Firstly, a brief understanding of light.
Light is waves. Depending on how long these waves are, we say that they have different wave-lengths!
As you can see on the picture, Radio-waves are "light" that you just can't see. These waves are, as shown, about as long as buildings. In the center of the image there is the small portion of "light" that is visible to us. The longer side has red, with the shorter wave side having purple.
The shorter the wavelength, the more energy to the light. This means that those really short Gamma Rays on the far right have very high energy.
Mathematically, since frequency is just (1/wavelength), the energy of light is directly proportional to it's frequency.
Ultra-Violet light are just past the visible part. Their frequency (thus energy) is in alphabetical order:
UVA, UBV & UVC.
As you can see in the picture below, UVC light doesn't make it to the ground, but UVA and UVB do.
As you can also see: The higher the frequency (thus energy) of the light, the more it gets blocked!
Lifeforms have adapted as such. We didn't need to develop extra protection for those harmful, high-energy, UVC and above light, but the melanin in our skin does the job for protect us against UVA and UVB in moderate exposure.
So to summarize it: Light packets are waves. The shorter these waves, the higher the frequency, and the more energy to it.
Higher energy light gets blocked more and more by our atmosphere. Therefore, lower energy gets blocked more and more.
The higher the energy the more damage it does to your skin and the deeper it passes into you. This damages and kills your cells, and goes as far mutating the DNA of cells, which can stop them from dying off and thus reproduce when they aren't functioning anymore, this is called cancer.
Now, how do we see light?
Our eyes have two types of photoreceptor cells for interpreting light:
(1) Rod cells: There are many of these picking up photons, however they're not frequency/wavelength sensitive, thus they do not detect color. These cells can then from what directions the light particles reach and how many of those, in order to work out objects distances, shapes, brightness, etc.
(2) Cone cells: There are fewer of these, and they're not as sensitive to light, but they're responsible wavelength/frequency sensitive, which is why things look more colorful and it's bright, and black-and-white when it's dark.
For these cones, there are three of them, which are sensitive to a different wavelength of light. It's more like a small range of wavelength that they can detect, but it's small. As seen on the picture, there is one cone that detects light at lower frequencies and that is seen as red, then slightly higher than that seen as green, and higher than that one, seen as blue.
This means that the only colors we can possibly see are red, green, and blue! Every other "color" is an illusion, it is only a mix of these 3 colors to form something that looks different. For example, all 3 colors at equal brightness form white.
Don't believe me? Every screen only has these 3 colors:
Above, is all that is going on in your screen, if you zoom in far enough. If your screen looks white, then it looks like the image above; all colors appearing equally.
To play around with the amount of red, green and blue that your screen produces and what color it looks like, try this interactive website:
http://web.stanford.edu/class/cs101/image-rgb-explorer.html
Here is an example:
Another good website to explore which mixes or red, green and blue form which colors is this one:
https://www.rapidtables.com/web/color/RGB_Color.html
So now that you know all of this, recall the wavelength of light and the different colors:
Actually, we only see red green and blue from the chart, everything else is a mix of the two, but you get the wavelength differences.
Now also recall that the longer the wavelength (left, red side), the less it gets filtered by the atmosphere, and thus on the shorter wavelength (right, purple side) it gets more filtered.
With this information in mind, I'll explain:
Why is the sky blue?
When light hits things, there's usually an interaction at some wavelength of light, right? This is how you see objects.
The atmosphere is made up of various gas particles, clearly. Therefore, light is going to interact with them!
Turns out, the same way that (say) murky water has a colour to it, the sky works much the same way.
There are more particles in the atmosphere that are more likely to interact with blue light than with red light, and green being in the middle of the two.
When you look up at the sky, you're seeing the blue light that was picked up by particles and scattered in all directions; both towards the Earth and away from it. As such, a lot of blue light never makes it to the ground (your eyes).
Therefore, when you're looking at the sky, you're seeing the blue rays bouncing off of those gas particles and hitting your eye, thus they look blue, just like your hand looks like it's color because light is bouncing off of it.
