Glass is a melt that stiffened without crystallizing. Its recipe and its cooling set how long it stays workable, the stress it keeps, how it bends light, how it resists water and its color. This page follows one piece from batch to showroom and computes each from measurements or a model it names.
Color comes first because it is the easiest to see. Each piece below is colored by what it absorbs from white light, and the later stages show where that rule fails.
Cool most liquids and at one temperature their atoms drop into a repeating crystal. Cool a silicate melt and it only gets stiffer, smoothly, until it is too stiff to rearrange at all. What is left keeps the liquid's disorder and gains a solid's rigidity. Glass has no melting point, and everything a glassblower does depends on that slow stiffening.
Silica is the network former. Each silicon sits inside four oxygens, a tetrahedron, and each oxygen is shared by two tetrahedra: a bridge. In quartz the tetrahedra join in a repeating pattern. In silica glass they join just as firmly, corner to corner, but the rings they close have five, six or seven members in no order. W. H. Zachariasen proposed this picture in 1932 from the rules an oxide must obey to form a glass, eighty years before a sheet of silica glass two atoms thick was imaged atom by atom and looked like his drawing (Huang et al., 2012).
Pure silica glass is too stiff for any studio furnace. Soda is the flux. Each Na₂O brings one more oxygen, which cuts a bridge into two non-bridging oxygens with a sodium ion beside each. Fewer bridges make a looser network that flows at lower temperature. A soda–silica glass also dissolves in water; it is sold as water glass. Lime is the stabilizer. A Ca²⁺ ion holds two non-bridging oxygens at once and moves far less readily than sodium, so the glass stops leaching.
Model. Drawn in two dimensions, as Zachariasen drew it: triangles stand in for tetrahedra, with three corners instead of four. The glass is made from the crystal by Stone–Wales bond switches and spring relaxation, after Wooten, Winer and Weaire's method for amorphous silicon (1985); it is a sketch of that method, not its energy-minimised result. The drawing cuts the same fraction of corners that the composition does in three dimensions, NBO/T = 2x / (1 − x) for a mole fraction x of modifier oxide, with potash counted alongside soda and alumina ignored. Sodium and calcium ions are placed in the gap they open, not at modeled sites. The standard glass is NBS glass No. 710: 70.5 SiO₂, 8.7 Na₂O, 7.7 K₂O, 11.6 CaO by weight.
The atoms of a liquid are always rearranging, and the time that takes, the relaxation time, grows with viscosity. Cooling gives them less time at each temperature. At some point the melt can no longer keep up and its structure freezes in as it was. That point is the glass transition, Tg, and it belongs to the cooling as much as to the glass: cool faster and the structure freezes in hotter, looser and larger. A quenched glass and a slowly cooled one of the same batch differ in density and refractive index.
Model. Relaxation time τ = η / G∞ (Maxwell), with G∞ ≈ 30 GPa as in Zanotto (1998) and η from the curve below. The melt falls out of equilibrium where q · τ · |d ln τ / dT| = 1: where the time to cool through one e-fold change in τ has grown as long as τ itself. At 10 K/min that gives Tg near 552 °C, close to the measured annealing point of 546 °C, as the usual rule of thumb (Tg near η ≈ 10¹² Pa·s) expects. Below 560 °C the viscosity fit is extrapolated, so the slow end of the slider is the least certain. Volumes are schematic: the liquid is drawn expanding three times as fast as the glass, and the transition is smoothed over a few kelvin. Crystallization, which a very slow cool through the liquidus range invites, is not modeled here; the Structure Lab runs it with atoms.
Viscosity is the number the studio works by. Between the melting point and the strain point it rises by more than twelve orders of magnitude, and every step in making a piece sits somewhere on this one curve. Glassmakers name its points: melting, where the melt is runny enough for bubbles to rise out; working, stiff enough to hold a shape on the pipe; softening, where a hanging fiber stretches under its own weight; annealing, where stress relaxes in minutes; and strain, where it takes hours and below which nothing moves at all on a human timescale. For scale, water is 10⁻³ Pa·s.
Measured, then fitted. The curve is the Fulcher fit to NBS standard glass No. 710, log₁₀ η [poise] = -1.626 + 4239 / (T − 265.7) with T in °C, fitted to measurements from 560 to 1400 °C by Napolitano and Hawkins (1964); it is drawn solid where it was fitted and dashed where it is extrapolated. Rings are the average of the laboratories' measured softening (724 °C), annealing (546 °C) and strain (504 °C) points. The fit runs 25 °C hot at the strain point, the usual sign that a Fulcher curve rises too steeply below its range. The furnace and glory-hole marks are typical studio temperatures, not measurements, and studio color glasses each have their own curve. The sag time, η / (ρgR) for a 10 cm gather of density 2.5 g/cm³, is an order of magnitude, not a prediction. The gather is drawn in its cold color, clear glass with its trace of iron; how it glows is stage 04's subject.
A popular story says medieval windows are thicker at the bottom because glass is a very slow liquid that has run downhill. The curve above cannot answer the question: its fitted form goes to infinity at 266 °C, far above room temperature. Zanotto (1998) instead extrapolated the gentler curve of germania glass, which stiffens more slowly on cooling than window glass and so gives a lower bound, and found a room-temperature relaxation time near 10³² years, against a universe about 10¹⁰ years old. By his estimate a medieval glass would have to be held near 414 °C to flow noticeably in 800 years. Gulbiten, Mauro and colleagues (2018), working from the composition of 13th-century glass at Westminster Abbey, found it could flow about a nanometer in a billion years.
The thick bottoms come from how the glass was made. Window glass was blown into cylinders, split and flattened by hand, so panes came out uneven, and glaziers often set the heavy edge down.
Zanotto, Do cathedral glasses flow? ↗ Gulbiten, Mauro, Guo and Boratav, Viscous flow of medieval cathedral glass (2018) ↗ Zachariasen, The atomic arrangement in glass (1932) ↗ Wooten, Winer and Weaire, Computer generation of structural models of amorphous Si and Ge (1985) ↗
Each Na₂O brings an extra oxygen that cuts a bridge between two tetrahedra into two non-bridging oxygens. With fewer bridges the network is looser, so it flows at lower temperature.
A Ca²⁺ ion holds two non-bridging oxygens at once and moves far less readily than Na⁺, so the glass stops leaching in water. Soda–silica glass alone dissolves; it is sold as water glass.
The one cooled faster. Tg is where the melt's relaxation time outgrows the time cooling allows, so faster cooling makes the structure freeze in sooner, at a higher temperature, looser and less dense.
Melting (bubbles rise out), working (holds a shape on the pipe), softening (a hanging fiber stretches under its own weight), annealing (stress relaxes in minutes), strain (stress takes hours; below it nothing moves on a human timescale).
No. Extrapolated viscosity gives room-temperature relaxation times near 10³² years (Zanotto 1998), and Westminster Abbey glass would flow about a nanometer in a billion years (Gulbiten et al. 2018). The thick bottoms come from hand-flattened cylinder glass set heavy edge down.
