= Infrared
{wiki}
<Infrared> is <electromagnetic radiation> with <wavelengths> longer than the red end of ordinarily visible <light>. A useful named convention is the CIE range $780\,\mathrm{nm}$ to $1\,\mathrm{mm}$; the approximate visible range $400$–$700\,\mathrm{nm}$ used in some teaching texts puts the boundary nearer $700\,\mathrm{nm}$. https://openstax.org/books/astronomy-2e/pages/5-2-the-electromagnetic-spectrum[Andrew Fraknoi, David Morrison and Sidney C. Wolff, Astronomy 2e, §5.2: approximate visible range]{ref}. Neither number is a sharp physical cutoff of human vision. The CIE divisions IR-A, IR-B and IR-C are respectively $0.78$–$1.4\,\mathrm{\mu m}$, $1.4$–$3\,\mathrm{\mu m}$ and $3$–$1000\,\mathrm{\mu m}$; the boundaries of near-, middle- and far-<infrared> vary between applications. https://cie.co.at/eilvterm/17-21-004[CIE, International Lighting Vocabulary (2020), infrared radiation: ranges and boundary caveats]{ref}.
Use <vacuum> <wavelength> $\lambda$ when comparing these ranges. With <frequency> $\nu$, <speed of light> $c$, <Planck constant> $h$ and <photon> <energy> $E$,
$$
\nu=\frac{c}{\lambda},\qquad E=h\nu=\frac{hc}{\lambda}.
$$
Thus the CIE <infrared> interval corresponds approximately to $3.00\times10^{11}$–$3.84\times10^{14}\,\mathrm{Hz}$ and $1.99\times10^{-22}$–$2.55\times10^{-19}\,\mathrm J$ per <photon>, with the smaller <energy> at the longer <wavelength>. A $940\,\mathrm{nm}$ <infrared> <photon> has $E\simeq2.11\times10^{-19}\,\mathrm J$, whereas a $254\,\mathrm{nm}$ <ultraviolet> <photon> has $E\simeq7.82\times10^{-19}\,\mathrm J$. These are calculations from $hc/\lambda$, not measurements of a particular source. A television remote is a familiar approximately $940\,\mathrm{nm}$ source; its information is carried by variations in the emitted <radiant flux>. https://science.nasa.gov/ems/07_infraredwaves/[NASA Science Mission Directorate, Infrared Waves: remote controls and thermal imaging]{ref}.
Detection and visual perception answer different questions. A <photodetector> can respond to <infrared> even when an observer perceives no <light>; a <thermometer> detects an increase in <temperature> after <photon absorption>. Conversely, a small readout can reflect a small <spectral responsivity>, rather than absence of incident <electromagnetic radiation>. Images made from <infrared> readouts use display colors chosen by the imaging system; those colors are not the colors of the incoming <infrared>.
The important microscopic mechanisms also differ. In <infrared spectroscopy>, <photon absorption> often increases the <energy> of a <normal mode> in which <chemical bonds> stretch or bend. The corresponding <optical spectrum> helps distinguish <molecules> by their motions. For the usual <electric dipole> mechanism, the motion must change the <electric dipole moment>; matching the <frequency> alone is not sufficient. https://ocw.mit.edu/courses/5-35-introduction-to-experimental-chemistry-fall-2012/3f54ecef6f159a0a11dd60251491e075_MIT5_35F12_Mod1_Background.pdf[MIT 5.35, Fundamentals of Spectroscopy, p. 6: electric-dipole condition for infrared absorption]{ref}. Electronic processes can also emit or absorb <infrared>, so it is not exclusively radiation from molecular motion. https://openstax.org/books/organic-chemistry/pages/12-6-infrared-spectroscopy[John McMurry, Organic Chemistry, §12.6: molecular motions and infrared absorption]{ref}; https://openstax.org/books/college-physics-2e/pages/24-3-the-electromagnetic-spectrum[Paul Peter Urone and Roger Hinrichs, College Physics 2e, §24.3: sources of infrared radiation]{ref}.
<Infrared> is especially useful for observing <thermal radiation> from objects near everyday <temperatures>. For an ideal $300\,\mathrm K$ <blackbody>, <Wien's displacement law> gives a <wavelength> peak near $9.66\,\mathrm{\mu m}$. A thermal camera's readout nevertheless depends on <emissivity>, reflected surroundings and transmission along the path, as well as <temperature>. https://www.flir.com/discover/professional-tools/how-does-emissivity-affect-thermal-imaging/[Teledyne FLIR, How Does Emissivity Affect Thermal Imaging?: emitted and reflected contributions]{ref}. A source emitting <infrared> need not be hot: an <infrared> remote is useful precisely because a <photodetector> can distinguish its signal from a background. Visible <light> and <ultraviolet> can also cause heating when absorbed; “infrared” names a <wavelength> range, not a unique form of <heat>.
