A NEW METHOD FOR MEASURING LIGHT PRESSURE

As is known, the principal difficulty arising in the experimental determination of the magnitude of the pressure of light consists in the fact that in these experiments there is a radiometric effect superimposed on the effect of light pressure. The occurrence of the radiometric effect is due to the presence of gas surrounding the thin plates on which the light pressure acts.

To get around this difficulty, one may use two different methods: either attempt to create conditions under which the radiometric effect will be equal to zero, or, by comparing the results of appropriately selected measurements, eliminate the influence of the radiometric effect.

P. N. Lebedev, in his classic experiments that first proved the existence of light pressure, followed the second path[^1]. Nichols and Hull[^2], on the contrary, experimented at a gas pressure corresponding to a zero radiometric effect. Lebedev, however, pointed out quite justifiably that the results of the experiments of Nichols and Hull do not possess the same fundamental conclusiveness as the results of his own experiments[^3].

The point is that it is impossible to prove by direct experiment the equality to zero of the radiometric effect in experiments to determine light ...

pressure. However, further investigations did not follow the path so brilliantly begun by P. N. Lebedev, but rather the path lying closer to the method of Nichols and Hull. In connection with the improvement of vacuum technique, later experiments[^4] on measuring light pressure were carried out at very high vacuum, and by extrapolating the results to a gas pressure equal to zero, in these experiments they seemingly passed to conditions corresponding to a radiometric effect equal to zero.

Yet here too, as in the work of Nichols and Hull, the necessity of using a certain hypothesis about the dependence of the magnitude of the radiometric effect on pressure greatly reduces the fundamental convincingness of these experiments.

G. Kastelitz points out this shortcoming in his recently published work.[^5] G. Kastelitz developed an extremely simple and ingenious method for measuring light pressure, which is essentially an improvement of P. N. Lebedev’s method. Kastelitz, like Lebedev, does not try to eliminate the radiometric effect, but very simply excludes it from the measurements.

From Fig. 1 the principle of Kastelitz’s method is clear. A blackened plate is attached to the beam of a torsion balance, forming with it an angle of \(45^\circ\), as shown in the figure. \(O\) denotes the axis of rotation, \(S\) the blackened plate, and \(P\) the counterweight. The first measurement of the rotation of the torsion balance is made when a light beam falls on the plate \(S\) in direction \(I\), the second when the beam falls in direction \(II\). It is easy to see that in the first case the force of light pressure will impart to the balance beam a certain rotating moment, the magnitude of which will be equal to the product of this force by the arm of the beam. In the second case the incident radiation imparts no rotating moment to the beam, since the direction of the beam passes through the axis. The reflected radiation in both cases has a diffuse character and has the same magnitude, and therefore imparts equal impulses to the beam.

Fig. 1.

On the other hand, the radiometric effect will have the same value in both cases owing to the symmetrical arrangement of the plate with respect to both directions of the rays.

Thus it is perfectly clear that if one takes the difference between the angles of rotation in the first and second cases, this difference will be equal to the angle of rotation caused only by light pressure. By this method the radiometric effect is completely excluded and the magnitude of the light pressure is determined. Let us recall that in his experiments P. N. Lebedev illuminated opposite sides of the plate. Kastelitz’s method is more reliable, for in it the same side is at work the entire time, and the temperature gradient inside the plate is not significant.

Like Lebedev, Kastelitz measured not simply the angle of rotation of the balance, but the displacement of the zero of the oscillations of the beam when the plate was illuminated. The measurements were carried out at gas pressures of the order of \(10^{-6}\) mm Hg. The dimensions of the parts of the torsion balance were as follows:

The light source was an incandescent lamp (cinema lamp) of 650 W. Measurements were made at three different values of the filament current,

If along one axis one plots the angles of rotation for the first direction of the beam, and along the other the angles of rotation for the second direction, the results of measurements at different gas pressures fall well on straight lines with a slope of \(45^\circ\). This confirms that in both cases the radiometric effect is indeed the same. These straight lines do not pass through the origin, which is evidence of the existence of light pressure. The segments cut off by the straight lines on the coordinate axes give the magnitudes of the angles of rotation caused by light pressure. The greater the illumination, the higher the corresponding straight line passes. Having processed the results obtained, Castelli obtained, instead of the theoretical equality \(p = \dfrac{E}{c}\), the following equality:

\[ p = 1.04\,\frac{E}{c}, \]

where \(p\) is the pressure, \(E\) is the energy incident in \(1\) sec, and \(c\) is the speed of light. He regards this result as preliminary and expects in the future to attain still greater accuracy.

V. Fabrikant, Moscow

Literature

1. P. N. Lebedev, Rapp. près du Congrès de Phys., 2, 133, Paris, 1900; ZhRFKhO, Physical Section, 33, 53, 1901. Light Pressure. Classics of Natural Science, GIZ, 1922.

2. E. F. Nichols and G. F. Hull, Phys. Rev., 13, 293, 1901; Ann. d. Phys., 12, 225, 1903.

3. P. N. Lebedev. Collected Works, Moscow, 1913, p. 395.

4. A. Golsen, Ann. d. Phys., 73, 624, 1924; M. Bell and S. E. Green, Proc. Phys. Soc., 45, 320, 1933.

5. H. Castelli, Z. Physik, 96, 677, 1935.