First, you need to understand the Tyndall effect.
Secondly, you need to know about the light that comes from the sun.
The light that comes from the sun includes all of the colors of the spectrum (red, orange, yellow, green, blue, purple, and all of the shades in between).What that means is that the light coming from the sun comes in a wide range of wavelengths. (The sun also gives off ultraviolet and infrared, but we're going to focus on visible light here.
Of the colors of visible light, red has the longest wavelength, while blue and purple have the shortest.
Below, you'll see a representation of three of these wavelengths (red, green and blue)
Lastly, you need to understand how the Tyndall Effect is influenced by wavelength and particle size.
Note: what follows is a simplification of the truth, but it's a good starting point to understand.Light waves are much more likely to bounce off of particles that are similar in size to their wavelength (or larger).
Now, we can talk about why the sky is blue.
All of the different colors of light leave the sun and travel to Earth, as shown in this picture.
Note: The scale of this picture is horrendous. The sun is actually big enough to hold about a million Earth's, the distance between them is so big that if the sun were this size, the distance would be more than 10 feet, and the actual atmosphere of the Earth is as thin as the skin of an apple.
Our atmosphere, however contains LOTS of little particles. Many (most?) are so small that they don't interfere with visible light. However, some (water vapor and certain pollutants included) are large enough that the interfere with the light with the smallest wavelengths.
In the picture below, the longer wavelengths travel "straight" through the atmosphere and reach your eyes. But the shorter wavelengths (in this diagram - blue), are bounced all around. Some of that light is reflected back into space, some of that light gets bounced to other places. Some of the light, gets bounced around but ends up getting to you.
What is important here is that, although most colors of light come straight at you from the sun, the blue light that reaches you is (often) coming from seemingly random directions.
So, no matter where you look, SOME of the blue light from the sun is coming at you from that direction. In other words, no matter what part of the sky you look at...you see blue.
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