In 1800, English astronomer William Herschel (1738–1822) made one of the most far-reaching experimental discoveries in the history of physics: the existence of infrared radiation. With an apparatus no more complex than a glass prism and three thermometers, he proved that the electromagnetic spectrum extends far beyond what the human eye can see — a revelation that would eventually lead, through Kirchhoff, Boltzmann, Wien, and Planck, directly to quantum mechanics.

1. Historical Background¶

The Scientific Landscape of 1800¶

At the turn of the nineteenth century, the dominant model of light was Isaac Newton’s corpuscular theory (Opticks, 1704): light was believed to be a stream of tiny particles. Christiaan Huygens’ 1678 wave theory had been largely set aside. The visible solar spectrum (violet to red) produced by a glass prism was well known since Newton, but the physics governing heat radiation and its relationship to visible light remained completely obscure.

The prevailing assumption was simple and unexamined: the heating power of sunlight is uniformly distributed across the visible spectrum. No one had posed the question of whether thermal radiation might exist outside the visible band — because no framework existed even to ask it.

William Herschel: Astronomer and Experimentalist¶

Friedrich Wilhelm Herschel was born in Hanover, Germany in 1738, emigrated to England, and became the pre-eminent observational astronomer of his era. His greatest achievement was the telescopic discovery of Uranus in 1781 — the first new planet found in recorded history. He also catalogued over 2,500 nebulae and 800 double stars.

By 1800, Herschel had turned his attention to a very practical problem: when observing the Sun through coloured glass filters, some filters heated the eyepiece far more than others even when the transmitted brightness appeared similar. He resolved to study this systematically — and the resulting investigation changed physics forever.

2. The 1800 Experiment¶

Apparatus¶

Herschel’s setup was deliberately simple and reproducible:

• A glass equilateral triangular prism mounted to disperse a admitted beam of sunlight into a spectrum of colours on a white card
• A narrow slit in a window shutter to admit a well-defined beam of sunlight into a darkened room
• Three mercury-in-glass thermometers with blackened bulbs — blackened with Indian ink to maximise heat absorption (effective absorptivity $\alpha \approx 1$)
• One thermometer used as a control (placed in the shadow, away from the spectrum) to track ambient temperature drift
• A ruler to precisely record the position of each measurement relative to the spectral colour bands

Procedure¶

Herschel placed the thermometer bulbs sequentially at each colour position across the full visible spectrum — from violet through indigo, blue, green, yellow, orange, to red — and recorded the temperature rise above the ambient control after a fixed exposure time (typically 10 minutes). He then moved the thermometer into the dark region immediately beyond the red end of the spectrum.

Experimental Data¶

Note: Herschel’s original measurements were in degrees Fahrenheit. Wavelengths are modern assignments.

The Critical Observation¶

When Herschel pushed the thermometer just beyond the visible red band — into a region of total darkness — the mercury climbed to its highest reading of the entire experiment. He wrote in his paper to the Royal Society:

“The thermometer No. 1 rose 7 degrees in 10 minutes when placed in the most refrangible colour; but when I pushed it further, beyond the red colour… the mercury rose more than 9 degrees.”

He named this invisible heating agent “calorific rays”, initially believing it to be a phenomenon distinct from visible light — a separate radiation responsible only for heat, not illumination.

3. Key Scientific Findings¶

3.1 The Spectrum Extends Beyond Visible Red¶

The central discovery: the thermal output of solar radiation does not stop at the red end of the visible spectrum. It continues — and peaks — in an invisible region immediately beyond red. This region is now universally called the infrared (Latin infra = below, meaning below red in frequency).

3.2 Heating Power Varies Monotonically Across the Spectrum¶

Herschel’s data showed a clear, monotonic increase in heating power moving from violet toward red and beyond. This contradicted the prevailing assumption of uniform heating across the spectrum and constituted the first empirical proof that different spectral regions carry different amounts of thermal energy.

3.3 Invisible Radiation Obeys the Same Optical Laws as Visible Light¶

In a series of follow-up experiments, Herschel demonstrated that his calorific rays:

• Were reflected by mirrors exactly as visible light is
• Were refracted by prisms, following Snell’s Law
• Could be focused by lenses to a point

These results (later confirmed more rigorously by Macedonio Melloni in the 1830s) eventually established that infrared and visible light are the same kind of phenomenon — electromagnetic radiation — differing only in wavelength.

