Working of the optical fibre I read about the mechanism of an optical fibre. It works on the basis of total internal reflection.
But for total internal reflection it is necessary that the incident angle is more than the critical angle.
How is the incident angle in an optical fibre always greater than the critical angle?
If, in any case, the incident angle will be less than the critical angle then light will pass out through the cladding.
 A: 
How is the incident angle in an optical fibre always greater than the critical angle?

Fibers are characterized by a numerical aperture and a minimum bend radius.
The numerical aperture is the sine of the maximum angle from the optical axis at which an incoming light ray can enter the fiber and still encounter the core-cladding boundary at more than the critical angle. (For single mode fibers it is a bit more complicated, but the principle still stands: the fiber can only capture light propagating relatively close to the fiber axis)
The minimum bend radius ensures that light already inside the fiber continues to encounter the core-cladding boundary at a sufficiently high angle. For the most common types of multimode and single mode glass fibers, the minimum bend radius is typically on the order of 1 cm.
If either specification is violated, then the light will indeed fail to be totally reflected and the fiber will not guide the light beam.
A: In this link

Fibers in bundles are surrounded by a cladding material that has a lower index of refraction than the core. (See Figure 4.) The cladding prevents light from being transmitted between fibers in a bundle. Without cladding, light could pass between fibers in contact, since their indices of refraction are identical. Since no light gets into the cladding (there is total internal reflection back into the core), none can be transmitted between clad fibers that are in contact with one another. The cladding prevents light from escaping out of the fiber; instead most of the light is propagated along the length of the fiber, minimizing the loss of signal and ensuring that a quality image is formed at the other end. The cladding and an additional protective layer make optical fibers flexible and durable.



Figure 4. Fibers in bundles are clad by a material that has a lower index of refraction than the core to ensure total internal reflection, even when fibers are in contact with one another. This shows a single fiber with its cladding.