Glass starts as sand, soda and lime, and sand carries a trace of iron. Look through a windowpane face on and you cross a few millimeters of it, too little for the iron to show. Look into the edge and you cross the whole width of the sheet. Over that distance the same faint absorption adds up to a visible green.
Beer–Lambert. Absorption compounds with distance: if 1 mm lets through 99% of some color, 50 mm lets through 0.99⁵⁰, about 60%. Thickness and concentration play the same role, which is why the edge and a heavily dosed batch look alike.
Iron is a trace. The batch itself is mostly three oxides: silica, the network former; soda, the flux that breaks the network so it melts at a temperature a furnace can reach; and lime, which mends enough of it that the glass does not dissolve in rain. Every other glass on this page is a variation on that recipe, and each change moves the properties the later stages depend on: how long the gather stays workable, how strongly a cut piece bends and splits light, how much stress the lehr has to take out, and which way the iron leans.
Pick a glass, or move one oxide at a time. Silica makes up the rest. The dashed curve and the open dot are window glass, for comparison.
Why lime. Water attacks a soda–silica glass in two steps. First its hydrogen ions trade places with the sodium ions held beside non-bridging oxygens: sodium leaves, and the surface fills with Si–OH. The sodium hydroxide this leaves in the water raises its pH, and in alkaline water hydroxide ions break the Si–O–Si bridges themselves, so the network goes into solution (Bunker 1994). With enough soda the sodium sites join into continuous paths through the network, the channels of Greaves's modified random network, and the exchange runs on inward instead of stopping at the surface. A Ca²⁺ ion holds two non-bridging oxygens at once and moves far more slowly than Na⁺, so it blocks those paths. The plot below puts every batch on one axis: the soda its other oxides have not taken up.
Model, fitted here. The crosses are the boiling-water tests of W. E. S. Turner's Department of Glass Technology at Sheffield, set up in 1915: 53 glasses measured between 1919 and 1929, among them Dimbleby and Turner's series of 1926, read from SciGlass. Ten grams of grains about half a millimeter across were boiled for an hour in water and weighed; Turner put the repeatability at 5 to 10% (International Critical Tables, 1927). In each series one oxide replaced soda at about 75 mol% silica. The curve is a fit made here, not a published model. It assumes every oxide acts by cancelling soda: one mol% of lime cancels 1.1 mol% of soda, lead oxide 1.0, magnesia 1.5 and alumina 2.3, more than the one Na₂O per Al₂O₃ that charge balance alone would take up. Boric oxide cancels 0.8 at first and less as it grows, until past about 24 mol% it adds to the attack. Against the soda left free, the loss is S-shaped: below about 12 mol% the test reads its floor of 0.2%, above it the loss rises tenfold for every 5 mol%, and at about 26 mol% half the grains dissolve. A soda–silica glass with 32 mol% soda dissolved completely. The fit misses a measured glass by a median factor of 1.26, and 1.37 when that glass is left out of the fit. Its limits: each oxide's number rests on one series from one laboratory; lime and magnesia were never measured together, as they are in float glass; potash appears in no series and is counted as soda; and the test cannot tell durable glasses apart, since all of them sit on its floor. The modern grain test, ISO 719 (2 g of 300–500 µm grains, an hour in water at 98 °C, the leached alkali titrated with acid), sorts them into five classes; Fluegel fitted a model to 561 such measurements, but its coefficients are in a spreadsheet the bench could not download.
How this was computed. SciGlass keeps each paper's original table as text. A script read the tables from Turner's laboratory that used the one-hour boil, kept the glasses made only of this bench's oxides, and fitted the curve by least squares on the logarithm of the loss, with one scale factor for each of the three grain sizes. The script is fit_durability.py, and the 53 glasses, with their compositions and measured losses, are in durability.json. Run on the same SciGlass copy, the script reproduces the coefficients the page uses, and a test checks that the page's code gives the same misses.
Inside the network. Every curve above traces back to one count: how many of each silicon's four oxygens still bridge to another tetrahedron. A silicon with n bridges is called Qⁿ. Silica is all Q⁴. Each oxygen a modifier brings cuts one bridge into two non-bridging oxygens, and nuclear magnetic resonance of ²⁹Si can count the result. The diagram follows the cuts for this batch's modifiers, frozen in at its own annealing point.
The network model. The diagram reimplements the statistical-mechanics model of Bødker, Sørensen, Mauro and Smedskjaer (2019). Each new non-bridging oxygen lands on a silicon of kind n with a probability proportional to how many there are and to a Boltzmann factor, exp(−Hn/RTf), where Hn is a relative enthalpy fitted to ²⁹Si NMR of soda–silica and potash–silica glasses (Maekawa and colleagues, 1991) and Tf is the temperature at which the structure froze. A higher Tf means a more random network. Here Tf is the bench's own annealing point, 1012 Pa·s, from the viscosity model above; mixed modifiers average their preferences by amount, as in the StatMechGlass paper (2022). The equations are rewritten from the papers, not taken from StatMechGlass's code. Three choices are the bench's own and are labeled as such. Alumina is taken to claim one modifier oxide per Al₂O₃, alkali first, to balance its tetrahedra. Boron claims modifier next, turning BO₃ triangles into BO₄ tetrahedra, up to Dell, Bray and Xiao's limit of 0.5 + K/16 modifier per B₂O₃, with K = SiO₂/B₂O₃ (1983), every modifier counted alike. Lime, magnesia and lead oxide, for which no fitted enthalpies were found, are counted as soda; small, highly charged cations such as Ca²⁺ and Mg²⁺ are generally reported to leave a broader spread of Qⁿ than soda does (a general account, not checked against a cited source here), so for lime-rich glasses read the Q³ peak as an upper bound. The Structure Lab sets the model beside the NMR it was fitted to. How this was computed: the model is qn.js, its numbers qn.json; modifier is added a hundredth of a non-bridging oxygen per silicon at a time, and tools/qn/validate.mjs prints every figure quoted here.
