In the spring of 1800 the astronomer William Herschel split sunlight with a prism and laid thermometers in the colours, to find out which of them carried the most heat. The answer surprised him, and what it meant took most of the next century to settle.
Chapter 7 · Beyond the visible
The Thermometer Beyond Red
A prism, a sunny window and a few thermometers. Where on the table is the warmest place, and what does the answer say about the light you cannot see?
Look first
A rainbow on the table
Herschel came to this as an astronomer with a practical problem. To look at the Sun through a telescope he had to put darkened or coloured glass in front of his eye, and some glasses that let through very little light still made his eye uncomfortably hot. Did heat travel with the colours, or separately?
So he let sunlight through a prism at a window and spread its colours across a table. He blackened the bulbs of his thermometers so they would soak up whatever fell on them, set one in a colour, and kept others beside the spectrum, in the shade, to measure the room. Then he waited for the readings to settle, and moved on to the next colour.
Below is the same arrangement, computed. Three thermometers sit in the blue, the yellow and the red. Their readings are hidden for now.
Sunlight through a flint prism. Each colour lands where the glass bends it; the Sun’s half-degree disc softens every edge.
Commit to a prediction
Where is it warmest?
Herschel moved a thermometer slowly along the spectrum, from the violet end to the red end, and then on past the red, into the part of the table that looks like shade.
Where did it read highest?
The curve is the heating a blackened bulb would feel at each place on the table, scaled so the warmest place reads 100.
Slide it past the red and keep going. The heating climbs after the last colour you can see, peaks, and only then falls away into a long, faint tail.
Why the first guesses made sense
Your eye has a favourite colour
If you chose the yellow, you trusted your eye, and your eye was telling the truth about itself. The spectrum really does look brightest in the yellow-green. But the eye is a detector with its own sensitivity: daylight cones respond most strongly near 555 nm and hardly at all past 700. What you see is the light weighed by that curve. A blackened thermometer weighs every wavelength the same.
If you chose the red, you were reading a real clue. Embers and stove rings glow red because almost everything they send out is infrared, and red is the visible edge of it. Hot things look red for the same reason this table is warmest past the red.
If you chose the violet, you were right that each grain of violet light carries more energy than a grain of red, which is why ultraviolet fades fabric and burns skin. But a thermometer adds up all the grains that land on it, and sunlight has comparatively few violet ones, spread thinly by the prism.
Along the same table: heating (solid) and how bright it looks to a daylight eye (dashed). Same light, two detectors, two different peaks.
See it yourself
- Point a television remote at your phone’s camera, in a dim room, and press a button while you watch the screen.
- Many phone cameras show a flickering light at the tip that your eye cannot see. It is infrared, a little past the red. Front cameras often show it best; many rear cameras carry a filter that blocks it.
The bench
Two reasons, one peak
Two things put the warmest place in the dark. The first belongs to the Sun. An ideal glowing body at the Sun’s temperature sends out about half of its power at wavelengths longer than red: more than in all the colours together.
The second belongs to the glass. A prism bends long wavelengths less than short ones, and the difference between neighbouring wavelengths shrinks the further you go past the red. So the whole stretch from 700 to 2500 nm, more than seven times as wide as the visible in wavelength, lands on a narrower strip of table than the colours do. The same power on less table means more heat under each thermometer.
Change the glass and watch the peak move. Then switch the Sun from the ideal glowing body to real sunlight as it reaches the ground, measured through a standard clear sky (the data from chapter 9). The curve turns ragged: water vapour cuts notches near 940 and 1130 nm, right where the heat is greatest. The warmest stretch becomes a broken plateau from about 750 to 1100 nm. It is still in the dark.
The table
The third spreader opens after the case you have not seen.
What you can now say
Where a spectrum is warmest depends on how it is spread. Through a glass prism, sunlight’s warmest place is past the red, where the eye sees nothing.
A thermometer measures power per strip of table. The Sun decides how much power each wavelength carries; the prism decides how wide a strip each wavelength gets. Change either, and the peak moves.
For the determined reader: the prism, the density of a spectrum, and the limits of this model
The prism
For a prism of apex angle A and index n(λ), a ray entering at angle θi leaves deviated by
δ(λ) = θi + arcsin( n sin( A − arcsin( sinθi / n ) ) ) − A
Here A = 60° and θi is fixed at minimum deviation for 589 nm. The index comes from the Sellmeier formula n² = 1 + Σ Bkλ²/(λ² − Ck), with Schott’s published coefficients for F2 flint and N-BK7 crown.
