What is the intensity of sunlight required to form a rainbow. I read in the love of physics by Walter Lewin than
"“For you to see a rainbow, three conditions need to be met. First, the Sun needs to be behind you. Second, there must be raindrops in the sky in front of you—this could be miles or just a few hundred yards away. Third, the sunlight must be able to reach the raindrops without any obstruction, such as clouds.”
I did not understand the third point.
The formation of the rainbow results from geometric optics, so the incoming photons need to have the same direction to make a bright rainbow appear. Thus you need direct sunlight. In case of clouds you get diffuse illumination (photons hitting the water droplets under different angles).
The answer from Charles is right and to see why the photons need to come from the same direction for a clear rainbow...
One can always use a garden hose to make a small, but very own rainbow.
This way, it is possible to try and check all of these conditions.
The Sun must be behind you. In theory, higher-order rainbows (created by multiple reflections inside the droplets) can exist in the Sun direction, but they are at least as faint as the first-order one and the Sun is much brighter, so one needs pretty unusual conditions to see them.
You need water droplets to send the properly colored light in your direction, or no rainbow for you.
These droplets must receive direct sunlight. If they are in a shadow, no rainbow either.
p.s. the rainbow is a profoundly distorted image of the Sun. Water droplets are simply not a good mirror.