Models, not measurements. Each property comes from a published composition model: an equation fitted by its authors to many measured glasses, good inside the range it was fitted to and a guess outside it. Viscosity is Fluegel's (2007) fit to more than 2,200 measured silicate glasses, which gives the temperatures at 101.5, 106.6 and 1012 Pa·s; a Fulcher curve is drawn through the three. His data span about 42 to 89 mol% silica, and the bench warns when a batch leaves that range. With his coefficients the bench reproduces the paper's own predictions for its five standard glasses within half a degree. His data stop short of the magnesia-rich sodium aluminosilicates that fill SciGlass from patents of 2011–2016, and on those melts his model runs 20 to 80 °C cold. The bench adds one term of its own, alumina times magnesia, fitted to 2,971 melts in SciGlass, and draws Fluegel's curve faint and dashed beside it whenever that term moves the curve by 2 °C or more. The term removes the bias, not the scatter: alumina-rich melts still miss by about 30 °C either way at the median. Index and Abbe number use Young and Finn (1940), who found specific refraction and dispersion additive by weight; the index also needs a density, from a fit made here to 7,452 measured room-temperature densities in SciGlass. Tested on laboratories it was not fitted to, it misses by a median 0.017 g/cm³, but it puts Pyrex-type borosilicate about 0.035 heavy, and so its index 0.005 to 0.008 high. Expansion uses Appen's additive factors, which put window glass at about 9 ppm/K against Pilkington's measured 8.3. Lehr stress is scaled by expansion alone, with stiffness held at window glass's. The temperature jump a sheet survives is Pilkington's mean breaking strength for annealed float glass, 41 MPa, over its thermal stress of 0.62 MPa per °C, scaled the same way: an order of magnitude, not a rating, since real breakage depends on edges and flaws. Iron uses the composition terms of Sack and colleagues (1980), fitted to lavas, not to soda glass, and blind to lead and boron: read it for direction, not degree. The furnace is held fixed so window glass keeps the 60:40 split the slab above uses.
And the measurements. The crosses come from SciGlass, a database of about 420,000 glasses gathered from the literature over decades and released openly in 2019 (ODbL; the site's extract, bench.json, is under the same license). The bench keeps the 12,513 glasses made only of its nine oxides, inside Fluegel's range, that have a measured viscosity, index, Abbe number or liquidus temperature. Run on each of the 6,172 with a viscosity, the model's median miss is about 9 °C for soda- and potash-lime glasses, 17 °C for lead glasses, 25 °C for borosilicates and 29 °C for glasses with 5 to 10 mol% alumina, with no lean either way (before the alumina–magnesia term, which was fitted to these same melts, the alumina glasses came out 20 °C too cold); the index model misses by 0.003 for soda-lime glass and 0.004 overall. This is not an independent test: Fluegel fitted his model to published measurements, many of them the same ones SciGlass collects. The database also carries mistyped entries, so a lone cross far from its neighbors may be an error rather than a discovery.
Model. The dotted curve, the liquidus line and the hollow square come from GlassNet (Cassar 2023), a neural network trained on SciGlass that predicts 85 properties from composition alone, with no physics inside it. It is GPL-licensed and its weights are large, so it does not run in this page: a GitHub Actions job runs it (GlassPy 0.6.0, tools/glassnet/glassnet.py) and saves only its numbers, in glassnet.json.
What was run. GlassNet at each of the five presets, set exactly as the sliders set them, and along each slider's whole range in 41 steps from each preset. For your batch the page starts from the preset you last picked and adds the change each moved slider makes on its own. That is exact with one slider moved. With two or three moved it ignores how the oxides interact, and against GlassNet itself it strays a median 18 °C at the working point and 39 °C at the liquidus, and 128 and 175 °C at the 95th percentile. GlassNet predicts each viscosity level separately, so its curve can bend back on itself; where it does, the page lifts the hotter level to meet the cooler one.
Checked against measurements. Run on the 12,513 SciGlass melts above, GlassNet misses measured viscosity temperatures by a median 20 °C, where the bench's own model misses by 16 °C, and the index by 0.005 against 0.004. Its liquidus misses by a median 48 °C, reading about 10 °C cold. None of this is an independent test: 10,465 of those melts were in GlassNet's own training set. On the 2,048 not found in its training set, the misses are much the same (viscosity 23 °C against the bench's 19, liquidus 48 °C).
Known misses. The liquidus is the temperature at which the first crystal appears, and which crystal that is (devitrite, wollastonite, tridymite and others in soda-lime glass) changes abruptly with composition. A smooth network rounds those corners off, so the liquidus is the least trustworthy number here. GlassNet is also touchy to traces: the 0.04 mol% of iron in a real float glass moves its liquidus by tens of degrees, which is why the presets were run as the sliders set them, without iron.
The same iron can sit in the melt as Fe²⁺ or Fe³⁺, and the two absorb differently. A furnace starved of oxygen pushes iron toward Fe²⁺, which absorbs red and leaves glass blue-green. Plenty of oxygen favors Fe³⁺, which absorbs mostly in the ultraviolet and only weakly in the violet, green and red, and leaves it a pale yellow-green. Nothing was added; only the atmosphere changed.
Not shown: the brown of beer bottles. Strongly reduced glass with sulfur forms an iron–sulfur chromophore, a different absorber from either ion. This model has only the two ions.
A glassblower calls a glass long when it stays workable over a wide span of temperature after it leaves the glory hole, and short when it sets soon after. Every glass passes through the same viscosities as it cools, from about 10³ Pa·s, where it is gathered and blown, to 10⁶·⁶ Pa·s, where it no longer sags under its own weight. What differs is how many degrees that takes.
Part of the answer is where a glass sits on the temperature scale, and part is the shape of its curve. To separate the two, C. Austen Angell plotted each liquid's viscosity against its own glass transition divided by temperature, Tg/T. On that axis every curve reaches 10¹² Pa·s at Tg/T = 1 and they differ only in how they get there. A liquid whose curve is close to a straight line is called strong; one that stays runny until near Tg and then stiffens steeply is called fragile. The slope where the curve meets Tg is the fragility index, m.
Hold the glass transition fixed at window glass's and change only the fragility. The span between the working and softening points shrinks as m rises: a fragile glass stays fluid longer as it cools and then sets over a few degrees.
Start from window glass, as the stage 01 bench does, and put one oxide in place of silica. The bold line is ViscNet's prediction with its own spread outlined; the dashed line is the bench's viscosity model, read for its slope at Tg. Faint lines are the other oxides.
Models, and what they rest on. Every curve here is the MYEGA equation of Mauro and colleagues (2009), log₁₀ η = log₁₀ η∞ + (12 − log₁₀ η∞)(Tg/T) exp[(m/(12 − log₁₀ η∞) − 1)(Tg/T − 1)], which ties the rise of viscosity on cooling to the loss of configurational entropy (the Adam–Gibbs picture) and needs only three numbers. With η∞ fixed, the straight line is the least fragile curve the equation allows, m = 12 − log₁₀ η∞. The predictions come from ViscNet (Cassar 2021), a small neural network that outputs those three numbers from composition, trained on SciGlass; it runs in GlassPy, which is GPL-licensed, so the site ships only its numbers (viscnet.json), computed once at build time. The crosses and the measured m are fits of the same equation to melts in SciGlass made only of the bench's nine oxides (fragility.json, ODbL). SciGlass stores each melt's curve as temperatures at whole decades of viscosity interpolated from the source's own points, and the fit uses those. Each fit holds log₁₀ η∞ at −2.93 Pa·s, the value Zheng and colleagues (2011) found common to silicate liquids, and fits Tg and m; a melt is kept if it has five or more points, reaches 10⁹ Pa·s and goes below 10⁶ Pa·s, and the equation follows it within 0.15 decades. The words long and short are glassblowers' terms, not defined quantities; reading them as the working-point to softening-point span is this page's choice.
