Light Pressure

the pressure produced by light on reflecting or absorbing bodies. The pressure of light was first discovered and measured experimentally by P. N. Lebedev (1899). Its value, even for the most powerful light sources (the sun or an electric arc), is extremely small and under terrestrial conditions is masked by side effects (convection currents or radiometric forces), which may be thousands of times greater.

Lebedev made special instruments to detect the pressure of light and conducted experiments that are a remarkable example of experimental art. The main part of Lebedev’s instrument was formed by light, flat vanes 5 mm in diameter, made of various metals (platinum, aluminum, and nickel) and mica (Figure 1). The vanes were suspended on a fine glass thread and placed in a glass vessel G (Figure 2) from which the air was evacuated. Light from a powerful electric arc B was directed onto the vanes by a special optical system and mirrors. By moving the mirrors S₁ and S₄, it was possible to alter the direction of incidence of the light on the vanes. The design of the instrument and the method of measurement made it possible to cut disturbing radiometric forces to a minimum and to detect light pressure at the reflecting or absorbing vanes, which were deflected by it, twisting the thread. In 1907–10, Lebedev studied the pressure of light on gases, which was even more difficult, since it is hundreds of times less than on solids.

Figure 1. Various systems of vanes (I, II, and III) in Lebedev’s experiments: (O) platinum loop, (C) gimbal suspension

The results of Lebedev’s and later workers’ experiments completely agree with the values for light pressure given by the electromagnetic theory of light (J. C. Maxwell, 1873), a further important confirmation of the Faraday-Maxwell electromagnetic field theory. According to the electromagnetic theory of light, the pressure exerted by a plane electromagnetic wave incident perpendicular to the surface of a body equals the density u of the electromagnetic energy (the energy per unit volume) near the surface. This energy is made up of the energy of the wave incident on and reflected from the body. If the energy of an electromagnetic wave incident on 1 sq cm of the surface of a body is 5 ergs/-(cm²-sec) and the coefficient of reflection of electromagnetic energy from the surface is R, then near the surface the energy density is u= S(1 + R)/c, where c is the speed of light. This quantity is also equal to the pressure of light on the surface of the body: ρ = 5(1 + R)lc ergs/cm³, or joules/m³. For example, the energy of solar radiation incident on the

Figure 2. Diagram of Lebedev’s experiment: (B) light source (carbon arc); (C) condenser; (D) metallic diaphragm; (K) lens; (W) glass vessel with plane parallel sides, filled with water and acting as a light filter; (S₁–S₆) mirrors; (L₁) and (L₂) lenses; (R) image of diaphragm D on vanes (not shown in figure) inside glass globe G; (P₁) and (P₂) glass plates; (T) thermopile; (R₁) image of diaphragm on thermopile

earth is 1.4 x 10⁶ergs/(cm^2.sec), or 1.4 x 10³ watts per sq m; consequently, for an absolutely absorbing surface (for R = 0), ρ= 4.3 x 10^-5 dyne/cm² = 4.3 x 10^-6 newton per sq m (N/m²). The total pressure of solar radiation on the earth is 6 x 10¹³ dynes (6 x 10^{8 n}), or 10¹³ times less than the sun’s gravitational attraction.

Isotropic equilibrium radiation also exerts a pressure on a system (body) with which it is in equilibrium:

p = u/3 = 1/3σ T⁴

where σ is the Stefan-Boltzmann constant and T is the temperature of the radiation. The existence of light pressure shows that a flux of radiation has not only energy but also momentum, and hence mass.

From the point of view of the quantum theory, light pressure is a result of the transfer to bodies of the momentum of photons (energy quanta of an electromagnetic field) in processes of absorption or reflection of light. Quantum theory gives the same formulas for light pressure.

Light pressure plays a particularly important part in two fields of phenomena that are opposite in scale—astronomical and atomic phenomena. In astrophysics, light pressure, in addition to gas pressure, provides the stability of stars, opposing gravitational compression forces (at temperatures of about 10⁷ degrees in the interior of stars, light pressure reaches tens of millions of atmospheres). Light pressure is essential for the dynamics of circumstellar and interstellar gas. Some shapes of comet tails are explained by the action of light pressure. Light pressure causes disturbances of the orbits of artificial earth satellites (especially of light satellites of the Echo type, with a large reflecting surface). Among the atomic effects of light pressure is “light recoil,” which an excited atom experiences upon emitting a photon. A phenomenon closely related to light pressure is the transfer by gamma quanta of part of their momentum to the electrons on which they are scattered or to the nuclei of atoms of a crystal in radiation and absorption processes.