Pixel-art torsion balance in a glass bulb with bright and blackened discs on a hanging wing, a yellow beam of light from the left and a green arrow showing the push, captioned light pushes

Lebedev 1900: How the Pressure of Light Was First Measured

Light carries momentum, so it pushes on whatever it hits. Maxwell published that prediction in 1862, and the first person to measure the push on a solid body was the Russian physicist Pyotr Lebedev, who announced his result in 1900 Radiation pressure, Wikipedia[1] Pyotr Lebedev, Wikipedia[2]. Ernest Fox Nichols and Gordon Ferrie Hull confirmed it independently in 1901 Radiation pressure, Wikipedia[1]. Lebedev’s experiment counts as the first quantitative confirmation of Maxwell’s theory of electromagnetism Pyotr Lebedev, Wikipedia[2], and it is the story behind our Pressuria light-pressure sticker.

Formula plate in Pixelated Physics pixel style: p = E/c; Pabs = I/c; Prefl = 2I/c; Prefl(1 au) ≈ 9.08 μPa

How strong is the pressure of light?

Electromagnetic radiation that delivers energy E to a surface also delivers momentum Radiation pressure, Wikipedia[1]

p = E/c

where p is momentum in kg m s⁻¹, E is energy in joules and c = 299 792 458 m s⁻¹ is the speed of light. A beam of intensity I (power per unit area, in W m⁻²) that is completely absorbed at normal incidence therefore exerts a pressure Radiation pressure, Wikipedia[1]

Pabs = I/c

in pascals. A perfect mirror reverses the momentum of the light instead of just stopping it, so it receives twice the push Radiation pressure, Wikipedia[1]:

Prefl = 2I/c

That factor of two is the formula on the Pressuria sticker. The numbers are tiny. For a perfect reflector facing the Sun at Earth’s distance, 1 astronomical unit, the radiation pressure is Radiation pressure, Wikipedia[1]

Prefl(1 au) ≈ 9.08 μPa

or about 4.5 μPa for a black absorber, half as much. Atmospheric pressure, about 101 kPa, is roughly ten billion times larger. To measure light pressure in a laboratory, an experimenter has to detect forces of order micronewtons per square metre while every other force on the apparatus is kept smaller still.

Pixel-style bar chart: full sunlight at 1 au gives 4.54 μPa on a black absorber and 9.08 μPa on a perfect mirror

Why was light pressure so hard to measure?

The trouble is the gas. Any vane hung in a bulb is surrounded by residual gas, and when light warms the vane the gas moves. Two effects are much stronger than the light pressure itself Grigoriev 2016[3]:

  • Convection. The illuminated vane becomes warmer than the glass bulb, and the warmed gas circulates and drags on the vane.
  • Radiometric forces. Gas molecules leave the warmer, illuminated side of a disk with larger speeds than they leave the shaded side, and the difference in their recoil can exceed the radiation pressure several times over Grigoriev 2016[3]. This is the effect that turns a Crookes radiometer.

A light-pressure experiment is mainly a fight against these gas forces. Both teams won it, by different routes.

How did Lebedev’s experiment work?

Lebedev worked at Moscow University, where he became professor of physics in 1900 Grigoriev 2016[3]. His apparatus was a torsion balance: light from an electric arc fell on a light “wing” hung from a thin filament inside an evacuated glass bulb, and the twist of the filament gave the force Grigoriev 2016[3]. The design details all target the gas problem Grigoriev 2016[3]:

  • A better vacuum. A drop of mercury was heated in the vessel so that mercury vapour displaced the air, which was pumped out. When the bulb cooled, the remaining vapour pressure fell, leaving a very good vacuum for the time.
  • Thin metal vanes. The wing carried pairs of thin platinum discs, 0.1 mm and 0.01 mm thick, chosen so that temperatures evened out quickly. In each pair one disc was bright on both sides and the other had one side coated with platinum black.
  • Reversing the beam. Light was sent first onto one side of the wing, then onto the other. Convection was the same in both cases, so the difference between the two deflections did not depend on the gas motion.
  • Taming the radiometric force. A larger bulb at lower pressure weakened it, and comparing the thick and thin blackened discs allowed the remainder to be taken into account.

Lebedev reported his results at the International Congress of Physics in Paris in 1900, during the Exposition Universelle, and published the full paper in Annalen der Physik in 1901 Pyotr Lebedev, Wikipedia[2] Lebedew 1901[4] Grigoriev 2016[3]. Later work by his group extended the measurement to gases. In 1909 he reported that the pressure of light on gases also agrees with Maxwell’s theory Pyotr Lebedev, Wikipedia[2]. Physicists at the Lebedev Physical Institute in Moscow connect these measurements to modern optomechanics, where light pressure moves mirrors in interferometers and microscopic resonators Berezanskaya, Doskoch and Man’ko 2016 (arXiv)[5].

