The sky isn't actually blue and the sun isn't actually yellow — they just appear that way. This short video from MinutePhysics above nicely explains why.
The sky, after all, is just transparent air, "a stage upon which all colors dance." But as light from the sun enters into Earth's atmosphere, the different colored wavelengths making up that light start bumping up against the air and "dancing" differently.
The shorter blue and violet wavelengths get scattered most by the air, making the sky around us appear blue. The remaining red, yellow, and green wavelengths mostly pass through and hit our eye at once — making the sun, in turn, appear yellowish .
During a sunset, meanwhile, all that sunlight has to pass through even more air to reach our eye, so even more blue and violet wavelengths get scattered. The remaining wavelengths that hit our eye appear as an even deeper red or orange. (Dust, pollution, and water vapor can also scatter some of those reds and yellows, making the whole sky glow.)
(You can find more MinutePhysics videos at their Youtube channel.)
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