The Star Garden
HTML Comment Box is loading comments...
The angle of incidence (i) equals the angle of reflection (r)
Refraction
Roman astronomer, Ptolemy first tried to experimentally derive the law of refraction in the 2nd century AD (Mark Smith, 1982). Refraction explains how a ray of light changes direction when it travels between different mediums, this is either because it slows down or speeds up. Refraction occurs when light hits the surface of water or travels through the atmosphere, it is atmospheric refraction which causes the stars to twinkle. Ptolemy measured the angles of incidence and refraction through different mediums and discovered that the angle of incidence was proportional to the angle of refraction, but he could never derive the full equation. Unlike Aristotle, Ptolemy accepted the idea that light is emitted in rays from the eye.
It was not until 984 that Ibn Sahl, a mathematician from Baghdad, discovered the law of refraction that Ptolemy had been searching for. Sahl showed that the angle of incidence is related to the angle of refraction using the law of sines (Rashed, pp.464-491).
Ptolemy's law of refraction; The angle of incidence (i) is proportional to the angle of refraction (r)
Ibn Sahl's law of refraction; Sine (i) x V2 = Sine (r) x V1
The sine function shows how the angle inside a triangle changes as the lengths of its sides change.
The Sine of angle A equals the ratio of two lengths; the length opposite the angle and the longest length, the hypotenuse.
Sine Angle = opposite length / hypotenuse (longest length)
Sine A = length a / length h
The Sin of 90 degrees is 1 because the opposite length will also be the longest, the hypotenuse. In the triangle above, Sine C would equal length h / length h, which equals 1. The sine of 180 is 0 because this will require the opposite length to be infinite meaning that there is no angle.
The first documented table of sine functions was compiled before 125 BC by Greek astronomer Hipparchus. Hipparchus work was referenced by Ptolemy over two hundred and fifty years later and so it is not known why he did not derive the sine law of refraction himself. Some historians argue that his measurements were not exact enough and others claim that his theory of perception led him astray. The sine wave could not be represented graphically until the invention of the Cartesian co-ordinate system by French Philosopher Rene Descartes and French mathematician Pierre de Fermat in 1637.
By 1021, Ibn al-Haytham, a mathematician from Basra, had proven that light enters, but is not emitted by, the eye (Steffens, 2007). He argued that light consists of tiny particles of energy that travel in straight lines and emanate from the Sun at a large but finite velocity. He also stated that vision occurs when the Sun's rays are reflected from objects and into our eyes. al-Haytham experimented with the laws of reflection and refraction using different shaped mirrors and lenses and accurately described how the eye functions as an optical instrument. He likened it to the camera obscura, the pinhole camera, and so suggested that images must also be inverted in the eye. This led him to argue that vision occurs in the brain, rather than the eyes and that it is, therefore, subjective.
The Islamic Golden Age begun to decline in the 12th century, this was mainly due to an increased number of invasions. In 1095, the Franks of France and the Holy Roman Empire began the crusades, a war against all non-Christens. They took the Turkish city of Nicea in 1097 and massacred the Muslim inhabitants. In 1206, the Mongol's invaded most of Eurasia, led by Genghis Khan. In contrast to this, science began to progress again in Europe after the Renaissance of the 12th century. This was mainly due to increased contact with the Islamic world. By 1200, al-Haytham's Book of Optics was published in Latin and it was reviewed by Roger Bacon, one of the earliest European advocates of experimental science, in 1267.
In 1307, Theodoric of Freiberg, now part of Germany, explained how rainbows form. He did this by experimenting with water-filled urine flasks which he used to represent raindrops. Theodoric showed that the light of the Sun is refracted, and then internally reflected, inside each individual raindrop. In the case of a double rainbow, secondary bows are caused by double reflection, this explains why the colours are reversed. Theodoric believed that colour arises from different combinations of light and darkness.
The sine law of refraction, first discovered by Ibn Sahl in 984, was rediscovered by Dutch mathematician Willebrord Snellius in 1621 (Fishman, pp.405-409). Snellius' theory was not published in his lifetime and in 1637, Descartes rediscovered the law again, independently (MacKay and Oldford, pp.254-278).
The Speed of Light
Descartes published his discovery of the Cartesian coordinate system the same year that he rediscovered the sine law of refraction. This form of coordinate system had originally been discovered by fellow Frenchman Pierre Fermat, although his paper was syndicated in 1636 it was not published until 1679, fourteen years after his death. The Cartesian co-ordinate system allowed the sine wave to be mapped for the first time.
