Why the shape of rainbow is semicircular after rain why not the whole atmosphere is colorful? I have a very simple question.
Everyone must have seen the rainbow after rain. According to the theory the rainbow is created due to the passing of sunlight from small drops of water in the atmosphere(means by dispersion of light).
Now my what I want to know is that after rain the rain drops are present in the entire atmosphere. So the whole atmosphere should look colorful.
Why only a semicircular shape is formed (or is colorful).
 A: I will point to a reference,
it says,

Three things must happen for you to see a rainbow's colors. First, the
  sun must be shining. Second, the sun must be behind you, and third,
  there must be water drops in the air in front of you. Sunlight shines
  into the water drops, which act as tiny prisms that bend or "refract"
  the light and separate it into colors.
Actually, the rays of light bend twice. As they enter the drops, the
  rays of light bend, then reflect off the back of the drops. Then they
  bend again, this time while exiting the drops. That's when the light
  appears before our eyes.
Each drop reflects only one color of light, so there must be many
  water drops to make a full rainbow. You'll see the brightest rainbows
  when the water drops are large, usually right after a rain shower.
The rainbow is circular because when a raindrop bends light, the light
  exits the raindrop at an angle 40 to 42 degrees away from the angle it
  entered the raindrop.

and regarding full circular rainbow,

But if the sun is very low in the sky, either just before sunset or
  just after sunrise, we can see a half circle. The higher the sun is in
  the sky, the less we see of the rainbow.
The only way to see the full circle of a rainbow in the sky is to be
  above the raindrops and have the sun behind you. You would have to
  look down on the drops from an airplane.

A: Rainbow light does reach you from a large fraction of the atmosphere. Here's a picture:

The inside of the rainbow is much brighter than the outside. So you're getting a lot of light from water droplets all over the inside of the rainbow.
Here's a picture I made showing what light does when it enters a water droplet

Incoming light from the sun gets spread out through many different angles, but it mostly piles up around the bottom edge of the picture.
Here it is with both blue and yellow light:

Blue light does pretty much the same, but the angles are slightly off. The place where blue light bunches up is a slightly different place.
So you see separation of colors out at the edge of the rainbow. Throughout the body of the rainbow you see all colors mixed together.
A: The rainbow formed by caustics, which are concentrated rays. This is why only portion of water drops reflect light to the given observer.
http://en.wikipedia.org/wiki/Caustic_%28optics%29
A: This is just a guess, as I have no formal training.
My guess would be that it is due to the spherical nature of the atmosphere the light is passing through. If you have a glass globe and shine a light through it the light is bent as it passes through and the pattern that is made on the object on the other side of the globe is circular (or semi-circular). 
It's also a question of relative position. If you took a snapshot at every point that can view the phenomena and super-impose them over each other, you would find that in a 3-D model that the whole area IS colored. It's just that you can only see it from your singular point of view. It's like a light-bulb, when you look at it straight on it is one color, we will go with white. That same white light is being passed through the entire room, but you only see the photons that are traveling straight at you. If you could 'see' the photons as they were in an instant it would light (or in the case of your question, color) the entire view-able area...
Is this close?