Strong and fragile. Angell introduced the classification in the 1980s and set out the plot in its usual form in Science (1995). Fragility in this sense is about the liquid's viscosity, not about how easily the cold glass breaks.
builds on01 the batch
Transition-metal ions are the most common colorants. Their outer d-electrons can be lifted between energy levels by light of particular colors, and the surrounding glass sets the spacing. Cobalt takes the orange and red. Copper takes the red end. Chromium takes violet and red, which leaves a green window. Pick a rod to see which part of the spectrum it removes.
Read: transition metal colorants → Rare-earth colorants →
A rod's color is not the color of the finished piece. Melted onto a gather and blown out, the same glass becomes a wall that is thin at the rim and heavy at the foot, and every part of it is colored by its own thickness. This is the windowpane edge from the batch, spread over a whole object.
The bowl is drawn in half section, the way a glass drawing shows it. On the left the near half is cut away: the cut wall is tinted by its thickness, and behind it you see the inside of the far wall. On the right is the bowl as you would see it held up to the light. It uses the rod and amount chosen above.
Glassblowers get around this by casing. They put the color on as a thin skin of strong glass and blow clear glass inside it, so every part of the piece crosses about the same amount of color however unevenly the clear behind it was blown. Switch to cased and the foot stops going dark.
Cut to clear. A cased skin can be ground through in the cold shop to the clear glass beneath, which is how overlay glass gets its windows: the color is only half a millimeter deep.
Model. The bowl is a solid of revolution 170 mm across and 100 mm tall. Its wall runs from 1.1 mm at the rim to about 6 mm at the base and sits on a 6 mm floor, all scaled by the slider; the 8 mm foot is a separate gather and stays fixed. On the right each point's color is Beer–Lambert through the glass a straight ray crosses there, front wall and back. On the left the cut wall is tinted by its thickness at right angles to the surface, and the floor and foot by the whole stack a ray straight up from the table would cross. Each rod is dosed so a 3 mm solid wall passes about 60% of daylight at amount ×1, since colorants differ in strength by an order of magnitude. The cased skin is 0.5 mm at six times that concentration, so face on it holds the same colorant as a 3 mm solid wall. The cane is 12 mm across with the same 0.5 mm skin, and the slice is 3 mm thick. Refraction at the curved surfaces, which bends real outlines, is ignored.
Its outer d-electrons, lifted between energy levels by light of particular energies. The surrounding glass sets the spacing of those levels, so the same ion absorbs differently in different hosts.
Cr⁶⁺ takes the violet edge and Cr³⁺ takes blue and orange-red, so what passes is the window between them, in the green.
Each point is colored by the glass a ray crosses there (Beer–Lambert), and the rim is blown thinnest while the foot is heaviest. Casing puts the color in a thin skin of strong glass, so every part crosses about the same amount of color however the clear inside was blown.
A ray through the middle of solid cane crosses the most glass. In cased cane the color is only in the skin: a ray down the middle crosses the skin twice, but a ray near the edge runs along the skin for a long way.
It turns blue-gray. Its absorption bands are narrow, and a tri-phosphor tube puts its light in a few narrow lines that the bands hit unevenly, so a different share of the lamp survives. The showroom stage shows it.
Pull a gather from the furnace and the color is gone: cobalt and copper both come out glowing orange. The reason is a law Gustav Kirchhoff published in 1860. At a given temperature, a body gives out at each wavelength exactly the share of a black body's light that it would absorb there. Cold, cobalt glass is blue because it takes away orange and red. Hot, it gives orange and red back. The blue it lets through it hardly emits, and at 1150 °C a black body has almost no blue to give anyway. Every colorant glows in its own absorption bands, so the color at heat is set by the temperature and the absorption bands together, and says little about the color the glass will have cold.
Below about 525 °C, the Draper point, even a black body's glow is too faint to see, and the colorant finally shows. Above it, a glassblower works a color that does not show until the piece cools.
How the glow is computed. The glow is Planck's law times the gather's emissivity, integrated against the color-matching functions. Its strength is that luminance on a log scale, so it fades the way the eye sees it fade, times the cube root of how much of a black body's light the glass gives (Stevens's exponent for brightness), so a dimmer emitter looks dimmer at the same heat.
Work a gather yourself in the forming lab: sag, blow, swing and cool it →
Everywhere else on this page, glass is colored by what it takes away. In the glory hole the same spectrum runs the other way. Below, three gathers share one temperature. Each card shows the gather cold on the light table, then hot in the dark, then its spectrum: a black body at that temperature on top, what this glass gives out underneath, and the line is its emissivity, one minus its transmission.
Clear glass glows least. It absorbs almost nothing you can see, so it gives almost nothing back. Beside cobalt, which absorbs nearly all of the orange and red a black body sends, a clear gather is dim, and its glow fades from sight well above the Draper point. Its heat leaves instead as infrared beyond the visible, where every glass absorbs.
And inside the glory hole? Hold any gather in a chamber whose walls are at its own temperature and it vanishes. What it fails to emit, it lets through from the wall behind, and emission plus transmission add up to the wall's own black-body light. Only out in the dark shop does a gather show its own glow. This follows from the law alone.
Sources. G. Kirchhoff, "Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht", Annalen der Physik 109 (1860) 275–301; Balfour Stewart reached a version of it independently in 1858 (D. M. Siegel, "Balfour Stewart and Gustav Robert Kirchhoff: Two Independent Approaches to 'Kirchhoff's Radiation Law'", Isis 67, 1976). Kirchhoff's first step, in October 1859, was the sodium line: a sodium flame in the path of sunlight darkened the solar D lines, because the flame absorbs exactly where it emits ("Über die Fraunhofer'schen Linien", Monatsberichte der Berliner Akademie, 1859, 662–665). That is the same doublet the glasses below are built to stop. For glass itself, R. Gardon, "The Emissivity of Transparent Materials", J. Am. Ceram. Soc. 39 (1956) 278–285, works out the emissivity of transparent sheets from their thickness and absorption: the familiar total emissivity of window glass, about 0.91, holds only for sheets thick enough, from 3/16 in at 200 °C to as much as 8 in at 1000 °C, and a 3/16 in sheet at 1000 °C has an emissivity of only 0.59.
Model. Emissivity is 1 − T(λ) for the path through the gather, the same path whose color the cooled gather shows; reflection at the surface (about 4% on each side) is ignored, and so is the flame's light scattered in the glass. Clear glass is a trace of ferrous and ferric iron at an illustrative level, not a measured batch, and the colorant spectra are the page's illustrative ones. The "fades from sight" temperature is where the glow reaches the bottom of this page's strength scale, which puts a black body's fade at about the Draper point; it is a comparison, not a measured visibility threshold.
