Optical fibers are being widely used across the world for communication. Light is guided through the fiber by multiple reflection at the core cladding interface. This depends on a physical phenomenon called the phenomenon of total internal reflection; the ray that enters the fiber with an angle less than the acceptance angle is reflected in an angle so that when the incident angle is change the exit angle will also be changed. When the incident angle is changed, a displacement will take place; this displacement affects the value of the exit angle, in such a case there will be a difference between the point of the incidence and the point of refraction, this difference will lead to a variance in the distance and the arrival time at the end point which is an indication of acceleration in the speed of light which will be discussed in this paper. General Terms: Communication media, network signally, physics.