In the early 19th century, William Rowan Hamilton mathematically predicted a curious phenomenon called conical refraction and Humphrey Lloyd was the first person to demonstrate the effect experimentally. This achievement was a strong argument for the wave theory of light and highlighted the importance of mathematics in understanding physical phenomena.
Conical refraction is a phenomenon that occurs in a special type of crystal called biaxial crystal. One common example of such crystal is calcium carbonate. If you were to take one such crystal, place it on top of this article and look through it, you would see a double image of the text. This is due to the structure of the crystal that bends light in a different way depending on which direction the light travels through it. This bending of light is called refraction. Now, if you set up an experiment where a beam of red laser light is passed through this crystal and the image of outgoing light is observed on a sheet of paper, two red dots are observed. This effect is called double refraction.
In 1832 Hamilton published a third supplement to his Theory of Systems of Rays. In this supplement, he predicted that if a biaxial crystal is positioned, such that the light beam passes through it along a line called the optical axis, instead of the two red dots, one would observe a bright ring. Hamilton explained that the light travelling along the optical axis inside the crystal is not refracted into two points, but into a hollow cone that then emerges as a hollow cylinder. Hence the name conical refraction. William Rowan Hamilton was one of the greatest Irish mathematical physicists. He entered Trinity College at the age of 18 and published his first paper at the end of his first year of his undergraduate degree. In 1827 the Board of Trinity College appointed Hamilton Professor of Astronomy, while he was still an undergraduate student aged 21. He took up the position, but quickly lost interest in astronomy and focused on mathematical physics. He is famous for many things including the quaternions, Hamiltonian mechanics and coining the word “tensor”.
Hamilton’s work attracted the attention of many physicists. Some even spoke of his prediction as “perhaps the most remarkable prediction that has ever been made”. His colleague, Humphrey Lloyd described the predictions as “in the highest degree novel and remarkable”. Lloyd was the provost of Trinity College between 1867-1881. In 1831 he succeeded his father as Erasmus Smith’s Professor of Natural and Experimental Philosophy. Hamilton turned to him to verify conical diffraction experimentally. Lloyd obtained a crystal of arragonite, a mineral form of calcium carbonate, and in December of 1832 he demonstrated the effect. The experiment was not easy and the angle of the cone was very small and several regions of the crystal had to be explored to detect the effect.
Triumph of the Wave Theory of Light
The prediction and the subsequent experimental demonstration of conical diffraction brought great fame to Hamilton. It was also a triumph of the wave theory of light over the particle theory of light, because the latter could not explain the effect. The wave theory was first proposed by a brilliant Dutch physicist Christiaan Huygens. This theory treats light as a transverse wave. The particle theory was formulated by one of the greatest British physicist Isaac Newton. Newton saw light as made up of particles called corpuscles. In the 1820s and 1830s the wave theory gained the upper hand. Physicist for years had very vigorous debates for and against the wave theory. In the dawn of quantum mechanics, Louis de Broglie settled the debate with his wave-particle duality which means that light, along with everything else, can be treated as both a particle called photon and as a transverse wave.
Hamilton’s great success led to a controversy with his colleague in Trinity College, James MacCullagh. In 1830 MacCullagh published some theorems on double refraction. In 1833 he published a note in the Philosophical Magazine showing how conical diffraction can be deduced from his theorems and wanted to claim credit for the discovery. Hamilton never saw MacCullagh’s paper and was very annoyed by his claims, but following Lloyd’s intervention MacCullagh published another note admitting that his deduction was subsequent to Hamilton’s discovery and hence failed to gain any credit.
MacCullagh’s mental health was very unstable and he was a very sensitive individual. Some suggest that he felt overshadowed by Hamilton and that this lead to him wanting to commit suicide. In 1847 at the age of 38, James MacCullagh was found in his College apartment with his throat cut. The verdict was suicide and no one who knew him questioned it, however later some doubt did arise, because his collection of manuscript papers had disappeared. Although Hamilton and MacCullagh were rivals, they had great respect for each other. One of the most sincere tributes was paid by Hamilton, who wrote a short but very emotional poem on the occasion of MacCullagh’s death.
In 1839 Poggendorf published a paper explaining that Hamilton’s ring is not just a single ring but it is actually two rings separated by a thin dark ring, now known as the Poggendorf’s dark ring. Lloyd could not detect it and it took over 65 years before the dark ring was first observed by Voigt. Hamilton did not predict the dark ring because he assumed the laser beam was perfectly collimated and infinitely narrow, which is incompatible with the nature of light. In 1941 Raman also investigated further and saw that by moving the crystal such that the laser beam hits it at a point slightly away from the optical axis, a bright spot forms in the middle of the two rings, now known as the Raman spot.
In conclusion, the discovery of conical refraction has been a surprise to the physicists of the early 19th century and an important achievement for Hamilton and Lloyd. It is amazing how mathematical models, geometry and algebra were powerful tools in the hands of Hamilton. Along with his genius, he managed to predict a physical effect that escaped physicists for a long time. Although for many years the effect seemed to be purely theoretical, in recent times it has gained some novel applications in laser beam shaping devices.