Not modeled: absorption changes with heat. The spectra here are room-temperature spectra. At working heat, ligand-field bands broaden and shift, the balance between Fe²⁺ and Fe³⁺ moves with temperature, and the ultraviolet edge creeps toward the visible, so a real hot gather, clear ones included, absorbs and therefore glows more than shown (direction from general physics; size unverified). Band-gap colors move most: a semiconductor's gap narrows as it heats (Y. P. Varshni, "Temperature dependence of the energy gap in semiconductors", Physica 34 (1967) 149–154), so the cadmium yellows and reds absorb further toward the red when hot than they do cold.
The yellow glare around a hot gather comes from the flame, not the glass. Drag the glasses across the scene above. Soda in the glass boils off into the flame, and every sodium atom there emits at two wavelengths, 589.0 and 589.6 nm. The two lines are bright enough to hide the glass behind them. Didymium lenses absorb a narrow band at those wavelengths, so the flare disappears, the glass shows again, and most other light passes.
Didymium was named in 1841 as one element, the "twin" of lanthanum. In 1885 Carl Auer von Welsbach split it into two, neodymium and praseodymium, and the lens needs both: neodymium's strongest band sits at 585 nm and praseodymium's at 590 nm, so together they cover the doublet.
Infrared. Over 98% of what a 1150 °C gather radiates between 380 and 1400 nm is near infrared, which you cannot see and which reaches the lens of your eye. Years of it cause glassblower's cataract. Didymium does almost nothing about it. Around 1913 William Crookes, working for a Royal Society committee on the problem, made iron-bearing glasses to absorb it, and Coblentz and Emerson (1917) measured sage-green ferrous glass passing about 5% of a furnace's infrared. Furnace and glory-hole work calls for rated IR protection, not didymium alone.
Model. Lens bands are Gaussians at the didymium reference peaks (431, 473, 513, 529, 573, 585, 685, 741, 749, 807, 879 nm) plus praseodymium's 444, 469, 482 and 590 nm, on a 1 nm grid. Strengths are approximate, scaled so a 3 mm lens passes about 1% at 589 nm. The flare's brightness relative to the glass is illustrative; it is strongest at a torch. The view through the lens is shown after your eye has adapted to its overall dimming, so what changes is balance and hue.
Gold ruby comes out of the furnace nearly clear. The gold is dissolved as single atoms, which absorb almost nothing. Reheating lets them cluster into particles a few tens of nanometers across, and the conduction electrons in each particle oscillate together (a surface plasmon) and absorb green. The cadmium colors work differently: small semiconductor crystals absorb every photon with more energy than their band gap.
Models. The gold is computed, not drawn. Each particle is a sphere of gold in glass of index 1.5, and Mie's 1908 solution of Maxwell's equations for a sphere gives how much light it absorbs and scatters at each wavelength, from gold's measured optical constants (Johnson and Christy, 1972). In particles a few nm across the electrons also collide with the surface, which broadens the band; that correction (Kreibig and Vollmer, 1995) carries an uncertain constant. The schedule is a model: 200 ppm gold (as in Haslbeck's glasses) through 2 mm, a spread of sizes around the median, and radii chosen to span what the physics distinguishes rather than taken from one glass. Two things fall out of it rather than being put in. Over-struck gold goes purple and then blue in transmitted light, the direction Haslbeck et al. (2005) saw for fewer, larger particles. And the same large particles scatter orange-brown light back toward a viewer, one plausible source of the "livery" look glassmakers describe; the brown Haslbeck found in tin-rich glasses with many small particles is not reproduced, and no measured spectrum of over-struck gold ruby has been found to check either against. The band edge is an idealized step at λ = 1240 / Eg. Selenium narrows the gap, and very small crystals widen it again (quantum confinement, first recognised in glass by Ekimov and Onushchenko, 1981), which is why the strike temperature matters.
A finished piece cannot just be set down. Its outside cools first. Around 550 °C the skin stiffens while the inside is still soft enough to flow, and when the inside catches up and shrinks it pulls the stiff skin into compression and is left in tension itself. That stress stays in the glass when it is cold (the standard account of annealing, set out by Adams and Williamson in 1920; see below). In an uneven shape it is enough to crack a piece on the shelf hours or weeks later.
The lehr, the annealing oven, prevents it. The piece goes in hot, soaks at the annealing point until the stress relaxes, and is cooled slowly through the range where glass stops flowing and starts holding stress. Only that range matters. Above it the glass still flows. Below the strain point it is stiff enough that the stress of further cooling is elastic, and it goes away again once the piece is evenly cold.
Stress cannot be seen, but it makes glass birefringent. Light polarized along one principal stress travels a little slower than light polarized along the other, and after crossing the glass the two are out of step by a retardation. Between crossed polarizers that retardation becomes color, because the same retardation is a different fraction of a cycle for every wavelength. The piece here is the foot of the bowl from stage 03, a disc 64 mm across, on a light table that gives out polarized light. Drag the second polarizer over it.
Try it. A laptop or phone screen gives out polarized light, and polarized sunglasses are the second polarizer. Hold a glass or a clear plastic box in front of a white screen and look through the sunglasses, turning your head. Tempered car windows show a pattern of dark spots through polarized sunglasses for the same reason: the air jets that tempered them froze stress in unevenly.
Tempered glass is this on purpose. The profile through the edge is the one that makes toughened glass strong: the faces are held in compression, so a scratch has to overcome it before it can open. Tempering quenches evenly and hard; a blown piece is uneven, so its stress is uneven too, and it is the tension at the junctions and in the core that breaks it.
History. David Brewster reported in 1816 that squeezing or unevenly heating glass gives it the double refraction of a crystal ("On the communication of the structure of doubly refracting crystals to glass, muriate of soda, fluor spar, and other substances, by mechanical compression and dilatation", Phil. Trans. 106, 156–178). Annealing became a schedule rather than a craft rule after L. H. Adams and E. D. Williamson at the Carnegie Institution's Geophysical Laboratory measured how stress decays in hot glass, during the wartime push for optical glass ("The annealing of glass", J. Franklin Inst. 190, 597–631 and 835–870, 1920; "A note on the annealing of optical glass", JOSA 4, 213, 1920). Their law is that the rate of relief goes as the square of the stress remaining, dσ/dt = −Aσ², so 1/σ − 1/σ₀ = At. Retardation is read as stress through the stress-optic law Γ = C·(σ₁ − σ₂)·d, with C measured by ASTM C770.