So, if you reason, you'll realize that... the more atmosphere light passes through, then the more it's going to be "filtered"; that is, more and more blue light being scattered in random directions.
In the picture below, the red dot on the surface of the Earth represents you.
The vertical yellow line represents the sun rays passing through the atmosphere to you.
The horizontal yellow line with the other end being dark red represents the sun's rays from when the Sun is JUST over the horizon, what we call a sunset.
The atmosphere is made up of various gas particles, clearly. Therefore, light is going to interact with them!
Turns out, the same way that (say) murky water has a colour to it, the sky works much the same way.
There are more particles in the atmosphere that are more likely to interact with blue light than with red light, and green being in the middle of the two.
When you look up at the sky, you're seeing the blue light that was picked up by particles and scattered in all directions; both towards the Earth and away from it. As such, a lot of blue light never makes it to the ground (your eyes).
Therefore, when you're looking at the sky, you're seeing the blue rays bouncing off of those gas particles and hitting your eye, thus they look blue, just like your hand looks like it's color because light is bouncing off of it.
So, if you reason, you'll realize that... the more atmosphere light passes through, then the more it's going to be "filtered"; that is, more and more blue light being scattered in random directions.
In the picture below, the red dot on the surface of the Earth represents you.
The vertical yellow line represents the sun rays passing through the atmosphere to you.
The horizontal yellow line with the other end being dark red represents the sun's rays from when the Sun is JUST over the horizon, what we call a sunset.
As you can see, in the Sun's position at the sunset, it passes through more atmosphere than when it is midday! If you look at it, it's a whole "radius of the Earth" in length longer than it has to travel to get to you, which is ~6,371 km
Therefore, light at midday has less blue light scattered than at sunset, which means the light at the sunset has a bit less green and even less blue light in total. In midday, it's almost white.
Also, this is why the Sun looks yellow.
Remember what we went through about our eyes only seeing red, green and blue? Well, if you make a mix of mostly red, some green, and less yellow (sunset), what you get is:
That color reminds me of...
Sunset at the horizon: light travelling an extra 6371 km to reach you, as opposed to the middle of the day.
Water in lakes works the same way: if you look through a small amount of water in a cup it'll appear transparent (will depend on how murky the water is, but you get the point)
If you look at a small amount of air in front of you, it'll also appear transparent.
However, through a long enough distance, you can begin to see the colours, as the small amount of particle mixed in the air that scatter the light begin to 'add up'
hence this effect:
Sunset at the horizon: light travelling an extra 6371 km to reach you, as opposed to the middle of the day.
Water in lakes works the same way: if you look through a small amount of water in a cup it'll appear transparent (will depend on how murky the water is, but you get the point)
If you look at a small amount of air in front of you, it'll also appear transparent.
However, through a long enough distance, you can begin to see the colours, as the small amount of particle mixed in the air that scatter the light begin to 'add up'
hence this effect:
The same reason that those mountains look blue, is the same reason the sky is blue, however, you can only see the blue after a long enough distance. The reason for this...
The same reason why the water closer to the shore looks clearer than deeper water is why you can see clear in front of you and clear in that cup; but blue in the sky and blue in the water:
Among many particles, over a long distance, you'll see all the blue lights adding up:
Over a short distance, there are very small amounts of these blue particles. Over a long distance, as you can see, their light literally adds up. This is the same thing happening when it's foggy and you can see in front of you, but not a long distance away; it is then overcome by the fog.
The blue particles work just like a fog, just a much weaker one.
And that's the end of it. I just put the dots together in my physics lecture about electron bonding in different molecules absorbing different frequencies of light, some past knowledge in biology
and wah-la! An explanation to multiple phenomena you experience on a daily basis and don't give much thought to. Although i doubt most of you haven't asked "why is the sky blue"
It is satisfying though. The process of uncovering it all and connecting the knowledge felt like unfolding a mystery or making a conspiracy theory.