4. Mathematical Framework¶

4.1 Electromagnetic Wave Equations¶

Infrared radiation is a solution to Maxwell’s equations exactly like visible light. A plane infrared wave propagating in vacuum:

$$\mathbf{E}(\mathbf{r}, t) = \mathbf{E}_0 \cos\!\left(\mathbf{k} \cdot \mathbf{r} - \omega t\right)$$

$$\mathbf{B}(\mathbf{r}, t) = \frac{\hat{k} \times \mathbf{E}}{c}$$

with propagation speed:

$$c = \frac{\omega}{|\mathbf{k}|} = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \approx 2.998 \times 10^8 \, \text{m s}^{-1}$$

4.2 Wavelength, Frequency, and the Infrared Band¶

The standard modern definition of the infrared spans:

$$\lambda_{\text{IR}} \approx 700\,\text{nm} \text{ to } 1\,\text{mm}$$

with the relation:

$$c = \lambda\nu \implies \nu = \frac{c}{\lambda}$$

For near-infrared (NIR) at $\lambda = 900\,\text{nm}$ — close to Herschel’s detection peak:

$$\nu = \frac{2.998 \times 10^8}{900 \times 10^{-9}} = 3.33 \times 10^{14}\,\text{Hz}$$

4.3 Photon Energy¶

Every photon carries a discrete quantum of energy:

$$E_\gamma = h\nu = \frac{hc}{\lambda}$$

where Planck’s constant $h = 6.626 \times 10^{-34}\,\text{J·s}$. For $\lambda = 900\,\text{nm}$:

$$E_\gamma = \frac{(6.626 \times 10^{-34})(2.998 \times 10^8)}{900 \times 10^{-9}} = 2.21 \times 10^{-19}\,\text{J} \approx 1.38\,\text{eV}$$

Infrared photons ($0.001$–$1.7\,\text{eV}$) have energies matching molecular vibrational and rotational transitions, which is why they heat matter so effectively.

4.4 Planck’s Blackbody Radiation Law (Retrospective Explanation)¶

The reason Herschel found the peak heating beyond the red is fully explained by Planck’s Law (1900), giving the spectral radiance of an ideal blackbody at temperature $T$:

$$B_\lambda(T) = \frac{2hc^2}{\lambda^5} \cdot \frac{1}{\displaystyle e^{\,hc/\lambda k_{\!B} T} - 1}$$

where $k_{\!B} = 1.381 \times 10^{-23}\,\text{J K}^{-1}$. The peak wavelength follows Wien’s Displacement Law:

$$\lambda_{\text{max}} = \frac{b}{T}, \qquad b = 2.898 \times 10^{-3}\,\text{m K}$$

For the solar photosphere at $T_\odot = 5{,}778\,\text{K}$:

$$\lambda_{\text{max}} = \frac{2.898 \times 10^{-3}}{5{,}778} \approx 501\,\text{nm (green)}$$

The peak is in the visible green, but approximately 49% of total solar irradiance falls in the infrared ($\lambda > 700\,\text{nm}$) — exactly the dominant heating that Herschel’s thermometer detected.

4.5 Stefan–Boltzmann Law¶

The total radiated power per unit area, integrated over all wavelengths, is:

$$P = \sigma T^4, \qquad \sigma = 5.670 \times 10^{-8}\,\text{W m}^{-2}\text{K}^{-4}$$

This provides the theoretical underpinning for Herschel’s qualitative observation: the Sun’s intense output is dominated by infrared emission.

4.6 Molecular Vibrational Absorption¶

Infrared radiation heats matter through molecular vibrational excitation. For a quantum harmonic oscillator (diatomic molecule), vibrational energy levels are:

$$E_n = \hbar\,\omega_{\text{vib}}\!\left(n + \tfrac{1}{2}\right), \qquad n = 0, 1, 2, \ldots$$

An absorbed IR photon drives the transition $n \to n+1$, depositing energy $\Delta E = \hbar\,\omega_{\text{vib}}$ directly into lattice vibrations (phonons), increasing temperature.

The selection rule for IR absorption requires a change in electric dipole moment ($\Delta\mu \ne 0$), which explains why asymmetric molecules like H₂O and CO₂ are strong infrared absorbers (the physical basis of the greenhouse effect).

5. Infrared Spectrum: Full Classification¶

Herschel’s blackened thermometer responded primarily to NIR / SWIR radiation ($\sim\!700$–$2{,}500\,\text{nm}$).

6. Immediate Scientific Response¶

6.1 Herschel’s Four Papers (1800)¶

Herschel published four sequential papers in the Philosophical Transactions of the Royal Society in 1800:

1. “Experiments on the Refrangibility of the Invisible Rays of the Sun” — the discovery paper
2. “Experiments on the Solar, and on the Terrestrial Rays that Occasion Heat” — thermal properties
3. “Investigation of the Powers of the Prismatic Colours to Heat and Illuminate Objects” — quantitative comparison
4. “Observations on the Different Refrangibility of the Various Coloured Rays of the Sun’s Light” — optical follow-up

6.2 Johann Wilhelm Ritter Discovers Ultraviolet (1801)¶

Just one year later, German physicist Johann Wilhelm Ritter (1776–1810), directly inspired by Herschel’s work, searched for complementary invisible radiation at the opposite end of the spectrum — beyond violet. In 1801 he found that silver chloride (AgCl) darkened fastest in the invisible region beyond violet, revealing ultraviolet radiation. The visible spectrum was now bracketed on both sides by invisible radiation.

