Most people agree that Fiber Optics were first demonstrated in 1870 by John Tyndall. To do this he simply took 2 buckets of water, placed a hole in one, and while the water flowed from one to another, he also showed that light flowed within the water. So the light from one bucket appeared to light the water in the second. Simple!
From such humble (and wet) beginnings, other scientists helped to bring the notion of guided light (fiber optics) to the forefront of scientific research. In 1880 William Wheeling patented something called "mirrored light". He took a single light source and projected it through a mirrored tube. He showed that light could be branched of the original tube with additional tubing, taking light to another area, or another room, in the same way that water is piped around a home. He might have been better know today if he could have improved on an ineffective design, and if a certain Thomas Edison hadn't come up with the notion of an incandescent light bulb.
At around the same time, Alexander Graham Bell invented his "photophone" cleverly using reflected sunlight on a diaphragm attached within the mouthpiece. Two hundred meters away at the other end, the various intensities of light where converted by an electric receiver back into speech. Bell, way ahead of his time, believed that this method of speech transfer was greatly superior the less flexible wired telephone. He would later be proved right!
The term "fiber optics" was first used in 1956 by Narinder Kapany from the Imperial College of Science and Technology in London. Both Kapany and Brian O'Brien at the American Optical Company, concurrently developed the fiberscope, a huge leap forward in fiber optics. Up until then, the biggest problem had been the loss of signal due to light leakage. By taking an inner core of class, shielded with an outer cladding also of glass, this loss was dramatically reduced. This new fiberscope quickly found use in industrial inspection and medial instruments, ultimately enabling modern laparoscopic surgery.
The next leap forward was in 1957 when Gordon Gould discussed the use of lasers to generate a high energy, highly focused source of light. Although going through several development stages, by 1962 the Semiconductor laser would become a standard still in use today.
