Figure 16.20 shows a wave on a rope in several different situations. In (a) the rope is vibrating only up and down-it is vibrating in the vertical plane. We say the wave on this rope is polarized in the vertical plane or that it is vertically polarized. In (b) the rope is polarized in the horizontal plane. In (c) the wave on the rope is not plane polarized. It may be the kind of wave you create if you move the end of the rope in a circle-or, better still, move the end of the rope transversely but at various angles or directions. A transverse disturbance moves down the rope but it is not plane polarized. In (d) a barrier with a vertical slit is placed around the rope-somewhat like a picket fence. As the rope moves back and forth the barrier absorbs or cancels the movement. But when the rope moves up and down the barrier allows it to pass freely. Beyond the barrier the wave on the rope is polarized vertically as in (a). In (e) a barrier with a horizontal slit is placed around the vibrating rope as was done in (d). This time as the rope moves up and down the barrier absorbs or cancels the movement. But when the rope moves horizontally the barrier allows it to pass freely. Beyond the barrier the wave on the rope is polarized horizontally as in (b). These barriers act as polarizers and allow us to selectively create polarized waves from unpolarized waves.

Figure 16.21 shows a vertically polarized wave on a rope and a vertical polarizer. The wave is allowed to pass through freely. But a vertically polarized wave is stopped or absorbed by the horizontal polarizer. Of course, a horizontally polarized wave would be passed freely by a horizontal polarizer and blocked by a vertical polarizer. There is nothing similar to this for longitudinal waves.

Light is a transverse wave of electric and magnetic fields. Since light is a transverse wave it may be polarized. By the nineteenth century-but before the electromagnetic nature of light was known-it had been found that light could be polarized. But light is not always polarized. Light from a light bulb-or a candle flame or the Sun or most ordinary sources-is a flood of tiny bundles of light, called photons, that are emitted independently by thousands of thousands of individual atoms. Each atom emits its light with some polarization state. But the next atom is entirely independent or random. We say that such light is unpolarized-just as the wave on a rope in Figure 16.20(c). We can use a diagram like Figure 16.22 to indicate unpolarized light by indicating that vibrations in all different directions are present. Just as with the wave on a rope, unpolarized light can be passed through a polarizer and the light that passes through will be polarized.

The most common way of obtaining polarized light today is by passing ordinary, unpolarized light through a sheet of Polaroid, or a polarizing filter. Polaroid, although quite common today, was invented in 1928 by Edwin H Land while still a freshman Physics major at Harvard (You may know him more for the Polaroid Land cameras that produce instant pictures). Polaroid is made of long molecules oriented parallel to each other. The electric field parallel to these molecules is absorbed but the electric field perpendicular to them is transmitted. Thus, Polaroid acts as a series of fine, parallel slits somewhat like a microscopic picket fence.

Figure 16.23 illustrates unpolarized light becoming polarized as it passes through such a polarizer. Experimentally we can then check to see if this light is, indeed, polarized, by passing it through a second polarizer, now called an analyzer, as shown in Figure 16.24. Rotating the analyzer will cause the intensity of the polarized light to change from a maximum to zero. If light is completely unpolarized, then rotation of a Polaroid analyzer will have no effect on the intensity of the light (although it will change the plane of polarization). If light is only partially polarized, then rotation of a Polaroid analyzer will change the intensity of the light but the minimum intensity will not be zero.

Polarized light can also be produced by reflection of initially unpolarized light from a non-metallic surface. The reflected beam will be at least partially polarized in the plane of the reflecting surface. When the angle between the reflected and refracted rays is 90 the reflected ray is completely polarized. This was found experimentally in 1812 by David Brewster, a Scottish Physicist.

This polarization of reflected light is very useful. Most reflections of sunlight occur from nearly horizontal surfaces-a lake's surface, the hood of a car, a road's surface. That means the glare of reflected light will usually be partially polarized horizontally. If you wear Polaroid sunglasses with the transmission axes of the lenses vertical, much of the glare from reflected light will be eliminated. That is why Polaroid sunglasses are effective. Figure 16.25 shows a sketch of such a reflection. This polarization of reflected light is useful to photographers who can use a polarizing filter to control reflections from windows or the surface of water.

Figure 16.25 Light partially polarized parallel to the reflecting surface results when light is reflected from a non-metallic surface.

Skylight is polarized; you can easily demonstrate this by rotating Polaroid sunglasses while looking at the sky and seeing the brightness of the sky increase and decrease. This is most noticeable if you look at an area of the sky that is 90 from the Sun. This can be understood by looking at Figure 16.26. There sunlight is shown striking an air molecule. The sunlight causes the molecule to vibrate back and forth and reradiate another light wave. The reradiated wave will be very strong in a direction perpendicular to the vibrations and weak to non-existent along the direction of the vibration. The reradiated light that is seen in the direction shown in the figure will be polarized as shown. Skylight is actually the result of many such scatterings so the polarization is not complete.

Why is the sky blue? The scattering from air molecules of sunlight into skylight described in the previous paragraph is more efficient for shorter wavelength light because it is a resonance phenomenon. That means that it is the blue and violet light that is scattered many times so that we see this light coming from all directions. The longer wavelength light-the red and orange-continues on with far less scattering. At sunrise and sunset, light from the Sun travels through much more of our atmosphere so the light from the Sun is a deep orange or red. This is illustrated in Figure 16.27. Indeed, Physics is everywhere!

Q: In general, would you expect the sky to be darker or lighter from a very high mountain?

A: On the Moon, with no atmosphere to scatter sunlight at all, the sky is always black. Atop a very high mountain (or from a very high-flying airplane), with less atmosphere to scatter sunlight, the sky will be darker-still blue, but a darker blue. Moisture and dust particles in the air greatly affect the way light is scattered. But, generally speaking, the sky is a darker blue from very high mountains.