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.