Assuming that the answers to Earth Science: Why is the sky blue? and a discussion of Rayleigh scattering are a bit too much, take a container of water and a flashlight and make an impromptu prism.
A nice example by Dr. James Porter of the Lake County Educational Service Center in Ohio can be found at: http://porterscience.lcesc.k12.o...
Turn off the lights in the room, shine the flashlight, and show how light separates.
Explain that the air is kind of like the water. It can make light split into different colors. Connect the blueness of the sky to the different colors in rainbows.
You can also set up a glass on an elevated surface and use the sun for the light source directly. http://www.ehow.com/how_7667228_... That would be even better, since you directly see that the light from the sun has colors. If they understand how rainbows appear - light refracts through "leftover raindrops in the sky" - then you can make an even closer connection to why the sky is blue.
"Just like the raindrops in the air can split the colors in sunlight, the air itself can split colors - but when the sun is high in the sky, the air mostly splits blue out of the sunlight."
Once they're comfortable with that idea, wait until sunset and revisit the conversation.
Wouldn't you know it! When the sun is lower in the sky, the sky isn't only blue!
For the sake of scientific accuracy, I need to state here that the scattering that happens due to dust particles in the air is not the same as the refraction that happens when you shine light through a water prism. If your kindergartener is ready to make that distinction, then you can just go straight to the answers at the Why is the sky blue? question.
For most kids at this age, you can help them make the connections (1) that sunlight is made of many colors, (2) that shining sunlight through "something" can separate the colors, and (3) that the air in the sky is "something." When you cup your hands, it's easy to say that there's nothing in your hands... but there is air there. (If the five year old is puzzled by this, ask her, "If air weren't 'something,' then how could you breathe it?")
One final note: the seemingly ceaseless asking of "why...?" by a 3-5 year old is a shared (and often humorous) story amongst many parents and caregivers. If they're asking, "Why?" then it is possible that your child is playing a game with you. If you can subtly shift them to asking "How?" - as in How is the sky blue? - then you are both moving to what I believe is a more addressable question (why is existential, how is mechanical) and making it so that you and the child are now working out a puzzle together.
The image Sunset in Lüdenscheid, Germany is licensed under the Creative Commons Attribution-ShareAlike license.
Answer by Ariel Williams, Dreamer, Artist, and Writer
First, you need to know that white light is really all colors of light mixed together. So if you take a red, blue, green, and every other color light and shine them at something at the same time, you will see white light.
You can also shine a white light at a prism and watch the light split into a rainbow. Notice in the picture how big the stripe of blue is?
The sky is made blue because all of the white light from the sun to us gets scattered and shaken up by the gases in the air and little drops of water like the clouds and other stuff in the atmosphere, and only the blue light gets reflected back at us strongly enough to color the sky.
This is just like a bottle that has stuff in it but only has holes big enough for some of them to pass through. The blue light is the one color that slips through the reflections off the air and water in the sky. This is because blue light is smaller. The silly scientists call this Rayleigh scattering but you can just call it a perfect blue sky.