The propagation of a narrow beam of light in a scattering medium is one of the central problems in the optics of scattering media. It is clear that not enough experimental data have been published [1-9] in order to check the results of well-known theories (see, for example, [10-16] as well as the review in Chapter 3 of [6]) and to obtain convenient and reliable empirical approximations, describing the behavior of the propagation of a narrow beam in a scattering medium for practical use. In this work, we present the results of an experimental study of the spreading of a finite beam in a plane which is the bounding surface of a plane-parallel scattering layer and which is perpendicular to the axis of the incident beam. The features of the experiment are as follows: The energy characteristics of the radiation transmitted through the layer and not inside the layer are studied; media in which the photon survival probability A is close to i (I -A < 2.10-~), with extremely strong elongation of the scattering function of an elementary volume (the asymmetry coefficient is not less than 250), are studied; the scattering layers have a comparatively high optical thickness ~ (14 ~ ~ 580) and are illuminated by a beam with a variable optical diameter 2~r (r is the geometrical radius of the illuminating beam; e is the attenuation coefficient of the medium), whose values vary in the range 3-1100 (the indicated values of the optical thickness of the layers indicate that, for all practical purposes, direct transmission in them did not occur); the scattering layers have boundaries which reflect and refract the light beams in accordance with Snell's law and Fresnel's formulas. The indicated characteristics are determined by the properties of the material used to fabricate the objects used for the experimental study: plane-parallel polished samples of light-scattering glasses [17, 18], primarily MS23 glass. The measured quantity was the luminosity of the scattered radiation passing through the sample and propagating along the axis of the illuminating beam, i.e., along the normal to the surface of the layer. At the same time, photometric measurements were performed on the flux from a limited section of the surface of the sample, which had the form of the circle with radius R centered on the axis of the illuminating beam (see Fig. I). Successive measurements were performed for a series of values of Ri. The difference J(Ri+~) -J(Ri) gives the magnitude of the luminosity of the light scattered by an annular zone bounded by the radii Ri+, and Ri. In addition, dividing this difference by the area of the ring we obtain the average brightness L of the radiation emerging at a distance (Ri+~ + Ri)/2 from the axis of the illuminating beam. To perform the measurements, we used the setup described in [19], where a luminosity measuring head (the optical setup that realizes the conditions for measuring the luminosity according to the body-centered method) was placed in front of the photometer. The measurements were performed at ~ = 546 nm and aperture angles of the illuminating beam and the observed beam equal to 4 and i ~ respectively. In addition, pointwise probing of the surface of the samples with the help of the luminosity measuring head was also