The Story of Optics - The Awakening

Gautam Gangopadhyay

Translation: Sunando Patra

Photo: Sunando

Our five senses, namely eyes, ears, tongue, nose, and skin, with eyes being the foremost among them allow us to perceive the external world. Everyone knows that the eye is a light-sensitive organ; light falls on the retina of the eye and then that signal travels to our brain, enabling us to see. It’s not an exaggeration to say that light opens the door to the universe to us.

Even our school books teach us that we can only see when light comes from any object and falls on our eyes. The arrows on the rays of light indicate the direction they are traveling. In school, I made the mistake of putting the arrows in the wrong direction. My teacher jokingly said, “Hey, this is a great man! Light seems to come out of his eyes.” Though the whole class burst into laughter, later I learned that many had made such mistakes before. They weren’t all school students either! Among them were ancient Greek philosophers like Plato (circa 424-348 BCE), Euclid, the famous mathematician from Alexandria (circa 3rd century BCE), or astronomers like Ptolemy (100-170 CE), who believed that when light comes from the eyes and falls on any object, we can see it. They obviously couldn’t provide any answer to the question: Why doesn’t light come out of our eyes in a dark room?

This is not just an isolated example of ancient scientists’ thinking. We can trace the ancient era of optics back roughly from the 8th to 2nd century CE, spanning a thousand years of Greek civilization in Europe. During these thousand years, it sprawled from Athens on the eastern shore of the Mediterranean to Alexandria in Egypt, Anatolia in present-day Turkey, and Syria in the Middle East. On one side were the atomists in Greek civilization who thought of everything in terms of atoms. The renowned atomist Democritus (circa 460-370 BCE) believed that when the light comes from an object, it forms an image by shrinking the air in front of the eye, then that compressed air exerts pressure on the eye, and that signal goes to the brain. The famous philosopher Epicurus (341-270 BCE) thought that the image is formed within the eye itself. He argued that even though light particles come out from an object, the object doesn’t diminish because atoms from the air replenish that space. Roman poet and philosopher Lucretius (1st century BCE) stated that light and heat come in the form of particles from the sun.

Atomists did not necessarily have a significant influence on ancient Greek philosophy or science. Plato said that when light, emanated from the eye, is reflected by an object, we can see it. Plato’s theory somewhat resembles the idea of felling/experiencing an object by extending the hand towards it. From then on, for a thousand years, Plato’s view was somewhat accepted.

One thing can always be said about ancient classical science: empirical science was not present then—no one thought about checking what was right and what was wrong by experimenting. Philosophers of that time supported their own opinions or refuted rival ones solely through arguments. Naturally, various contradictory views coexisted without contention in classical science.

All ancient civilizations probably believed that everything visible, everywhere, consists of only a few basic elements. The concept of those ‘elements’ or basic substances however is entirely different from that of the modern age. Democritus or Plato thought about four basic elements: earth, water, air, and fire. Aristotle added aether to them. He could be considered the highest exponent of the Greeks in terms of understanding the nature of light. In ancient India, the five elements were Khsiti (earth), Apa[s] (water), Teja[s] (fire), Marut (air), and Vyom (ether). In Chinese imagination, there were five basic elements: earth, metal, wood, water, and fire. Light was considered a form of fire or Teja.

Ancient scientists did not care much about the nature of light. They generally discussed reflection and refraction when light travels through any medium. This was natural, as these played a special role in the technology of the time. It was necessary to understand reflection and refraction to make mirrors or lenses. When looking through water, the ground seems to have risen up and this happens due to refraction. Understanding this was necessary for sailing ships. There’s no doubt that the Greeks attached great importance to optics even two thousand years ago. They wrote several books on this subject. In the year 424 BCE, the famous playwright Aristophanes mentioned lenses in his play. If they got into plays, then the use of lenses must have been quite prevalent. Lenses were also used in ancient Assyrian and Egyptian civilizations. The Greeks even knew about curved mirrors. There is a very old story about Archimedes (287-212 BCE), which still circulates, that he could focus sunlight onto distant ships using a concave mirror, but it’s doubtful.

Plato’s Academy was in Athens. After the death of Alexander, his empire was divided among his generals. One of his generals, Ptolemy the First, established his kingdom in Egypt, which lasted until the first century CE. It was his effort that established Alexandria (in Egypt) as a center of learning and science. In ancient times, the most influential book on the nature of light was Euclid’s “Optics”, Written in Alexandria.