The density of a spectrum
If the Sun sends power S(λ) per unit wavelength, the power per unit angle on the table is
P(δ) = S(λ) · | dλ / dδ |
The first factor is the Sun; the second is the spreader. A prism’s |dδ/dλ| falls steeply past the red, so |dλ/dδ| grows, and P(δ) keeps rising after S(λ) has begun to fall. Each wavelength’s light is then smeared over the Sun’s disc, 0.53°, before the curve is drawn.
| Spreader | Warmest at | Width of 400–700 nm | Width of 700–2500 nm |
|---|---|---|---|
| Flint prism (F2) | |||
| Crown prism (N-BK7) | |||
| Even spread |
The Sun’s own peak, asked three ways
For a body at 5772 K, Wien’s law puts the peak of power per unit wavelength at 2898 µm·K / T = 502 nm. Per unit frequency, the peak is at 5.879 × 1010 Hz/K × T = 339 THz, which is a wavelength of 884 nm. Neither is the “true” colour of sunlight’s peak; each answers a different question about how the spectrum is spread. Of the total power, about 12% lies below 400 nm, 37% between 400 and 700 nm, and 51% beyond 700 nm.
Where this model stops
The Sun here is an ideal glowing body, without the dark lines of its real spectrum, and the air is empty. Real sunlight at the ground is missing bands in the infrared, near 940, 1130, 1400 and 1900 nm, absorbed by water vapour, and nearly everything below 300 nm, absorbed by ozone. The glass is treated as clear from 300 to 2500 nm and opaque beyond, which is roughly right for flint. A real thermometer responds slowly and loses heat to the room; Herschel waited minutes for each reading. None of this moves the peak back into the colours. The bench’s second Sun, the ASTM G173 direct beam at the ground, shows it: through flint the heating becomes a ragged plateau from about 750 to 1100 nm, highest near 830 nm, and with an even spread the peak moves from the blue-green to about 550 nm, because the air has scattered away some of the blue.
A case you have not seen
Spread it evenly
A diffraction grating, a plate of glass ruled with thousands of fine lines, also spreads sunlight into colours. At small angles it does something a prism does not: it gives every wavelength the same width of table. Each nanometre of violet gets as much table as each nanometre of red, and each nanometre of infrared the same again.
Imagine an ideal grating that makes one spectrum only, and lay the same thermometers along it.
Where is it warmest now?
The same Sun, spread evenly by wavelength. The table is cut off at 1300 nm; the faint tail runs on for several times this width.
Nothing about the Sun changed. Half of its power is still past the red, but spread evenly it is spread thin: the stretch from 700 to 2500 nm now covers six times as much table as the colours, so no single thermometer there collects much of it.
So when someone tells you the Sun is brightest in the green, the right reply is a question: per what? Per nanometre, its peak is at 502 nm. Per unit of frequency, it is at 884 nm, in the infrared. Through Herschel’s prism, it is past the red, a little under 1000 nm. Each is correct. They answer different questions.
Heat without light
Herschel read his results to the Royal Society on 27 March 1800. The heating rose toward the red and went on rising past it, and he concluded that the Sun sends out rays which the prism bends like light but which the eye cannot see. He called what they carried radiant heat.
He then spent the rest of the year testing them, and grew less sure they were light at all. Coloured glasses and liquids that stopped most of the light let much of the heat through, and others did the reverse. If heat and light could be separated so easily, perhaps they were different things.
The next year, in Jena, Johann Wilhelm Ritter looked past the other end. Silver chloride darkens in light. Laid along a spectrum, it darkened fastest beyond the violet, where again there was nothing to see.
Deciding what these invisible rays were took decades. In the 1830s Macedonio Melloni, using prisms of rock salt, which pass rays that glass absorbs, and James Forbes in Edinburgh showed that radiant heat reflects, refracts and can be polarised, as light does. When Maxwell described light as an electromagnetic wave in 1865, there was room in the theory for waves of any length. Herschel’s shade, and Ritter’s, were the first two pieces of the rest of the spectrum.
Where this explanation stops
A narrow window
Everything here treated the Sun as an ideal glowing body and the air as empty. Real sunlight reaches the table with gaps in the infrared, where water vapour has taken its share, and with almost nothing below 300 nm, where ozone has taken the rest. Of everything that does arrive, your eye uses a narrow band, from about 400 to 700 nm, and the thermometer’s warmest place is not even in it.
Of all the light the Sun sends, why do our eyes see this band, and not the band where the heat is?
End of chapter 7
Added to your notebook
Where a spectrum is warmest depends on how it is spread. Through a prism, sunlight’s warmest place is past the red, where you see nothing.
Why do eyes see this band of light, and not another?
Chapter 8 · The Window