Model. The reference points are the measured averages for NBS standard soda-lime glass No. 710 (Napolitano and Hawkins, 1964): strain point 504 °C, annealing point 546 °C, softening point 724 °C. The other material figures are for soda-lime float glass from Pilkington's ATS-129 bulletin (2013 edition), a close but not identical glass: E = 72 GPa, ν = 0.23 (the 09/2026 edition gives 0.22, which would lower the stress here by about 1%), α = 8.3 × 10⁻⁶ /°C, thermal diffusivity 0.43 mm²/s from its conductivity, density and heat capacity, and a stress-optic coefficient of 2.62 nm per mm per MPa from its strain-viewing rule. Studio furnace glasses are other recipes and anneal at their own temperatures. Stress is frozen in by "instant freezing": cooling at a steady rate q through the annealing range sets a parabolic difference ΔT = qd²/8D between core and faces, which becomes stress Eα(T − T̄)/(1 − ν) when cold. That overstates real stress, since glass sets over a range rather than at once. Face on, only the in-plane pattern shows; it is modeled as a disc whose rim set first, with a rim-to-center difference equal to ΔT, which is a guess at its shape and size. "On the bench" is about 300 °C/min, an estimate for an 8 mm piece radiating at 550 °C. Polarizers and plates are ideal and the same at every wavelength; the tint plate is a 550 nm full-wave plate, and its colors are held fixed beyond 3000 nm of retardation. Each color is the polariscope's transmission spectrum, computed by Jones calculus at every wavelength, under the page's lamp.
Dichroic glass is coated with stacks of oxide films a fraction of a wavelength thick. Light reflected from each layer interferes, so one band bounces back and the rest goes through. Nothing is absorbed, which is why the reflected and transmitted colors are complements. Tilt the piece and the band slides toward blue, because a slanted ray sees the layers as thinner.
Model. One reflection band, 80 nm wide at 90% peak, centered at λ₀√(1 − sin²θ / n²) with λ₀ = 640 nm and an effective index of 1.8. Real coatings have several bands and a thicker stack. Opal glass is the other structural color: particles about the size of a wavelength scatter all colors, so it reads white.
Read: structure and scattering →Bend light instead of reflecting it: rays through prisms and lenses in the Light Lab →
The cold shop grinds facets onto the piece, and a facet bends light. Glass slows light down, by a factor called its refractive index, n, and a ray that meets a surface at a slant turns as it crosses. The turn depends on n, and n is not one number: it is larger for violet than for red. So every wavelength leaves a prism at its own angle, and white light fans out into the colors it was made of.
Nothing here is taken away. The glass is as clear as it gets, and the color comes only from sorting wavelengths. That is the page's rule broken from the other side: dichroic glass sorts light by interference, a prism sorts it by bending. Drag the prism to turn it.
Electrons in the glass are bound to their atoms like weights on springs, and light drives them. Each kind of oscillator has a resonance, a frequency where it absorbs, and for glass the strongest lie in the ultraviolet, out of sight. Below a resonance the driven electrons slow the light, and the nearer the light comes to the resonance, the more it is slowed. Violet is nearest, so n climbs toward the blue end of every curve below. This is the classical (Lorentz) oscillator model, a picture rather than the quantum account, and it gets the shape right. Feynman's "The origin of the refractive index" derives it.
So dispersion also comes from absorption, in the ultraviolet where we cannot see it. A glass whose ultraviolet absorption sits closer to the visible has a steeper curve and a stronger fan.
Abbe number. Ernst Abbe's figure Vd = (nd − 1) / (nF − nC) sets how much a glass bends light against how much it spreads it, using the helium d line (587.6 nm) and the hydrogen F and C lines (486.1 and 656.3 nm). Above about 50 a glass is called a crown, below it a flint. The values here are computed from each glass's dispersion formula and agree with the datasheets.
Lead does two things to glass. The lead ion is large, with two loosely held outer electrons that light can push around easily, so it raises the index: the glass bends light more and each facet reflects more of it. Those same electrons bring the ultraviolet absorption closer to the visible, so it also steepens the curve, which spreads the colors further. (This is the oscillator picture applied to lead, from general glass chemistry; the datasheet figures above bear it out, but the mechanism is not taken from a cited source.) Thick, heavy glasses pay for it with a faint yellow, since the absorption edge reaches into the violet, as SCHOTT's note on transmittance (TIE-35) explains. A cut lead-crystal glass throws small spectra across the table, which is what cutters call fire. Pick F2 or SF11 above and watch the fan widen.
Other ions can do the same. Schott's N-SF11 replaces the lead in SF11 with titanium, another ion with absorption close to the visible, and reaches the same index and nearly the same Abbe number. The two curves above lie almost on top of each other.
History. George Ravenscroft took a seven-year patent in 1674 for a clear "flint" glass and soon added lead to cure its crizzling, which gave English glass its weight, ring and brilliance (Corning Museum of Glass: lead glass; the museum dates the larger lead addition to 1676). The name flint glass has stuck to lead glass ever since. Today EU law (Directive 69/493/EEC) lets glass be sold as lead crystal from 24% lead oxide and as full lead crystal from 30%, with a refractive index nD of at least 1.545.
Light leaving glass for air bends away from the normal to the surface. Past a certain slant it cannot leave at all: Snell's law would need the sine of the outgoing angle to exceed 1, and instead the surface reflects all of the light back into the glass. This is total internal reflection. It starts at the critical angle, θc = arcsin(1/n), which falls as the index rises: 41.0° for window glass, 38.1° for F2, 34.1° for SF11. A polished surface met head on reflects about 4% of the light; past the critical angle it reflects all of it.
A cut piece is shaped to use this. Below the girdle, its widest edge, the pavilion facets slope down to a point, the culet. In this section through the axis, light coming straight down through the table meets one pavilion facet at the pavilion angle α, the facet's slope from the girdle plane. If α exceeds θc the light is reflected across to the opposite facet, which it meets at 180° − 3α. If that too exceeds θc, it is reflected again and goes back up and out of the top. So the light comes back when θc < α < (180° − θc)/3. That window is 5.3° wide for window glass, 9.2° for F2 and 14.6° for SF11. A higher index makes the cut less exacting, and keeps returning light when it comes in at a slant.
The light that comes back leaves through the table and the sloping crown facets, and each exit face acts as a prism, so the colors part. A high index returns more of the light, and a high dispersion spreads it further; lead raises both. The colored spots this throws, which move as the piece or the light moves, are what cutters call fire. The piece below is cut to Tolkowsky's proportions for diamond, with the pavilion at 40.75°: in window glass, whose critical angle is 41.0°, most of the light falls out of the back. Pick LLF1 or F2 and it comes back.
Reading the chart. Each bar is traced, not drawn from the formula: a beam coming straight down through the table at the d line, its share coming back out of the top shaded from none (paper) to all (ink). The bar starts at the critical angle and ends near (180° − θc)/3. For SF11 the start is soft: below about 36.5° the returning ray meets the table past the critical angle too, and part of it is reflected inside again. Diamond (nD 2.417, θc 24° 26′, both from Tolkowsky) has a window more than 27° wide, so for diamond the cut is chosen for brightness and fire, not to keep the light in at all.
History. Marcel Tolkowsky worked out the proportions of the round brilliant in Diamond Design (1919) with this same analysis of a section through the axis: rays coming straight down reflected twice by the pavilion, oblique rays once, and the crown sized so the returning light leaves at a slant and disperses. His answer for diamond was a pavilion at 40° 45′, a crown at 34° 30′ and a table 53% of the width; the piece here uses that crown and table.
