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Pass sunlight through a narrow slit and a good prism, and the rainbow you see is crossed by many thin dark lines. The man whose name they carry was trying to solve a practical problem: how to make perfect telescope lenses. This post tells his story, explains why fixed lines mattered to a glassmaker, and works through the grating calculation he made famous.
Who was Joseph von Fraunhofer?
The Neue Deutsche Biographie entry, Germany's national biography, gives his dates: born in Straubing, Bavaria, on 6 March 1787 and died in Munich on 7 June 1826. His father was a glazier. The older entry on the same page records that he lost his mother at 11 and his father at 12, and that in 1799 his guardian sent him to Munich as an apprentice to a mirror maker who thought books were a waste of time.
In July 1801 the house he lived in collapsed. He was the only person pulled out alive, after four hours of digging. The Elector of Bavaria gave him a gift of money, and a wealthy patron, Joseph von Utzschneider, noticed him. Fraunhofer spent part of the money on a lens-grinding machine. In 1806 he joined an instrument-making institute, and by 1809 he ran its optical workshop at Benediktbeuern, where a glass furnace made the raw glass. He was ennobled in 1824, which is why he became "von" Fraunhofer, and was only 39 when he died.
What problem was he trying to solve?
Good telescope lenses pair two kinds of glass, crown and flint, so that their colour errors cancel. In Fraunhofer's day lens makers calculated roughly and then corrected by trial and error. The NDB entry says Fraunhofer wanted to calculate lenses exactly and make them exactly. That needed two things: glass that was the same all the way through, and precise values of how strongly each glass bends each colour.
The second part was the hard one. A colour is not a sharp target. Every attempt to cut a single colour out of a spectrum gave a smudge, so his measurements of bending had no fixed reference point.
What did he notice in sunlight?
Around 1814, the NDB records, Fraunhofer found the dark lines in the solar spectrum. William Hyde Wollaston had seen a few of them in 1802. Fraunhofer's step was to realise that the lines always sit in the same place in the spectrum, so they can serve as markers for measuring refraction and dispersion. He labelled the strongest lines with capital letters and chose two of them for his lens calculations. The lines also let him check each batch of molten glass and improve it.
He published this in 1817, in a long paper whose title translates as Determination of the refractive and dispersive power of different kinds of glass, for the improvement of achromatic telescopes. The purpose is right there in the title. The dark lines were a measuring tool before they were a mystery.
Why the lines exist was explained in 1860 by Gustav Kirchhoff, who showed that cooler gases absorb the same wavelengths they emit. Our post on Gustav Kirchhoff and the birth of spectroscopy tells that part.
How did he measure the wavelengths?
From 1817, the NDB entry continues, Fraunhofer studied diffraction, first with a single slit and then with gratings he made himself by scratching lines into glass with a diamond. In the spectra from these gratings he found his familiar lines again, and he measured the wavelengths of lines A to H with an accuracy not beaten for about 40 years. A prism shows how much glass bends a colour; a grating gives the wavelength itself.
Worked example: a grating and the D line
Today we know the D line is a close pair of lines from sodium. The NIST atomic spectra handbook lists them at 588.995 nm and 589.592 nm. Take a grating with 500 lines per millimetre, light falling straight on it, and use λ = 589 nm for the pair. The grating condition is d sin θ = nλ.
Spacing. d = 1 mm / 500 = 0.002 mm = 2000 nm.
First order. sin θ = 589 / 2000 = 0.2945, so θ ≈ 17.13°.
Second order. sin θ = 0.589, so θ ≈ 36.09°.
Third order. sin θ = 0.8835, so θ ≈ 62.07°.
Fourth order. sin θ = 1.178, which is impossible, so there is no fourth order.
Now run it backwards, as Fraunhofer did. If you measure the first-order D line at 17.1°, then λ = 2000 × sin 17.1° ≈ 588 nm.
How far apart are the two sodium lines in first order? Δθ ≈ Δλ / (d cos θ) = 0.597 / (2000 × 0.956) ≈ 3.1 × 10⁻⁴ rad, about 0.018°. Splitting the pair needs a fine grating and careful angle measurement.
Common mistakes with grating questions
Using lines per mm as d. d is the spacing, the reciprocal of lines per unit length. Convert to the same unit as λ.
Forgetting the order limit. If nλ/d is more than 1, that order does not exist.
Mixing up grating and prism. A grating sends red furthest; a prism bends violet most.
Grating spectra are not named in the JEE (Main) 2026 syllabus, but single-slit diffraction and the prism are, and the reasoning is the same path-difference idea. Check the syllabus for your exam year. Our guide to single-slit diffraction problems is the place to practise. If path differences are hard to picture, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
What can a student take from how Fraunhofer worked?
Find a fixed reference. His measurements improved only when he had markers that never moved.
Measure the thing you care about directly. He went from prisms, which compare, to gratings, which give wavelengths.
Let practical problems lead you. Better telescopes, not curiosity alone, led him to the lines.
Practice routine: redo the worked example for a grating with 300 lines per millimetre, find the highest order for λ = 656 nm, and then explain in two lines why a grating gives a wavelength but a prism does not.
Next step: take any diffraction grating question from your textbook and write d in nanometres before you do anything else.
