The rainbow is formed by the reflection and refraction of sunlight within droplets of water in mist or falling rain. The angle at which the colours of the rainbow exit from the water droplets depends on the wavelength of the individual colours and how much they are refracted within the water droplets. Because the angle of reflection/refraction is constant with respect to the source of light (the Sun) and the observer, the rainbow forms an arc (not ark) around the observer opposite to the Sun. The reason you see only a segment of the arc (the rain-bow) rather than a complete circle is that the water droplets of rain or mist are only present in those areas above the ground.
http://www.all-scienc...oad/0/03/Rainbow1.png
http://www.wonderquest.com/rainbow-42-deg.gif
While the angle of the arc of the rainbow with respect to the Sun and the observer remains constant, the apparent size of the rainbow will depend on your perspective, the distance from the observer to the ruler, that is the distance to the rainbow and the background upon which you base your measurement.
With the Sun behind you and a spray bottle of water set to mist, you can create a rainbow you can touch and yet your friend will not see a rainbow unless they are standing next to you with their back also to the Sun.