The Story of Optics - Wave vs. Particle

Gautam Gangopadhyay

Translation: Sunando Patra

Photo: Sunando

Despite the progress in optics, we didn’t witness any exploration of new ideas about the nature of light in the second chapter. This changed at the end of the seventeenth century and into the eighteenth century. We can mention two books here: Traite de la lumiere (Treatise on Light) by Christian Huygens (1629-1695), published in 1690. The second book is Opticks, authored by the greatest scientist of all time, Isaac Newton (1643-1727). The first edition of Opticks was published in 1704. Newton wrote his famous Principia in Latin; at that time only scholars could read that language. Opticks, however, was written in English, so it also gained popularity outside the scholarly community. Of course, Newton began publishing his optics essays as early as 1675.

Treatise on light, where the causes of what happens to it in reflection and refraction are explained, and particularly in the strange refraction of the Icelandic crystal. (Source: Wiki)

Everyone knows about Newton’s contributions to mechanics or mathematics. The branch of physics in which Newton experimented most vigorously, was optics. He researched the nature of light. When sunlight passes through a prism, it breaks into various colors, a phenomenon called dispersion. From this, Newton proved that white light is actually a mixture of different colored lights. It might seem like a simple matter now, but the circumstances were quite different in that era. Newton wasn’t the first to see light passing through the prism and dispersing into various colors; but at that time, it was thought to be just a property of the prism with no relation to light. He demonstrated that light passing through another similar prism would be transformed back into white light. He also showed that the refractive indices of different colors of light are different, with blue light having a higher refractive index than red light. Newton provided the correct explanation for the rainbow. When sunlight passes through water droplets suspended in the air, the light is refracted and dispersed into various colors, and through total internal reflection, we see a rainbow. The topic of total internal reflection is discussed in a later chapter.

Cover of the first edition of Newton’s Opticks (Source: Wiki)

After understanding that the refractive index of different colors of light is different, Newton concluded that it is not possible to make a good telescope using lenses. This is because the violet and the red light focus at different points. Newton made a reflecting telescope using a curved mirror. Newton’s assumption was incorrect; it’s not possible to prevent dispersion using a simple lens, but it is possible with compound lenses made using various types of glass. We use such lenses in our cameras. Newton’s method is followed in modern large telescopes, where mirrors are used instead of lenses, but for different reasons.

Isaac Newton investigating light. (Photo by Photos.com on Freeimages.com)

Video of an experiment of the dispersion and recombination of white light. (Source: Youtube)

By the time of Newton, there was already a consensus regarding the fact that light is a form of energy. The next question was: how does light travel from one place to another? This phenomenon was well understood in the case of sound waves. When a stone is dropped into water, we all observe the ripples spreading in all directions. The scientific term for these ripples is wave. Sound is a type of wave that travels through the air. René Descartes in France, Robert Hooke in England (1635-1703), and Christiaan Huygens in Holland – all called light a wave. Still, there wasn’t complete agreement among supporters of the wave theory about the medium through which light traveled. Newton didn’t accept light as a wave; he believed that light was made up of particles. It was Pierre Gassendi (1592-1655) who first proposed the particle theory of light in the modern era.

We’ll discuss the arguments on both sides of the ‘particle vs. wave’ debate. For the sake of further discussion, let’s now clarify some common aspects of waves. In the case of the waves on water, we’ll see that the water rises at one point, while at another point, it falls. An illustration shows a snapshot of a single wave. It depicts the positions of water particles at different points along the same line at one moment. Points like \(A\) and \(C\) are called wave crests, while points like \(B\) are called wave troughs. The distance between two consecutive points in the same phase, such as \(A\) and \(C\) in the picture, is called the wavelength.

Wave crests and troughs

There is no air in the space between the sun and the earth. Until that time, we assumed that a medium was needed for any kind of wave motion—just as air is needed for the propagation of sound. The reason was simple; at that time, ‘waves’ meant only mechanical waves. The particles of the medium need to vibrate for wave propagation—just like air particles are needed for sound or water particles for waves in the water. How does light from the Sun reach Earth? If light were particles, then this problem wouldn’t exist. A bullet, fired from a gun, no longer depends on the air for its motion. If a bullet can travel through a vacuum, then light particles can too. Christian Huygens, a contemporary of Newton, was the biggest proponent of the wave theory of light at that time. He imagined that there is a medium named ‘ether’ (luminiferous aether; luminiferous meaning ‘light-bearing’) present everywhere in the universe, including vacuum. This is a slightly modified version of Aristotle’s aether. Based on this idea, he formulated a theory about the motion of light waves, where light is a wave in the ether. Newton also mentioned ether; we will discuss more about this in the following chapter, where it will be seen that he even talked about waves in that medium, but he did not accept that light travels as waves in ether. We will discuss the nature of light waves in the next chapter—at that time, nothing was known about this topic.

