Sunset

A video of this demonstration is available at this link.

This demonstration illustrates the scattering of light that occurs in the earth’s atmosphere, and also in the interstellar medium. In the earth’s atmosphere, this scattering is responsible for the blue color of the sky during the day, and for red sunsets. In the interstellar medium, it causes a phenomenon called reddening, in which distant stars appear to be redder than they really are.

The beam from the projector shines through the glass container and onto a screen. In the container is a solution of sodium thiosulfate (Na2S2O3). At the start, the solution is clear, and the light passes through the vessel essentially unchanged, throwing a white spot onto the screen. Little or no light comes from the sides of the vessel (i.e., perpendicular to the incoming beam). When you add strong acid, it protonates the thiosulfate ion to form thiosulfuric acid (H2S2O3), which is unstable and decomposes to form colloidal sulfur:

S2O3= + 2H+ → S(s) + SO2(g) + H2O(l)

The sulfur crystals thus formed scatter the light coming from the projector. At first, the crystals are small and relatively few. As the reaction progresses, the crystals grow in size and number, until the suspension takes on a milky character and scatters essentially all the light from the projector. At this point, the crystals are probably approximately micron-sized.

To perform this demonstration, add the acid to the solution in the glass container, and stir the solution briefly to mix in the acid. The reaction takes time to proceed, so there is some delay until you begin to see the solution turning cloudy. As it does, you begin to see the beam of the projector as it passes through the solution, with the scattered light coming from the sides appearing bluish in color, and the light on the screen taking on a yellowish color. As more sulfur crystals form and they become larger, they scatter more light. The spot on the screen becomes redder and redder, until the scattering is so great that no light reaches the screen. The light scattered to the sides is vertically polarized (vide infra), which you can show by placing the sheet of polaroid near the side of the container and rotating it back and forth (between where the easy axis is vertical and where it is horizontal).

In a clear sky, and in interstellar regions where there is gas, but not much dust, light is scattered by gas molecules, which, for the range of visible light, are much smaller than the wavelength of the light (for nitrogen and oxygen, approximately on the order of 2000 times smaller). Incoming light interacts with the electrons in the gas molecules, in essence being absorbed and reemitted, with no change in energy. Most of the light continues in its original direction, but some is scattered sideways. This type of scattering, in which the scattering centers are much smaller than the wavelength of the light, is known as Rayleigh scattering, and it exhibits an inverse λ4 dependence. That is, shorter wavelengths are scattered to a much greater extent than longer wavelengths. This is why the sky is blue; blue light is scattered so much more greatly than red light that it gives the sky its blue color, and it leaves the light coming from the sun a yelowish color. (Warning: Never look directly at the sun, except with appropriate filters made expressly for that purpose!) In similar fashion, when light passes through the interstellar medium, shorter wavelengths are preferentially scattered, leaving the longer wavelength light coming through. Thus, as mentioned above, distant stars appear redder than they actually are.

At sunset, light from the sun takes a significantly longer path than during the day, so that most of the blue light, and light of other wavelengths shorter than that of red light, is scattered out, leaving mostly red light. This is why the sun appears red at sunset, as do clouds and other objects that reflect the red light coming from the sun.

This scattering phenomenon is also responsible for the fact that sunlight coming through the atmosphere is partially polarized. Light coming from the sun (or, in this demonstration, the projector) is randomly polarized in a plane perpendicular to its direction of travel. For example, if the sun is overhead, the electric vector of the sunlight points in all directions in a plane parallel to the ground. In our demonstration, the electric vector of the light from the projector points in all directions in a plane parallel to the front and rear faces of the glass container. Since an electric dipole cannot radiate along its axis, only light whose electric vector is perpendicular to the beam of light, and also to the line between an observer and the beam, is visible. Thus, with the sun overhead, skylight near the horizon is horizontally polarized. In our demonstration, light scattered from the sides of the container is vertically polarized.

A further note on scattering

The exact nature of light scattering depends on the size of the scatterers relative to the wavelength of light, and also on the number density of the scatterers. Generally speaking, when the diameter of the scatterers is 1/10 the wavelength of light or smaller, the scattering obeys the aforementioned inverse-fourth power relationship to the wavelength, and is called Rayleigh scattering. In Mie scattering, the diameter of the scatterers is between 1/10 and 100 times the wavelength of the light, and the power of the wavelength dependence varies from around -4 to +2. When the particle size is greater than 100 times the wavelength of the light, the scattering cross-section is roughly constant, and it is independent of wavelength. This type of scattering is called Tyndall scattering. Sometimes, people refer to the general phenomenon of scattering as the Tyndall effect. Scattering is most efficient when the size of scattering particles is about the same as the wavelength of the light.

As mentioned above, in a clear atmosphere, light scattering colors the sky blue and gives red sunsets. When there is a lot of particulate matter in the air, for example, in the aftermath of a large fire or volcanic eruption, this enhances the scattering and causes the sunsets to be even more spectacular than usual.

References:

1) Halliday, David and Resnick, Robert.Physics, Part Two, Third Edition (New York: John Wiley and Sons, 1977), pp. 1084-1086.
2) Sears, Francis Weston and Zemansky, Mark W.College Physics, Third Edition (Reading, Massachusetts: Addison-Wesley Publishing Company, Inc., 1960), pp. 946-947.
3) He, Guang S.; Qin, Hai-Yan and Zheng, Qingdong. “Rayleigh, Mie, and Tyndall scatterings of polystyrene microspheres in water: Wavelength, size, and angle dependences,” Journal of Applied Physics 105, 023110 (2009).
4) Ahn, Heejoon and Whitten, James E. “Monitoring Particle Growth: Light Scattering Using Red and Violet Diode Lasers” Journal of Chemical Education 82(6), 909 (2005).