Model. A two-dimensional section of a piece 20 mm across, with Tolkowsky's crown and table and a girdle 2% of the width thick. A real brilliant has 57 or 58 facets arranged around the axis, and most rays through it are skew to any one section, so the window above holds exactly only in the section. Light arrives as parallel rays; the share each surface reflects partially (Fresnel) is counted as lost, not followed. The ceiling and floor strips add up every wavelength at 1 nm steps and share one exposure, set by the brightest spot on either. Tableware lead crystal has no dispersion formula in these sources, so SCHOTT's LLF1 light flint, nd 1.548, stands in for it: EU law (Directive 69/493/EEC) requires nD ≥ 1.545, and real lead crystal varies with its lead content.
A lens is a prism bent round, so a plain glass lens brings violet to a focus nearer than red. Look at a black line through it and the edges fringe with color, a defect called chromatic aberration. Isaac Newton thought it could not be cured, because he supposed every glass spread light in proportion to how much it bent it. It can, because that proportion differs from glass to glass. A strong converging lens of crown, which spreads little, is cemented to a weaker diverging lens of flint, which spreads a lot. The flint undoes the crown's spread while keeping most of its bending.
History. Chester Moor Hall is said to have made achromatic lenses around 1733 without publishing them; John Dollond described his experiments with crown and flint in the Philosophical Transactions in 1758 (vol. 50, pp. 733–743) and patented the achromat. Newton's view, that refraction and dispersion go together so an achromat is impossible, is in his Opticks (1704; 4th edition, 1730). The Hall date is from memory and unverified.
Models. The index curves are the published dispersion formulas, not illustrations: Sellmeier fits from Schott's catalog for the optical glasses and from Malitson for fused silica, and Rubin's Cauchy fit for window glass. The ultraviolet resonance quoted is the Sellmeier term nearest the visible; a fitted term behaves like a resonance but is not a measured absorption line. Rays are traced in two dimensions with Snell's law at each face, unpolarized Fresnel losses, and total internal reflection; the card adds up every wavelength that lands at each point, so the white middle and colored edges of a near card are computed. The beam is 8 mm wide and the prism 60 mm on a side. Spectral colors lie outside what a screen can show and are drawn as near as sRGB allows. The lenses are thin lenses of 100 mm focal length at f/4, with the focus stretched along the axis in the drawing; a real achromat is bent to correct other aberrations too.
Sources. Malitson, JOSA 55, 1205 (1965) · Rubin, Sol. Energy Mater. 12, 275 (1985) · SCHOTT N-BK7 datasheet · SCHOTT LLF1 datasheet · SCHOTT F2 datasheet · SCHOTT SF11 datasheet · SCHOTT N-SF11 datasheet
Trace the fan yourself: these seven glasses as prisms and lenses, ray by ray, in the Light Lab →
These are 1,151 real rod and sheet colors from 9 suppliers, shelved by hue. Filter by the mechanism that makes them. Most suppliers do not publish recipes, so many rods are left unclassified.
Click a rod and the bench works backwards. It tries every melt of up to three of the page's twelve colorants and keeps the ones whose color through the glass matches the photo. Usually many do. A color is three numbers and a transmission spectrum is hundreds, so one swatch cannot determine what is in the glass. Seeing it under a second lamp narrows the candidates.
Swatch colors are sampled from supplier product photos, so they inherit each photo's lighting and white balance. They are approximate, not calibrated measurements. The bench fits the photo, not the glass, and its twelve absorption curves are illustrative rather than measured, so its recipes are candidates, never the supplier's formula. Under another lamp each swatch is relit through the smoothest spectrum that matches its daylight color (Jakob and Hanika's sigmoid fit), which is an estimate: two glasses that match in daylight can part ways under a sodium lamp or a fluorescent tube, and a photo cannot tell you which will.
Everything so far has been subtraction: light goes in, the glass takes some away, and the rest is its color. Uranium glass breaks the rule. The uranyl ion absorbs ultraviolet and violet, and instead of turning that energy into heat it sends much of it back out as green light. That green is not in the lamp, so no absorber could have produced it.
In daylight the effect is a faint cast on a pale canary yellow. Under a black light, which gives almost nothing visible for any glass to filter, every other piece goes dark and uranium glass glows bright green.
Subtraction has its own surprise. A glass does not have a color; it has a spectrum, and the color is what is left of a lamp after the glass has taken its share. Neodymium shows it best, because its bands are narrow: the 4f electrons that absorb sit inside the ion, shielded by its outer shells, so the glass around them barely blurs their levels. Its strongest band, at 583 nm in the yellow, is only about 15 nm wide, with a weaker one at 525 nm in the green.
Daylight is smooth, so the glass takes a slice of yellow and some green from it and the rest reads lilac. A tungsten bulb has little blue to begin with, so what survives is mostly red: pink. A tri-phosphor tube puts its light into a few narrow lines, and the glass lands on them unevenly. It takes the tube's orange lines between 580 and 600 nm almost completely, about two fifths of its red line at 611 nm, which sits on the band's long-wavelength wing, and only a little of the green and none of the blue. Red and orange go, blue stays: the same piece turns blue-gray.
Model. The absorption is measured: traced from soda-lime-silica glasses melted with 1 to 3 mol% Nd₂O₃ and measured 3 mm thick (Chimalawong, Kaewkhao & Limsuwan 2010, CC BY), with the figure's flat offset taken away. Its strength is scaled so the piece comes as close as it can to the lilac the page drew before; the paper's own numbers put that near 1 mol% through 10 mm, if its axis is true absorbance. The lamps are CIE tables on a 5 nm grid, D65, A and FL11, and each pane is drawn as the eye sees it after settling into that light. On a 5 nm grid the tube's red line is spread over 605–615 nm, across the steep wing of the band, so how much of it the glass takes is the least certain number here.
History. Uranium was identified by Martin Heinrich Klaproth in 1789. Franz Xaver Riedel made yellow and green uranium glass in Bohemia from 1830 to 1848 and named the colors annagelb and annagrün after his daughter Anna. It was most popular from the 1880s to the 1920s. In the United States the government took control of uranium for the Manhattan Project from 1942 to 1958, and production stopped. Most uranium glass holds about 2% uranium by weight.
Model. Absorption is a strong edge near 400 nm with weak bands at 418–472 nm, drawn to the published shape rather than measured. Emission is uranyl's vibronic comb: peaks evenly spaced in energy, about 830 cm⁻¹ apart (the O=U=O stretch), with the strongest at 527 nm, where a measured uranium-glass marble peaks. Half of the absorbed photons are re-emitted and half of those leave toward you; both numbers are illustrative. Under the black light the eye is set by the glowing glass itself, since there is no white in the room to adapt to.