According to Newton, when light enters a denser medium—such as water or glass—from air, its speed increases due to gravitation. That’s why light undergoes refraction. On the other hand, it was known that sound waves travel faster through denser media. Descartes said that this is true for light as well. Now we know that they both were mistaken; the speed of light decreases in denser media. We have seen before that Fermat was correct about this, but before the 19th century, it was not possible to measure the speed of light inside denser media.

Newton emphasized on the rectilinear motion of light. Even though we cannot see the other side of the wall, we can hear sound waves created on that side because sound waves bend around obstacles (like a wall) and reach our ears. Newton’s argument was that if light were waves, then it would bend around the edges of the wall and come to our eyes. This property of waves is called diffraction. If light were particles, it wouldn’t bend around the edges of the wall. Newton said that as light does not diffract, it must be composed of particles.

Newton’s immense contributions to physics and mathematics made sure that the wave theory of light was dominant during his time. We discuss Newton’s Rings in the appendix, where we will see that Newton observed the wave properties of light, but explained them differently. In his famous book ‘Principia Mathematica’, Newton made a famous statement, “Hypotheses non fingo”, meaning “I do not feign hypotheses”. If he had completely adhered to his own words, he might have discovered the wave nature of light then and there. In reality, bias against the wave theory had set back optics by almost a century. The special property of waves that is useful in explaining Newton’s laws is interference. In 1803, English scientist Thomas Young (1773-1829 CE) established the wave theory of light by demonstrating interference through a particular experiment. Let’s briefly discuss diffraction before moving on to this experiment.

Diffraction of a Wave through an aperture.

If light were waves, we should see its diffraction. But usually, we see light traveling in straight lines. Actually, to see the diffraction of waves, the obstacle in front of the waves should be close in size to the wavelength of the waves. The image below shows a wave hitting a screen. Two parallel lines indicate the crest of the wave, meaning the distance between the two parallel lines is the wavelength. Huygens proposed a rule to explain the motion of light. He assumed that each particle of the medium (luminiferous aether) gives birth to a new wave of light, which spreads out in all directions. According to Huygens’ rule, holes act as sources of light. In the left image, the size of the hole is larger than the wavelength, so the wave almost follows a straight path. In the right image, the wavelength and the size of the hole are close, so after passing through the hole, the wave spreads out in different directions, meaning it diffracts.

Video of Diffraction of a Wave through an aperture. (Source: YouTube)

The visible light has wavelengths between 400 to 700 nm (nanometers [1]). For comparison, the width of a human hair is about one hundred thousand nanometers. We are only able to see the diffraction of light for such tiny obstacles, which is why we generally assume that light travels in straight lines. Francesco Grimaldi (1618-1663 CE) first mentioned this while observing diffraction, but he didn’t fully understand it himself.

Thomas Young's sketch of two-slit diffraction for water waves, which he presented to the Royal Society in 1803. (Source: Wiki)

Let’s now talk about diffraction. The image above shows a schematic of light waves in Young’s famous double-slit experiment. Monochromatic light, i.e., light of the same wavelength, falls on a rough wall from one side. There are two very narrow slits on the wall. On the other side, there is a screen. If light were particles, only two spots directly opposite the slits on the screen would have been illuminated. Think of these moving particles as bullets to make things clearer. The wave theory says something else. Because the slits are narrow, when light enters, it diffracts and spreads out in all directions. The image shows semicircular lines indicating the crests of the waves.

If two crests of two waves coming from two slits fall together on the screen, the intensity of light will be very high there. Where one crest falls on the trough of another wave, the total amplitude of the resultant wave will be zero, meaning that the area on the screen will be dark. The places on the screen where two crests overlap are the brightest. We skip some descriptions here to make it easier to understand. Interested readers can learn more about Young’s experiment in the appendix. If light behaves as waves, we will see alternating bright and dark fringes on the screen. This phenomenon is called interference. It’s clear that particles can't create interference. Two light particles falling in the same place can never create darkness. If white light is used, the different colors of light will have their crests or troughs in different positions. So, on the screen, the crests of red light fall in one place, and those of violet light will fall elsewhere. As a result, we’ll see fringes of different colors of light on the screen. Newton thought about the play of light of various colors reflected from soap bubbles, and this is exactly what happens there. The play of light of various colors can be seen due to interference reflected from the two walls of the soap bubble.

Portrait of Thomas Young. (Source: Wiki)

The wave nature of light waves was proved by Young’s experiment. Newton’s followers resisted initially, but eventually, everyone accepted this idea. There has been almost no doubt for about a hundred years. Young also showed that light of different colors has different wavelengths.

Another characteristic of waves, called polarization, was observed in the field of light waves. Not all waves can be polarized. There are two types of waves possible. When you throw a stone in a pond, the waves move forward, but the water molecules move up and down on the surface. The type of waves where particles of the medium move perpendicular to the direction of the wave, like this, are called transverse waves. In the case of sound waves, air particles move parallel to the direction of the wave. These waves are called longitudinal waves. Only transverse waves can be polarized. Huygens believed that light was a longitudinal wave, i.e., wherever light goes, the particles of ether push each other successively. However, subsequent research by Fresnel and Maxwell has proven that light is actually a transverse wave. The nature of the emission of light waves will be discussed in the next chapter. We can explain phenomena like diffraction, reflection, etc., from Huygens’ principle, mentioned earlier.