We’ve all studied Euclidean Geometry in our childhood, the original book of which was “Elements”. Apart from the Bible, no other book has ever been as widely circulated or translated into so many languages in the history of the world. Over two thousand years, this book has been considered a textbook. Euclid proved many theorems of geometry from a handful of axioms (self-evident statements). The book is an excellent example of deductive reasoning. Science, on the other hand, proceeds by inductive reasoning; the difference between that and mathematics is that, in the second case, no experimental proof is required for the axioms. Those, even if correct from its their own perspective, may not be applicable in the real world. For example, if we assume Euclid’s fifth postulate[1] to be true, we get the geometry we learn in school. Mathematicians later showed that even without the fifth postulate, a different type of complete geometry could be obtained, and the real world follows that geometry.

Just like Elements, the book on optics also starts from axioms, but here, the first assumption itself was wrong. It assumes that light emanates from the observer’s eyes. Euclid explains that it is hard to find a dropped needle because it's less probable for the light emanating from the eyes to fall on a small object like a needle. Nevertheless, several important points about light can be found in Euclid’s book. Euclid assumed early on, that light travels in a straight line. However, Mozi (470-390 BCE) in ancient China or Aristotle (384-322 BCE) in Greece had described the pinhole camera, long before him. To describe the workings of a pinhole camera It was assumed that light travels in a straight line. The first discovery of the principle of reflection can also be found in Euclid’s book.

TWO PRINCIPLES OF REFLECTION:

• (1) When a beam of light is incident on the boundary surface of two media, gets refracted, the incident ray, reflected ray, and the normal at the point of incidence on the reflecting surface lie in the same plane.
• (2) The incident and reflected rays make equal angles with the normal.

In the diagram, light from point \(A\) is reflected from point \(P\) on the reflecting surface. The normal to the reflecting surface at point \(P\) is \(PQ\). According to the principle, the angle of incidence \(i\) and the angle of reflection \(r\) are always equal.

The book on optics written by the Hero (10-70 CE) of Alexandria was named Catoptrics, meaning reflection. He proved the principle of reflection based on the idea that light takes the shortest path from one point to another. Following Hero, we can say that among all the paths for light to go from point \(A\), reflect off a reflector, and reach point \(B\), the shortest will be the one for which the angle of incidence and reflection are equal.

The Greeks believed that the speed of light is infinite, or, at least, extremely high. When we look up at the sky and open our eyes, we can immediately see the sun, the stars and other celestial bodies. According to the Greeks: objects are only visible when light, emanated from the eyes, travels back to the eyes after getting reflected from those objects. Although the Greeks did not know how far the sun or stars were, they had no doubt that those distances were indeed great. Speed of light had to be extremely high for us to see these celestial bodies immediately after opening our eyes. Hero provided another argument for this. An object, thrown parallel to the ground, will eventually fall to the ground after going some distance. We now know that the object travels in a parabola, but before Galileo, this trajectory was not well known. It was assumed that the object would go parallel to the ground for some distance and then fall to the ground. Hero argued that an object with higher velocity would travel farther parallel to the ground. Since light always travels in a straight line, its velocity must be infinite.

The last ancient Greek scientist we have to mention in relation to optics is Claudius Ptolemy of Alexandria. Ptolemy’s geocentric model of the universe was universally accepted until Copernicus. His book on optics also influenced scholars for a long time, although the Greek text did not survive. Some excerpts from it have been found in other books. Ptolemy tried to determine the principle of refraction (for light passing from one medium to another) experimentally. Although experimental verification of scientific principles is very common in the modern era, very few scientists chose that path at that time. Ptolemy’s work, hence, is remarkable. He stated that the ratio of the angle of incidence to the angle of reflection is the same for all light-rays goes from air to water. We will see later that this principle is somewhat true for light falling almost perpendicular to the surface of two media.

After the decline of ancient Greek civilization, the Arabs took up the mantle of science. During this golden age of Islamic science, Greek and Indian texts were translated into Arabic. During the medieval period, Europe essentially plunged into darkness regarding scientific discourse, leading to the loss of most original Greek texts. These reached us and were preserved through their Arabic translations. Among the many fields in which the Arabs made original advancements, one was optics.

The renowned Arab philosopher and scientist Al-Kindi (800-873 CE) was the first to get particularly enthusiastic about optics. He critically compared the theories of Euclid and Aristotle. We will not get into the details of Aristotle’s theory of optics; let us only note that he did not consider the rectilinear motion of light. Al-Kindi, analyzing various properties of light, emphasized Euclid’s approach. Following Ptolemy, Al-Kindi was the first to make primary contribution to optics, which later influenced the development of optics in Europe through Latin translations of his works.