Pixel-style diagram of Lebedev’s apparatus: a wing of bright and platinum-black discs hung on a thin filament inside an evacuated bulb, lit from one side by an arc lamp

Nichols and Hull: the American measurement

Nichols and Hull used a different torsion balance: a pair of small silvered glass mirrors hung from a fine quartz fibre in an enclosure whose air pressure could be adjusted Nichols radiometer, Wikipedia[6]. By comparing light falling on the silvered and unsilvered sides they could measure the gas effect, and found it almost negligible at about 16 mmHg (2.1 kPa) Nichols radiometer, Wikipedia[6]. They measured the beam’s energy with a small blackened silver disk and found agreement between observed and computed radiation pressures within about 0.6% Nichols radiometer, Wikipedia[6]. Their first report appeared in 1901 Nichols and Hull 1901[7] and a second, fuller paper in 1903 Nichols and Hull 1903[8].

Where does light pressure matter today?

The idea is old. Johannes Kepler suggested in 1619 that something from the Sun pushes comet tails away from it Radiation pressure, Wikipedia[1]. Today radiation pressure steers spacecraft. Japan’s IKAROS, launched on 20 May 2010, became the first spacecraft to demonstrate solar-sail technology in interplanetary space IKAROS, Wikipedia[9], using a thin square sail 14 m on a side to fly past Venus IKAROS, Wikipedia[9]. Radiation pressure also shapes dust clouds and stellar interiors, and in the laboratory it powers optical tweezers Radiation pressure, Wikipedia[1]. To see what happens when an electric field accelerates a charge instead of a mirror, read our history of Faraday, Maxwell and electromagnetism. More designs about light and fields are in our electromagnetism collection and waves and optics collection.

Pixel-style log plot of solar radiation pressure on a perfect mirror against distance from the Sun, from 227 μPa at 0.2 au through 9.08 μPa at Earth to 0.34 μPa at Jupiter

Quick FAQ

Who measured light pressure first, Lebedev or Nichols and Hull?

Lebedev announced his measurement in 1900 and Nichols and Hull published theirs in 1901 Radiation pressure, Wikipedia[1]. The two measurements were independent and used different apparatus.

Is light pressure what spins a Crookes radiometer?

No. The radiometer is driven by gas forces of the kind Lebedev worked to remove Grigoriev 2016[3]. Light pressure on its vanes would turn it the opposite way. For the link between light and electric fields, see how electricity and magnetism are connected.

Why does a mirror feel twice the force of a black surface?

Absorbed light gives up its momentum once. Reflected light leaves with its momentum reversed, so the momentum change, and the force, is doubled Radiation pressure, Wikipedia[1].

References

  1. Wikipedia, “Radiation pressure”. https://en.wikipedia.org/wiki/Radiation_pressure
  2. Wikipedia, “Pyotr Lebedev”. https://en.wikipedia.org/wiki/Pyotr_Lebedev
  3. N. D. Grigoriev (2016), “He measured light pressure,” World of Transport and Transportation 14(2), 242–249 (DOI 10.30932/1992-3252-2016-14-2-30). https://doi.org/10.30932/1992-3252-2016-14-2-30
  4. Peter Lebedew (1901), “Untersuchungen über die Druckkräfte des Lichtes,” Annalen der Physik 311, 433–458 (DOI 10.1002/andp.19013111102; metadata verified via Crossref). https://doi.org/10.1002/andp.19013111102
  5. V. M. Berezanskaya, I. Ya. Doskoch and M. A. Man’ko (2016), “Light-pressure experiments by P. N. Lebedev and modern problems of optomechanics and quantum optics,” arXiv:1610.08439 [quant-ph]. https://arxiv.org/abs/1610.08439
  6. Wikipedia, “Nichols radiometer”. https://en.wikipedia.org/wiki/Nichols_radiometer
  7. E. F. Nichols and G. F. Hull (1901), “A Preliminary Communication on the Pressure of Heat and Light Radiation,” Physical Review (Series I) 13, 307–320 (DOI 10.1103/PhysRevSeriesI.13.307; metadata verified via Crossref). https://doi.org/10.1103/PhysRevSeriesI.13.307
  8. E. F. Nichols and G. F. Hull (1903), “The Pressure Due to Radiation. (Second Paper.),” Physical Review (Series I) 17, 26–50 (DOI 10.1103/PhysRevSeriesI.17.26; metadata verified via Crossref). https://doi.org/10.1103/PhysRevSeriesI.17.26
  9. Wikipedia, “IKAROS”. https://en.wikipedia.org/wiki/IKAROS

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.

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