Every color on this page so far was computed for one eye: the CIE 1931 standard observer, an average of seventeen people who matched colors in two English laboratories in the 1920s, ten for William Wright and seven for John Guild. Nobody has exactly that eye. The lens yellows with age and soaks up blue before it reaches the retina. A yellow pigment over the center of the retina, the macula, filters the middle of what you look at but not the edges. About one man in twelve of northern European descent has some red–green color deficiency, and something like one in forty is missing a cone type altogether (surveys differ).
The lamp switch at the foot of the page changes the light. This stage keeps the light and changes the eye. The left half of each piece is the page's eye; the right half is the eye you pick.
Two glasses with different spectra can look identical. That is a metamer, and the rack stage showed how many melts can hide behind one swatch. Here each glass is paired with a smooth-spectrum twin computed to match it exactly for the page's eye in daylight. Then the eye changes, or the lamp does, and the question is whether the match survives.
It mostly survives a change of eye, and it often fails a change of lamp. Eyes differ by smooth filters, the lens and macula, in front of broad cone curves, so a trichromat's eye changes the weights of a match only a little. A lamp can be made of a few narrow lines, and a glass like neodymium has narrow bands of its own, so the two spectra can disagree where the lamp puts all its light. A dichromat accepts every match a trichromat makes: if the three cone signals are equal, any two of them are.
Model. The 1931 eye is the page's analytic fit to the CIE 2° functions; the 1964 eye is the CIE 10° table. The cone eyes are the CIE 2006 physiological model built from its parts, as CIE 170-1:2006 specifies: photopigment absorbance, peak pigment density falling with field size, macular density 0.485·e−f/6.132, and lens density growing with age by the Pokorny–Smith–Lutze formula (valid 20 to 80). Dichromats are that eye with one cone signal replaced by Brettel, Viénot and Mollon's two-half-plane rule, a model of how dichromats' colors look to trichromats that rests on reports from people with one color-deficient eye. To draw another eye's experience on a screen made for the standard eye, each eye is taken to be fully adapted to its own lens and macula, which change over decades, and partly adapted to the lamp, as everywhere on the page; the screen shows the color that would give the standard eye the same adapted cone signals. Werner and Schefrin (1993) found that the white point of 50 observers aged 11 to 78 did not shift with age, which is the full-adaptation assumption's best support. The twins are fitted to the colors a screen can show, so for a piece outside sRGB, such as cobalt, the match is a match of what is drawn.
What the numbers say. Between trichromats the pairs split by about 0 to 3 units, where 1 is a just-noticeable difference side by side, and neodymium under the tri-phosphor tube splits most. Change the lamp from daylight to that tube and the page's own eye splits the neodymium pair by about 16. So for glass, the lamp matters far more than whose eye it is, and the large effects of the eye are a missing cone, or the slow fade of blue with age, which adaptation mostly hides. The CIE 2006 eye at 32 already differs from the 1931 eye in the blue, where the 1931 functions are known to be too weak (Judd corrected them in 1951).
Sources. CIE 1964 10° observer · CIE 170-1:2006 · Asano, Fairchild & Blondé 2016 · Brettel, Viénot & Mollon 1997 · Werner & Schefrin 1993 · all sources
Most of the colors above were found by glassmakers long before anyone could explain them. Each pin on this rail is colored by the same engine as the stages, so an Egyptian bead, a Roman cup and a 1939 light filter are computed from their spectra, not taken from photographs. Pick one to see what happened and which stage explains it.
Glass of Egypt's 18th Dynasty is already colored with cobalt, the same ion as in a modern blue rod. Cobalt was used as a blue on pottery of the same period too.
See it in stage 03 · the color rod → Internet Archaeology 52: cobalt-blue glass of the 18th Dynasty ↗CAMEO: Amarna blue ↗
A Roman cage cup that looks jade green in reflected light and glows red when lit from inside. About 300 ppm of silver and 40 ppm of gold sit in it, much of it as silver-gold particles 50–100 nm across. The pin shows the transmitted color; the green is scattered light, which this engine does not model.
See it in stage 05 · the reheat → Freestone et al., The Lycurgus Cup: a Roman nanotechnology, Gold Bulletin 40 (2007) 270 ↗Wikipedia: Lycurgus Cup (British Museum 1958,1202.1) ↗
North of the Alps, glass was melted in woodland furnaces with potash from wood ash. Iron in the sand and the furnace atmosphere left it green, from pale to deep.
Angelo Barovier of Murano is credited with a nearly colorless glass. Small additions of manganese oxide cancel the iron's tint: manganese absorbs in the green, iron at the ends, and together they take a little of everything, which reads as clear.
In 1676 the Hamburg physician Andreas Cassius reported the red that gold chloride gives. By about 1679 Johann Kunckel was making ruby glass in Potsdam and keeping the recipe secret. It comes out of the melt gray and turns red only on reheating.
In Bohemia, Franz Xaver Riedel named his uranium yellow and yellow-green glasses annagelb and annagrün after his daughter. In the US, production stopped in 1942 when uranium went to the Manhattan Project. Under ultraviolet light it glows green: it gives light out instead of taking it away. Its pin is drawn with the showroom's fluorescence model, so switch on the black light to see it glow.
See it in stage 09 · the showroom → Wikipedia: Uranium glass ↗
Carl Auer von Welsbach separated didymium, named in 1841 as one element, into neodymium and praseodymium. Didymium glasses need both to block the sodium flare.
Franz Welz of Klostergrab in Bohemia patented selenium as a glass colorant (German patent 63558, December 1891; US patent 479,689, 1892). Selenium alone gave a rose; with cadmium sulfide it gave orange-red to orange-yellow. The deep cadmium sulfoselenide ruby of signal lamps came later and was described in the Journal of the American Ceramic Society in 1919.
See it in stage 05 · the reheat → US patent 479,689: Welz, rose or orange stained glass (1892) ↗Yuryeva et al., Materials Research Bulletin, citing DE patent 63558 (6 Dec 1891) ↗Corning Museum of Glass: when was selenium first used? ↗
On 10 November 1913 the Royal Society's Glassworkers' Cataract Committee adopted William Crookes's report on "eye-preserving glass for spectacles". His glasses used iron to absorb a furnace's infrared.
See it in stage 04 · the glory hole → Royal Society archive: committee minutes, 10 Nov 1913 ↗
Walter Geffcken at Schott in Jena filed a patent for a light filter made of stacked thin films. Dichroic art glass is often credited to NASA, but the multilayer filter behind it is older.
See it in stage 07 · the cold shop → Patent DE716153C, filed 8 Dec 1939 ↗
Broken scale. The rail is linear within each span between its labeled years, and the spans are stretched so the last two centuries get room: the 3,000 years before 1000 CE take its first quarter. Dates were checked against the sources linked in each card in October 2026; where a source is weak the card says so.
The long read is about color, the strand this site started from: one essay per mechanism. Structure, viscosity, annealing, optics and durability are in the stages above and in the labs.
Each piece is a real melt from the site's colorant table, computed under daylight like every other color here: cobalt, gold ruby, trace iron, chromium, copper with cadmium sulfide (and both together where they overlap), neodymium.