The velocity of a sine wave can be found using the equation; speed = distance / time, because a wavelength is a distance and frequency refers to the number of wavelengths that pass in that time (frequency = 1 / time). This means that velocity = wavelength x frequency.
Descartes did not take advantage of these equations, he believed that light was a wave but thought that its speed was infinite. The frequency and wavelength of light was not accurately measured with this technique until 1950, using Maxwell's electromagnetic wave theory of light. English physicists Louis Essen and A.C. Gordon-Smith used a cavity resonance wavemeter, an electric circuit which oscillates at a known frequency and calculated the wavelength based on the dimensions of the wavemeter. They determined that light travels at just under three hundred million metres per second, this is over six hundred and seventy million miles per hour, the value accepted today.
In 1638, one year after Descartes publication, Galileo attempted to determine the speed of light by measuring the time it takes to travel between two observers. The first observer flashed their lantern at the second and they replied by flashing their own lantern back. Galileo suggested that the experiment was best performed if the observers remain about three miles apart, giving a total distance of six miles. He claimed to have tried the experiment at less than a mile, but was unable to determine whether or not the speed was infinite (Galilei, pp.43). In 1667, almost thirty years later, the experiment was repeated by the Accademia del Cimento (Academy of Experiment) which was founded in Florence, fifteen years after Galileo's death. Their results were equally inconclusive.
In 1676, Danish astronomer Olaus Roemer was able to show that light travels at a finite speed by utilising another of Galileo's discoveries, the moons of Jupiter. Io orbits Jupiter once every 42.5 hours and for much of this time it is shrouded by the shadow of Jupiter. Roemer kept a record of how long these eclipses lasted and found that they vary over a year as the Earth moves around the Sun. Io appears to remain shrouded for longer when the Earth is further away.
The approximate distance between the Earth and the Sun had been calculated by French astronomers Jean Richer and Giovanni Domenico Cassini in 1672. They concluded that the Sun was about 140 billion metres from the Earth, underestimating the distance by less than 10 billion metres. Roemer calculated that light took about 10 minutes to travel the distance between the Sun and the Earth. This allowed him to estimate that light travels at about 230 million metres per second, or 514 million miles per hour (Goldstein et al., pp.122). This underestimation was partly due to Roemer's overestimation in the length of time it takes for the light from the Sun to reach Earth, which is now known to be about 8 minutes.
Diffraction
In 1660, Italian physicist Francesco Grimaldi discovered, and coined the term, diffraction. Grimaldi showed that a single beam of light splits into different directions, creating fringes of light and dark, if it is shone though very small slits. This was an important finding for those that advocated a wave theory of light since the sharp boundaries created by shadows implied that light could not bend around corners in the same way that a sound or water wave can. Grimaldi's findings were published in 1665, two years after his death.
A diffraction pattern showing light and dark fringes
References
Fishman, R.S., 2000, 'Thomas Harriot and the Sine Law of Refraction', Archives of Ophthalmology, Vol.118
Galilei, G., 1954, 'Dialogues Concerning Two New Sciences', Crew, H. and de Salvio, A. (trans.), Dover Publications, Mineola
Goldstein, S. J., Jr., Ogburn, T. J., III, and Trasco, J. D., 1973, 'On the Velocity of Light Three Centuries Ago', Astronomical Journal, Vol.78
Lingberg, D. C., 1981, 'Theories of Vision from Al-Kindi to Kepler', University of Chicago Press, Chicago
MacKay, R.H. and Oldford, R.W., 2000, 'Scientific Method, Statistical Method and the Speed of Light', Statistical Science, Vol.15
Mark Smith, A., 1982, 'Ptolemy's Search for a Law of Refraction: A Case-study in the Classical Methodology of "Saving the Appearances" and its Limitations', Archive for History of Exact Sciences, Vol.26
Rashed, R., 1990, 'A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses', Isis, Vol.81
Steffens, B., 2007, 'Ibn Al-Haytham: First Scientist', Morgan Reynolds, Greensboro
Reflection, Refraction and Diffraction (100-1600s)
Reflection
After the death of Alexander the Great in 323 BC, the Roman Empire took over parts of Greece, including Alexandria. It was here that Euclid, born in 300 BC, discovered the law of reflection. This states that light travels in straight lines and will reflect from a smooth surface at the same angle with which it impacted it. Light is reflected in the same way that a ball would bounce off of a frictionless surface. Euclid claimed that light travels in rays that are discrete, like atoms, but appear continuous, like waves, because they move so quickly (Lingberg, pp.12). Euclid accepted the idea that light is emitted in rays from the eye and argued that because light is discrete, some of the objects in our visual field will always remain unilluminated, and therefore undetected.