Why aren't rainbows more common?
There are no billions of water drops in the air on any given day. Water in the air is normally in the form of vapor, not drops. For drops to form, the relative humidity should be 100% causing condensation, such as during or after a rain.
The second requirement is a direct sunlight from behind. You can easily create a rainbow on a sunny day while watering your lawn. Stand with your back to the sun and spray (or better mist) water widely in front of you. You should see a rainbow centered around the shadow of your head. And when you see a real rainbow after a rain, notice that it is also centered around the spot where the shadow of your head is or would be at the moment. This typically implies that the sun should be fairly low in the sky (e.g. it is less likely to see a rainbow at noon when the sun is high).
It is also possible, although rather rare, to see a rainbow from an airplane. I have seen it only once in over 200 flights. It was in multiple full circles around the shadow of the plane when it was passing over the clouds.
A number of conditions have to be just right in order to see a rainbow.
- The Sun has to be visible in the sky. Rainbows don't occur on overcast days. The light hitting the raindrops needs to come from what is close to a point source to have the reflections and refractions in a myriad number of raindrops combine to form a rainbow. Diffuse light (overcast conditions): No rainbow.
- The Sun has to be fairly low to the horizon. The primary bow forms a cone with your eye as the vertex and the line from the Sun through your head as the axis, with the red light at an angle of about 42° from the axis and the blue, about 40°. The Sun needs to be below 40° above the horizon to see a rainbow, and at that high of an angle, the rainbow won't be very good. Rainbows are best in when they form less than an hour or so after sunrise or less than an hour or so before sunset.
- Rain needs to be falling opposite the Sun. Off to the side: No rainbow. From a very low cloud at the horizon: No rainbow.
- It has to be rain rather than a fog or a mist. Cloud droplets are far too small to form a rainbow. Cloud droplets are about the same size as the wavelength of visible light. This means light hitting cloud droplets is diffracted rather than reflected and refracted. Clouds form glories, coronae, and fogbows. The latter are similar to rainbows, but without color. Mists form at best fuzzy rainbows; the drops are small that diffraction dominates over reflection and refraction. The drops need to be about a millimeter in diameter to form a rainbow.
Altogether, this makes rainbows rather rare.
The drop size has a direct correlation to the saturation of the colors in the rainbow. You can see examples here, notice how the rainbow is much brighter when the drops are larger, and the fades as they become smaller in the mist.
The "drops" in the air around you are normally microscopic, and as a result, the rainbow you would see if you looked in the right direction simply isn't visible. You might see one around the sun or through some clouds, but generally its simply not strong enough to overpower the strong blue (or grey) background.
You also need to remember that you can only see it when the sun is low in the sky, so for most of the day they aren't visible anyway.