Actually, 96% of the light hitting the “other side of a water droplet” does pass out of the droplet. What you see in the rainbow is the 4% that reflects back from the far side of the water droplet. If all of the light reflected, the rainbow would be much brighter.
Not exactly. A puddle contains water, which reflects light directly. Light from the blue sky travels toward the puddle and illuminates it. As the light enters the water, with its higher refractive index, part of the light reflects. You see this light when you look at the surface of a puddle. But a mirage involves refraction (bending) of light. As light from the blue sky enters a regions of hot air near the surface, that light bends upward. You again see light from the sky, but bent upward by the air rather than being reflected upward by a surface of water. Since the two appear similar, you interpret the shimmering blue light of a mirage as coming from a pool of water. But it is just hot air.
The sun appears bluer when viewed from outside our atmosphere. The earth’s atmosphere scatters a substantial fraction of the violet and ultraviolet light in sunlight, leaving a reddened sun disk to our view. Without that scattering, the sun’s disk will appear to contain more blue and ultraviolet light.
The colors of flames can be deceiving because they involve emissions from particular atoms (which impart their own characteristic colors to the light they emit). However, a blue-hot object such as a star is hotter than a red-hot object such as a glowing coal in the fireplace.
Yes. Pollution does tend to make the sky bluer and the sunsets redder. However, pollution also imparts colors directly by absorbing certain wavelengths of light. The orange haze that hovers over cities is often caused by nitrogen oxides, which are simply orange in color and act like pigments to make everything appear orangish. However smoke and dust certainly change the look of the sky by increasing scattering. Natural disasters are even more effective: volcanic eruptions create the most beautiful sunsets of all by tossing vast amounts of dust into the air.
Black light is ultraviolet light. You cannot see it so a room illuminated only by ultraviolet light appears dark or “black”. However any fluorescent materials in the room (e.g. brighteners in your clothes) will absorb the ultraviolet light and reemit it as visible light. That is why things with fluorescent pigments on them glow when illuminate by black light.
The problem with looking at the sun during a solar eclipse is not that it is somehow brighter than normal but rather that (1) you tend to stare at it and (2) the size of its bright region is reduced so that it doesn’t hurt as much to stare at it. It’s hard to stare at the full sun because it feels uncomfortable but looking at a tiny part of the sun may not feel bad enough to make you avert your eyes. Nonetheless, that tiny part of the sun can cook your retina and cause permanent damage.