Why should optical fibers be thin? What are the reasons that optical fibers have to be thin (small radius of the fiber)? Is there a good picture which explains this in detail?
 A: The answer comes from the use of optical fibers: information transfer for one. The thinner the more channels in a bundle. 
Also the attenuation of the light is smaller in a thin fiber . There is an article explaining this.   
A: If they are thicker then light can take many different paths, bouncing at slightly different angles and still being reflected - this means that the time taken for each photon a pulse to go down a fibre is slightly different which smears out the pulse and so reduces the bits/second that can be sent.
Thick plastic fibres are used for simply illuminating something because they are cheap, rugged and easy to make, thinner glass fibre is used for short distances and very thin very expensive single mode fibre is used for higher bandwidth long distance
A: Just to add a little more info, there are also monomode optical fibers that are even thinner (8 to 20 µm). These are useful to transport light pulses, and only allow one spatial mode within the fiber. That means that instead of the typical picture of light bouncing in the walls of the fiber, you get that light can only propagate forward with a certain intensity profile. Check this link or just google for a comparison of the three main types of fibers: multimode, graded-index and monomode.
A: Size of optical fiber mean outer diameter of the fiber 
In short for long transmission fiber should be thin to avoid the dispersion and power loss in optical fiber.
A: By using a thinner core, the light reflects less and travels in a more direct line and travels faster. This reduces modal dispersion.
