The people who invented that tale were well aware of the impossibility of reaching the rainbow itself. Knowing that the rainbow moves with you, they were free to promise anything about what lies at the base of the rainbow.
The ring that you see surrounding the sun is probably the 22° halo caused by refraction from ice crystals in the upper atmosphere. These tiny ice crystals are hexagonal prisms and they deflect the light that passes through them to form a ring of light around the sun. Because the particles are large enough to bend all the colors of light equally, the ring appears white—or blue-white when superimposed on the blue sky. The deep blue of the surrounding sky is caused by Rayleigh scattering of the sunlight passing through it. In this process, small groups of air molecules and tiny dust particles deflect sunlight toward your eye. Since they deflect short wavelength light (blue light) more effectively than long wavelength light (red light), they give the sky a bluish glow. Finally, the white appearance of the horizon is probably light scattered toward your eyes by surface haze. Relatively large particles in the air scatter sunlight in all directions so that you see a white glow from the air near the ground.
A wonderful reference for some of these ideas is “Rainbows, Halos, and Glories” by Robert Greenler.
A white shirt doesn’t absorb visible light (or at least very much visible light), but it may absorb lots of infrared light. Since much of the sun’s light and heat are in the form of invisible infrared light, that infrared absorption can be very important. There are many materials that appear white to your eye that do absorb strongly in the infrared and thus get very hot in sunlight.
A thin layer of oil on water creates interference effects, just like those seen in a thin soap film. Sunlight reflects from both the top and the bottom of the oil layer and these two reflections can interfere with one another. If the blue/green wavelengths of light interfere destructively on their way to your eye, you will see the oil layer as red. If the green/red wavelengths of light interfere destructively, you will see the oil layer as blue. How you see the oil layer depends on its thickness and the angles of the light.
Tanning beds emit ultraviolet light in order to trigger your skin’s tanning response. This ultraviolet light can and does cause chemical damage to your skin. Like all light, ultraviolet light is absorbed and emitted as particles. The energy in each light particle depends on its wavelength and, since ultraviolet light has short wavelengths, ultraviolet light particles carry lots of energy. They carry enough energy to rearrange the molecules that absorb them. If those molecules are part of the genetic information of a cell, the cell may die or, worse yet, may become cancerous. The shorter the wavelength of the ultraviolet light, the more energetic its particles and the more damage it can do. Tanning beds walk a narrow line between inducing tanning and causing significant damage. Leather skin is one end result of too much chemical damage. Tanning beds that emit relatively long wavelength ultraviolet are probably less harmful than those that emit shorter wavelength ultraviolet (these wavelength ranges are sometimes designated by letters A, B, and C…I think that A is the longest wavelength and least harmful). Still, you skin’s tanning response is a defense against chemical damage and is probably not worth trying to trigger with light. Recent research seems to have found chemicals that trigger tanning. These chemicals mimic light-damaged molecules in your skin. Your skin senses these molecules and responds by tanning. If these chemicals work, you’ll soon be able to develop a true tan without exposure to light.
The sheet polarizers that are used in sunglasses or in the demonstrations in class contain molecules that absorb electromagnetic waves of only one polarization. These molecules form long chains that interact with electromagnetic waves only when the electric fields push charge along the lengths of the molecules. In the polarizing sheets, the molecules are all oriented along the same direction so that they all absorb light of the same polarization. The other polarization of light passes through the sheets virtually unscathed. When unpolarized (randomly polarized) light enters one of these sheets, any waves that are polarized along the molecules are absorbed while any that are polarized across the molecules are permitted to pass. About half the light makes it through and that half is polarized across the molecules. If this remaining light is sent through a second polarizing sheet, turned 90° so that the molecules of the second sheet are aligned with the polarization of the light leaving the first sheet, then the remaining light will be absorbed in the second sheet and essentially no light will emerge from the pair of sheets. This arrangement, two polarizers turn 90° with respect to one another, is called “crossed polarizers”. It is a useful arrangement for observing materials that rotate polarization by distorting the electric and magnetic fields. If a distorting material is placed between the two crossed polarizers, light from the first polarizer may be altered by the material and thus be able to pass through the second polarizer.
The sun is a ball of incandescent gas. That gas moves about, flowing up and down as well as across the sun’s surface. This movement keeps the sun’s temperature roughly uniform but there are occasionally imperfections; regions of the sun’s surface that get out of balance with the rest of the sun. When you cook a thick soup on the stove, there will also be regions of the surface that are cooler than others.
Light from the sun travels in straight lines (apart from some wave effects called diffraction, that are unimportant in this case). As sunlight passes objects, those objects absorb or scatter the sunlight, leaving regions of space that no longer contain any electromagnetic waves. Regions of space behind the objects contain no sunlight and do not appear illuminated. We perceive those dark, unilluminated regions as shadows.
Brown water contains colored contaminants that provide the color. Brown is the typical end result for a random mixture of pigments. The blue ocean is caused mostly by the sky. Since the ocean reflects some of the light from the sky, it appears blue. Pure water is almost completely colorless. Thus a glass of water has no color (unless you illuminate it with colored light). But if you look at a white light through many meters of water, that light will become slightly colored. Water absorbs a very small amount of visible light and you will see only what is not absorbed. I’m not sure what color pure water has. It may appear slightly green.
Some of them may be polarized materials, blocking horizontally polarized light, but most are simply absorbing materials that are embedded directly in the glass during its manufacture. Chemically tinted glass just darkens the sky be absorbing some of the light passing through the glass, regardless of polarization. It’s not possible to chemically treat the glass to make it absorb only one polarization of light because that treatment would have to carefully align its molecules. In the plastic polarizing sheets, there is an alignment process (usually stretching in one direction) that lines up all the absorbing molecules.