of the bending, with a concave lens of flint. The steep curves still caused blurring, which he cured by choosing the surfaces so that the two lenses' errors were equal and opposite.
Who really invented the achromatic lens?
The Linda Hall Library account sets out the dispute. Around 1730 Chester Moor Hall (1703-1771) had the idea of a flint and crown pair and commissioned lenses, though he did not bring an achromatic telescope to market. The Swedish mathematician Samuel Klingenstierna had worked out the curvatures needed and sent his results to Dollond in 1755.
Dollond patented his lens. After his death on 30 November 1761, his son Peter enforced the patent, and London instrument makers challenged it in court, arguing that Hall was the true inventor. The challenge failed, on the reasoning that Hall had not brought his lens to market. The patent ran until 1772. When Jesse Ramsden later charged that Dollond had taken Hall's idea, Peter published a defence of his father in 1789. Historians still argue about credit; a whole book, Francis Watkins and the Dollond Telescope Patent Controversy (2016), is given to it. The Linda Hall account finds general agreement that Dollond built his lens independently from his own experiments.
Worked example: designing a colour-free doublet
For a thin lens of power P and glass of dispersive power ω, the spread in power between violet and red is ωP. Two thin lenses in contact are free of this colour spread when
ω₁P₁ + ω₂P₂ = 0, while the total power is P = P₁ + P₂.
Sample numbers: crown glass ω₁ = 0.020, flint glass ω₂ = 0.030, and you want a doublet of focal length +50 cm, so P = +2.0 D.
From the colour condition: P₂ = −(ω₁/ω₂)P₁ = −(2/3)P₁.
Total power: P₁ − (2/3)P₁ = P₁/3 = 2.0 D, so P₁ = +6.0 D (f₁ = +16.7 cm).
Then P₂ = −4.0 D (f₂ = −25 cm).
Check colour: 0.020 × 6.0 + 0.030 × (−4.0) = 0.12 − 0.12 = 0.
Each lens is much stronger than the pair, which is the steep-curve problem Dollond met. The condition is not named in the JEE (Main) 2026 syllabus, but it uses only the combination of thin lenses in contact, which is. For more on that rule, see our post on lens combinations and the lens maker's formula.
Which mistakes should you avoid?
Adding focal lengths. Powers add; focal lengths do not.
Dropping the sign. The flint lens is concave, so its power is negative.
Using one glass for both. If ω₁ = ω₂, the condition forces P = 0: no colour, but no focusing either.
Confusing ω with n. Dispersive power measures spread of colours, not how much the glass bends light.
If you get stuck on the set-up of a lens problem, the Fermi Problem Library has a step-by-step solver that explains the reasoning rather than printing an answer.
What can a student take from Dollond's way of working?
Re-test what everyone accepts. Dollond wrote that the accepted rule had never been confirmed by a clear experiment, so he made one.
Expect one fix to expose the next problem. Removing colour brought steep curves; he solved that with a second free choice.
Keep your evidence. He offered his apparatus to anyone who doubted him.
Try it now: redesign the doublet for a focal length of +40 cm with the same two glasses, and check that the colour terms cancel.