6.3 Macedonio Melloni Confirms Optical Equivalence (1830s)¶

Italian physicist Macedonio Melloni (1798–1854) used a thermopile detector (far more sensitive than Herschel’s thermometers) to prove that infrared radiation obeys every law of geometric optics: it is reflected, refracted, diffracted, polarised, and focused in exactly the same manner as visible light.

6.4 Maxwell Unifies the Spectrum (1864)¶

The theoretical unification came with James Clerk Maxwell’s “A Dynamical Theory of the Electromagnetic Field” (1864), which demonstrated that light is a transverse electromagnetic wave. This framework showed that infrared, visible, and ultraviolet radiation are all solutions to the same wave equation, differing only in frequency $\nu$.

7. Legacy and Long-Term Impact¶

7.1 Foundation of Spectroscopy¶

Herschel’s technique — measuring a physical property (temperature/heating power) as a function of position in a dispersed spectrum — is the direct ancestor of all modern spectroscopy. Infrared spectroscopy (IR spectroscopy) is today one of the most widely used analytical tools in chemistry, identifying organic functional groups through their characteristic bond vibrational frequencies ($\sim\!500$–$4{,}000\,\text{cm}^{-1}$).

7.2 The Greenhouse Effect and Climate Science¶

The same molecular IR absorption mechanism Herschel unknowingly probed underlies the greenhouse effect. Atmospheric CO₂ and H₂O absorb outgoing terrestrial IR radiation ($8$–$14\,\mu\text{m}$ atmospheric window), retaining heat in the atmosphere. Eunice Newton Foote (1856) and John Tyndall (1859) built directly on the spectral physics Herschel opened.

7.3 Infrared Astronomy and JWST¶

Because Earth’s atmosphere strongly absorbs many IR bands, infrared astronomy has required progressively higher-altitude and ultimately space-based platforms:

• IRAS (1983) — first complete all-sky infrared survey, discovered proto-stellar disks
• Spitzer Space Telescope (2003–2020) — revealed stellar nurseries, exoplanet atmospheres
• James Webb Space Telescope (2021–present) — operates at $0.6$–$28\,\mu\text{m}$; detected CO₂ in exoplanet atmospheres and resolved galaxies at $z > 13$

7.4 The Direct Path to Quantum Mechanics¶

Herschel’s discovery initiated the formal study of the blackbody radiation spectrum, which became the central unsolved problem of late 19th-century physics. Classical attempts — the Rayleigh–Jeans Law and Wien’s approximation — both failed: the Rayleigh–Jeans Law diverged at short wavelengths (the ultraviolet catastrophe). To resolve it, Max Planck in 1900 was forced to postulate:

$$E = nh\nu, \qquad n = 0, 1, 2, \ldots$$

This was the birth of quantum mechanics. The direct chain is:

$$\text{Herschel 1800} \to \text{Kirchhoff 1859} \to \text{Stefan–Boltzmann 1879–84} \to \text{Wien 1893} \to \text{Planck 1900}$$

8. Key Figures and Connections¶

9. Key Takeaways¶

• Year: 1800
• Key Figure: William Herschel — English astronomer, discoverer of Uranus (1781)
• Core Discovery: Proved that the solar spectrum contains invisible thermal radiation (infrared) beyond the red end, with the highest heating power of any spectral region
• Apparatus: Glass prism, blackened-bulb mercury thermometers, darkened room
• Primary Result: Temperature rise of +9°F in the dark region beyond red, vs. +7°F at the red limit and +2°F at violet
• Physical Mechanism: IR photons ($1\,\text{meV}$–$1.7\,\text{eV}$) excite molecular vibrational states ($E_n = \hbar\omega_{\text{vib}}(n+\tfrac{1}{2})$), converting electromagnetic energy into thermal kinetic energy
• Theoretical Framework: Fully explained by Planck’s blackbody law $B_\lambda(T)$ and Wien’s law $\lambda_{\text{max}} = b/T$
• Legacy: Founded spectroscopy; opened the blackbody radiation programme; directly enabled Planck’s 1900 quantum hypothesis

Primary Source: Herschel, W. (1800). “Experiments on the Refrangibility of the Invisible Rays of the Sun.” Philosophical Transactions of the Royal Society of London, 90, 284–292.