We have seen that Ptolemy’s law of refraction only holds true for near-perpendicular incidence. The accurate law of reflection, which we call Snell’s law, was discovered by the Dutch astronomer Willebrord Snellius (1580-1626 CE) in 1621. However, it was independently rediscovered by the French scientist René Descartes (1590-1650 CE) afterward, so although the law is known worldwide as Snell's law, it is referred to as Descartes’s law in France.

SNELL’S LAW:

The relationship between the sine of the angle of incidence (\(i\)) and the sine of the angle of refraction (\(r\)) when light passes from one medium to another is expressed by a constant called the refractive index (\(\mu\)). The value of this constant depends on the two media involved. We can write: \[\frac{\sin(i)}{\sin(r)} = \mu\]

In the diagram, we see the light rays from point \(A\) fall onto the separating surface of two mediums at point \(P\). At point \(P\), the light rays are incident on the separating surface at an angle \(i\), which is the angle of incidence. Similarly, the reflected rays create an angle \(r\) with the normal to the surface. The constant \(\mu)\ is called the refractive index.

In reality, Ibn Sahl (940-1000 CE) discovered the law of refraction six centuries before Snellius or Descartes. In 984, he wrote a book on curved mirrors and lenses, where he wrote about this relationship while discussing the focusing of light by lenses. Since he did not write the law explicitly, it did not gain much recognition. Later, both Snellius and Descartes rediscovered it independently[2].

One name that first comes to mind, in relation to the contributions of the Arabs to optics, is the famous scientist Abu al-Hasan ibn al-Hasan ibn al-Haytham (965-1040), commonly known as Al-Haytham to science historians. It is said that Al-Haytham wrote more than two hundred books in his lifetime, of which more than fifty have reached us. Apart from optics, his expertise is evident in various fields like mechanics, mathematics, astronomy, and others, through his writings. Two hundred years later, when his books were translated into Latin, he became known in Europe as Alhazen. His book on optics, ‘Kitab al-Manazir’, was published between 1011 and 1021, and 2015 was selected as the International Year of Light in 2015 to remember this fact.

Those, who are enthusiastic about the history of science, know that Alhazen’s greatest contribution to science was his emphasis on experimental testing. In the Middle Ages, Roger Bacon (1220-1292 CE) emphasized experimentation in European science, whereas Alhazen initiated experimental methods in Arab science, more than two hundred years before him. Kitab al-Manazir is divided into seven parts. In the first part, he explained that only the results of his own experiments on optics would be found in his book. He would write nothing that’s not supported by experiments. He did not concern himself with theories that had no relation to reality.

Alhazen discussed the hypotheses of many of his predecessors about light, sometimes demonstrating their errors. Previously, scientists like Plato, Ptolemy, or Euclid believed that light travels from the eyes to fall on an object for us to see it. Alhazen was the first to say that light travels from an object to the retina and reaches the brain through nerves. His theories on various other subjects align with modern science. He stated that when light travels through different media, its speed changes. Remember, most ancient scientists, including Euclid and Ptolemy, believed the speed of light to be infinite—so there was no chance of it varying in different media. Alhazen proved conclusively that light does not come out of the eyes, thus nullifying the Greek argument in favor of its infinite speed. He considered light as rays of particles; he was also the first person to explain how lenses work as magnifiers.

Alhazen’s experimental demonstration, that light does not come out of the eye, is quite noteworthy. If light from two lanterns fall on the wall of a dark room, after passing through two openings, two light spots will be created on the wall for the two openings. If one of the lanterns is extinguished now, only one light spot remains. From this, Alhazen concluded that light definitely doesn’t come out of the eye but from the lanterns.

His books, translated into Latin, influenced scientists in Europe such as Roger Bacon, René Descartes, Galileo Galilei, and Johannes Kepler. His contemporary Ibn Sina (980-1037 CE) was known in Europe as Avicenna. Ibn Sina also challenged the theory of light coming out of the eye and stated that the speed of light is finite.

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[1] There are many ways to write the fifth postulate. One of them is that the perpendicular distance between two parallel lines is the same everywhere.
[2] For very small angles expressed in radians, \(\sin(\theta) ≈ \theta\). For near-perpendicular incidence, both \(i\) and \(r\) are very small, and we can write Snell’s Law as: \(\sin(i) / \sin(r) ≈ i/r = \theta\). Ptolemy reached the same conclusions for refraction.