Why is the sky blue in the day and red at sunset?

The answer is that sunlight is a spectrum - when you see white light it's actually made up of lots of different wavelengths of light. You can split them with a prismto reveal all of the different colours which make up white light. When that light comes from the sun and hits the earth's atmosphere, the atmosphere is made up of a lot of nitrogen and oxygen, and this nitrogen and oxygen strongly bounces around, or scatters, light which is at the blue end of the spectrum - the wavelength is about 480 - 500nm. The blue light bounces around all over the place like bullets ricocheting around a room. But light which has a much longer wavelength towards the red, green and yellow, goes straight through the atmosphere without being scattered about, and reaches your eye directly. So what you see is light from the sun, with some of the blue taken out because it's bounced all over the place. Because your eye can't work out exactly where the blue light have come from (because it is coming from all directions) your brain interprets it as the whole sky being blue, rather than just one spot. So that's why you see a blue sky. Now what happens at sunset is that because the earth has moved (rotated), the sun has moved towards the horizon and its light is now coming through a lot more of the atmosphere than when it was directly overhead. So because it's coming through more atmosphere even more at the blue light is taken away, making the sky look even more red than it was before. So that's why you get the red colouration of the sunset. The other thing that affects this is how many particles there are in the atmosphere, so you tend to see much redder sunsets and yellower moons at harvest time, and at times when there's been big volcanic eruptions. So when Mount Pinatubo blew up on the Philippines a few years ago, you saw beautiful sunsets, and very very orange coloured moons, and that was because of the dust in the atmosphere adding to the effect we've just described.