The genius of James Clerk Maxwell and the Theory of Colours Oscar Burke Figure 1: Statue of James Clerk Maxwell, George Street, Edinburgh. 13 In Nature I read Quite a different creed, There everything lives in the rest; Each feels the same force, As it moves in its course, And all by one blessing are blest. The end that we live for is single, But we labour not therefore alone, For together we feel how by wheel within wheel, We are helped by a force not our own So we flee not the world and its dangers, For He that has made it is wise, He knows we are pilgrims and strangers, And He will enlighten our eyes. (James Clerk Maxwell, 1858, Tune, Il Segreto Per Esser Felice, III.) Introduction James Clerk Maxwell is said to be one of the greatest minds in physics, rivalling that of Isaac Newton and Albert Einstein; curiously, however, his name is not a house hold name. His work inspired physicist Albert Einstein to say that James Clerk Maxwell’s contributions to physics “changed the world forever.” German physicist Max Plank, who found that energy came in little packets called quanta, said Maxwell “achieved greatness unequalled.” American astronomer and narrator of the popular science documentary show Cosmos Carl Sagan, said “Maxwell's equations have had a greater impact on human history than any ten presidents.” So who is James Clerk Maxwell and what is all the fuss about? Figure 2: James Clerk Maxwell with his James was born on the 13th of June 1831 in Edinburgh at 14 colour top - which led him to confirm Young's theory of colour7 India Street; James was born into a loving and esteemed family. His mother, Frances, died in 1839, which formed a very close relationship with his father, John, who was a lawyer. He started schooling at Edinburgh Academy, an elite school where his country attire of square shoes and being dull in class gained him the name “Dafty”. However, James was notorious for being good-humoured and was able to ferociously defend himself, much to the surprise of his bullies in the school yard. He also showed strong academic promise, questioning things far beyond the people of his age around him. It was here that his father John decided to get him a tutor, who used traditional means of punishment like the cane to ‘help’ James understand each lesson. This torment got to such a point that James ran down to the lake with a large washing tub and paddled out to the middle of the lake, beyond the reach of his violent tutor! James found Edinburgh Academy rather dull, but at home he read and made his own discoveries, and with little formal knowledge of geometry created a tetrahedron, dodecahedron and two others ‘he did not know the name of’. It was his Figure 3: Plaque with Maxwell's Equations demonstrating how friendship with Lewis Campbell that put electricity and magnetism are linked together an end to his isolation at school, Lewis (By Lourakis - Own work, CC BY-SA 4.0, - Wikimedia had a similar inquisitive mind to James and their chatter was endless full of thought- provoking ideas. At fourteen, James had produced and had published his first paper on oval curves (which he made using pins and string). His father John showed James’ solution to James Forbes, a mathematics professor at Edinburgh University. To his surprise, James had found a more general and less complex solution than the solution by the famous philosopher and mathematician Rene Descartes in the seventeenth century. It was here that James got his first taste of academia. James went to discover that electromagnetic radiation moved so close to the speed of light that it must also be light (this theory was confirmed a quarter of a century later by German physicist, Heinrich Hertz!). He was the first to show how to calculate stresses in suspension bridges. He predicted why there were gaps in between the rings of Saturn, and he helped to create the world’s first colour photograph (Figure 3). His work “A Dynamical Theory of the Electromagnetic Field” helped Einstein create the theory of General Relativity in 1915 and has shown the mathematics, known as “Maxwell’s Equations” (figure 3), behind electromagnetic radiation. Applications of Figure 4: The world’s first colour photograph – a picture of a tartan which have helped develop radio, television, ribbon (no one could repeat this experiment as the dyes to make the photos back then did not work. 100 years later, Kodak discovered radar, microwaves and thermal imaging. that the ribbon reflected ultraviolet light (purple UV light) as well as red, which exposed the film where the red should have been! Nice This paper immerses students in accident! (Illustration: Photograph: Thomas Sutton/ James Clerk mathematics through simulating the colour Maxwell/ SSPL - Getty Images) top experiment, which led Maxwell to confirm how we perceive colours and how it was used to diagnose colour-blind people and to produce the world’s first colour photograph.8 History Maxwell introduced to colour Maxwell was an intensely curious boy, finding lots of different uses for regular objects. Bored of using a spoon as spoons ought to be used, he was found using the back of the spoon to bring the sun into the house. When told about a blue rock, he answered “How d’ye know it’s blue?”