from the following picture, you will find that the intensity of the first rainbow is about 2*4.5% of the incoming red light. So the intensity is indeed small.
The rainbow you saw was coming from many different raindrop.
The primary and the second rainbow also create from differnet raindrop and different light path. Remember light need to enter your eye for you to see the image.
The angle shown on the applets is assume the sun light is horizontal.
If the sun is higher you need to substract the angle of the sun ray relative to horizontal.
If the angle is less than zero , you would not be able to see rainbow on the ground.
That why you never saw rainbow at noon (after 9am or before 3pm) on the ground.
The angle for the second also shown on the applet, as indicated in the following picture.
The following applet show you why why the color spectrum is seen as a "bow" or arc.
(The other half will be underground if there are raidrops and can refelect sun light, which is impossible.) However, it is possible when you were on an airplane.