Herschel's 1800 discovery made the distinction between sight and detection experimentally concrete. His report describes a <optical prism> spreading sunlight across a white, ruled receiving surface, with three <thermometers> at different positions near the end of the visible <optical spectrum>. He observed heating beyond the red edge where no visible color appeared. The result established that sunlight contained invisible radiation less strongly refracted by that <optical prism> than the visible red; it did not measure a <photon> <energy> or establish today's <infrared> boundaries. https://makingscience.royalsociety.org/items/l-and-p_11_125/paper-experiments-on-the-refrangibility-of-the-invisible-rays-of-the-sun-by-william-herschel[William Herschel, Experiments on the refrangibility of the invisible rays of the sun (1800), Royal Society manuscript record]{ref}; https://en.wikisource.org/wiki/Page:Proceedings_of_the_Royal_Society_of_London_Vol_1.djvu/42[Royal Society proceedings, contemporary abstract of Herschel's experiment: apparatus and observations]{ref}.
A documented modern version by Caltech/IPAC uses a glass <optical prism>, white paper in a shaded box and three blackened liquid-filled <thermometers>. Initial readings in shade provide each <thermometer>'s baseline; subsequent readings compare blue, yellow and just beyond red after the bulbs have had time to warm. The measured quantity is the rise in <temperature>, not a “temperature of a color”. The lesson reports the expected largest rise beyond visible red and specifically discusses matching the bulb coatings and <thermometer calibration>. Clouds and changes in the projected <optical spectrum> affect the comparison. https://coolcosmos.ipac.caltech.edu/page/lesson_herschel_experiment[Caltech/IPAC Cool Cosmos, The Herschel Experiment (2022): apparatus, readout and calibration controls]{ref}.
For a stronger modern interpretation, an additional shaded <thermometer> would monitor ambient drift, exchanging bulbs between positions would test differences between <thermometers>, and blocking the incident beam would distinguish beam-dependent heating from warmed supports or air. These are suggested controls, not claims about Herschel's historical procedure. <Thermal conduction> through the mounting and <convection> can change the readout. A broad bulb also samples a range of <wavelengths>; the <optical prism>'s transmission and <optical dispersion>, the bulb's absorption and heat loss all affect the position of the largest rise. In particular, the result does not show that an <infrared> <photon> carries more <energy> than a visible <photon>.
A simple analytical illustration makes those limitations explicit. Let $\theta=T-T_{\mathrm{amb}}$ be the bulb's excess <temperature>, $C$ its <heat capacity>, $G$ its effective heat-loss coefficient in $\mathrm{W\,K^{-1}}$, and $P_{\mathrm{abs}}$ the absorbed <power>. Assume one uniform bulb <temperature>, constant ambient <temperature>, constant $C,G$, and losses linear in $\theta$. Then
$$
C\frac{d\theta}{dt}=P_{\mathrm{abs}}-G\theta,\qquad
\theta(t)=\frac{P_{\mathrm{abs}}}{G}\left(1-e^{-t/\tau}\right),\qquad \tau=\frac{C}{G},
$$
for a beam switched on at $t=0$ with $\theta(0)=0$. After switching the beam off at $t=t_s$, $\theta(t)=\theta(t_s)e^{-(t-t_s)/\tau}$. The <exponential function> follows by solving this <linear differential equation>. The steady excess <temperature> measures $P_{\mathrm{abs}}/G$; it is not a direct measurement of the <optical spectrum>. With illustrative $C=0.020\,\mathrm{J\,K^{-1}}$ and $G=0.0010\,\mathrm{W\,K^{-1}}$, $\tau=20\,\mathrm s$. Absorbed <powers> of $1.0$ and $0.5\,\mathrm{mW}$ give steady rises of $1.0$ and $0.5\,\mathrm K$, regardless of which <wavelengths> supplied that absorbed <power>.
\Image[/infrared-ultraviolet-herschel-thermal-model.png]
{title=Detecting <infrared> by a <temperature> rise: a Herschel-style schematic and an analytical thermal-response model}
The upper schematic represents the logic of the <optical prism> experiment; its <light ray> positions are not a calibrated <wavelength> scale. The lower curves use the illustrative heat-balance model, with the beam blocked at $60\,\mathrm s$; they are not historical or modern measured data. The beauty of the experiment is that a simple change of detector extends observation beyond what the eye can perceive.
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