.5 A question that we still find troubling when asked today. He carried this burning curiosity along with his fascination with colours, with him to his adulthood. Young, a famous physicist, thought that the human eye has only three types of receptors, which he couldn’t prove. James Forbes, James Maxwell’s professor at Glasgow Figure 5: Diagram of Maxwell's Coloured top. An inner circle and outer circle of University, was experimenting with this problem himself. coloured disks. The amount that each disk He found that by placing and overlapping multiple pieces of could be exposed could be varied. 6 circular coloured paper (so that the paper looked like a pie chart) and then spinning the top produces some very interesting results. He found that the colours on the spinning top began to merge together into one colour when the top was spinning at sufficient speed! Merging colours and blurring were nothing new, there were a wide range of popular optical toys that were available in the 1830s.3 However, what baffled Forbes was that the single colour that the spinning disks were making did not match the colour that was expected. Forbes knew from painters and dye makers that three colours; being red, yellow and blue; were required to make paint or dye of any other colour in the visible spectrum! Forbes tried blue and yellow pieces of paper together (which according to the painters and dye-makers should make green) and he instead produced a dull pink! With other projects and duties to occupy him, Forbes gave young James Maxwell free reign in his laboratory. Maxwell wanted to solve Young’s theory of colour! But, before we find out how he went, let’s have a look at the mathematics behind what was known about light in Maxwell’s time. The Enlightenment – A new look at Light and Colour In 1621, Willebrord van Snel van Royen (also known as Snell or Snellius) determined that coloured light rays bend or refract when they travel between substances of different densities (like glass and air). His law, known as Snell’s Law, appears as below: �"����" = �(����(, Where n1 and n2 are how well the substance bends the light (known as the refractive index, with air being 1) and angles �" and �" are the angles at which the beam enters and leaves the substance (Figure 6a). This law helps us explain how light rays travel through lenses, microscopes and telescopes. René Descartes, applied the mathematics of Snell’s Law to investigate how rainbows form. Descartes found that when the incoming light angle is great enough, the light reflects instead of refracts, in effect bouncing back off the water droplet surface (Figure 6a, 6b). Descartes noted that light does this in a spherical water droplet once, making a primary rainbow, or twice, creating a secondary rainbow (Figure 6c, 6d). These findings were published in 1637 in his book Les Météores. a b c d Figure 6: a) Snell’s Law – how light is bends/refracts at the surface of water and air (Wikimedia) b) At the right angle, light reflects instead of refracts/bends. Descartes noted that light can be bent once (visible at 42 degrees) or twice (visible at 51 degrees). Forming a double rainbow (Hyperphysics) c) Sketch of double rainbows (Adapted from Descartes’ Les Météores 1637 – Plus Maths1 d) A double rainbow, consisting of a primary rainbow and secondary rainbow. Note how the secondary rainbow is considerably fainter than the primary and the colours are inversed! (Hyperphysics) Sir Isaac Newton – Opticks and the seven colours of light In 1704, English scientist Sir Isaac Newton greatly improved what was known about colour and light through his discoveries published in his book, Opticks. Newton noticed that white light itself splits up into a rainbow of seven colours when passed through glass prisms (Figure 7). As Newton said, ‘Light itself is a heterogeneous mixture of differently refrangible rays’.11). When Newton placed these seven colours onto a spinning top he noticed that, when spun fast enough, the colours merge and white is formed. He concluded, therefore, that the reverse is also true. Combine all seven colours (violet to red), white light is made.