Appendix

Interference and Young’s Experiment

One of the most famous experiments in the history of physics is Young’s double-slit experiment, not just optics. In the diagram below, there are two extremely fine slits, with a distance \(d\) between them. Light from a monochromatic (of a specific wavelength) source passes through these two slits and falls on a screen at a distance of \(L\). The light travels a path of \(\sqrt{L^2 + (x-\frac{d}{2})^2}\) from the center of the screen to the point \(x\), for the first slit. For the second slit, this distance is \(\sqrt{L^2 + (x+\frac{d}{2})^2}\). So, the difference between the two paths is easily found. Now, if \(d\) or \(x\) is much smaller than \(L\), the difference in the paths can be written as \(x \frac{d}{L}\).

Source: Wiki

Constructive interference occurs when the value of this path difference is an integral multiple of the wavelength of light, i.e., two crests (or troughs) overlap—we see bright spots at that point. So, the condition for constructive interference is \[\frac{x d}{L} = n\lambda, ~~~~~~ n = 0, 1, 2, \ldots\] Similarly, the condition for destructive interference is for one crest to overlap another trough. The distance between two consecutive crests and troughs is \(\lambda/2\), hence, \[\frac{x d}{L} = \left(n+\frac{1}{2}\right)\lambda, ~~~~~~ n = 0, 1, 2, \ldots\] In Young's experiment, we see fringes on the screen, meaning we can see alternating bright and dark lines or patches of light and darkness. These can only be explained through interference. At different points on the screen, the value of \(x\) is different, so at times constructive interference happens, and destructive interference happens at others. By measuring the distance between two consecutive patches on the screen, we can determine the wavelength of light.

Why haven’t we seen interference until now, or why don’t we usually see interference between two lights? The reason is that the phase difference between two different light sources changes randomly and constantly. That’s why we can’t see interference— conditions for constructive interference, met at one moment, don’t match immediately afterward. Instead, we see an average brightness. Young illuminated both slits with the same light, so the phase difference between the light coming out of the two slits didn’t change.

Newton’s Rings and Light Waves:

After several hundred years, today it’s easy to say where Newton went wrong. That era was different, back then there wasn’t certain proof for the wave-nature. But some parts of Newton’s Opticks do make it seem as if he could have talked about light waves if he wanted to. A very familiar experiment for undergraduate physics students is Newton’s rings. A plano-convex (one side flat and the other curved) lens is placed on a flat glass plate such that the curved side of the lens touches the plate. When a monochromatic light is shone from above, you can see the creation of concentric dark and bright circles. Although Robert Hooke observed this phenomenon before, Newton was the first to deeply investigate it and write in detail about it, so they are named after him.

Method to observe Newton’s Rings . (Source: Link

The explanation of these rings is quite simple if the light is considered to be a wave. The gap between two glass surfaces isn’t evenly wide – it gradually widens as it moves away from the center. When light falls on the top glass’s rounded surface (inside the lens), some of it gets reflected, while some reflects from the flat glass at the bottom. The light in this second part travels a longer path, so its phase is different from the first part’s light. When the phase difference between these two reflected lights is zero (or \(n \times 360^{\circ}\), \(n\) is any integer), then the two lights reinforce each other, resulting in constructive interference. But if the phase difference is \(180^{\circ}\) (or \((2 n + 1 )\times 180^{\circ}\), for any integer \(n\)), then the two lights cancel each other out, resulting in destructive interference and we observe darkness there. As the thickness of the air layer changes gradually, so does the phase difference, resulting in alternating patterns of constructive and destructive interference. This creates patterns of light and dark bands. If white light is used instead of monochromatic light, bands of various colors can be seen. Different colors have different wavelengths of light, so they require different thicknesses of the air layer for destructive or constructive interference to occur. Perhaps where blue light undergoes destructive interference, red light undergoes constructive interference; hence, bands of different colors are observed. Newton did observe this. The same thing happens in soap bubbles.

Newton explained: “Nothing more is requisite for putting the Rays of Light into Fits of easy Reflexion and easy Transmission than that they be small Bodies which by their attractive Powers, or some other Force, stir up Vibrations in what they act upon, which Vibrations being swifter than the Rays, overtake them successively, and agitate them so as by turns to increase and decrease their Velocities, and thereby put them into those Fits.” (Opticks, 4th Edition; spelling and sentence structure are unchanged from the original) This means light particles create vibrations through the medium (ether). These vibrations, move faster than the speed of light particles within the medium. As a result, these vibrations change the speed of these particles and occur in such a way that sometimes they only reflect, and sometimes they only refract. This causes the creation of light and dark bands. Newton talks about the ether waves, and mentions their role in the case of light, while he objects to accept light as wave!

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[1] One Nanometer is one billionth part of a Meter. Mathematically, we say, \(1 nm = 10^{-9} m\)