History: optics diffraction
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Grimaldi a Jesuit monk with an interest in mathematics and science, performed a series of careful experiments with light. He described these In his 1665 book Physico-Mathesis de Lumine [@Grimaldi1665-physico]. He described multiple examples of light spreading as it passed through a small aperture or near an edge. He specifically described light passing through a pinhole and generating a large spot on a surface, and the size of the spot increased as the pinhole became smaller. Grimaldi gave the phenomenon its name, diffraction. His work, published posthumously, spread across Europe although its impact might have been somewhat limited because it was published in Latin.
Grimaldi’s observation is incompatible with the idea that light is made up of a stream of particles traveling along a straight line (raya). The Dutch physicist Christiaan Huygens was an active member of the European scientific community, and it is likely he knew of Grimaldi’s work. He proposed that light is a wave, not a ray, and in his book, Traité de la lumière (1690), [@huygens-1690-traite], he explained reflection and the quantitative properties of refraction (Snell’s Law) as light passed from one medium to another.
His descriptions of a wave are based on a key idea: every point on a wavefront acts as a source of secondary spherical wavelets. Initiating a wave at one point, say a light source, creates a set of secondary wavelets at nearby points ?@fig-huygens-waves. The wave we observe is the sum of these small, secondary wavelets as they spread out in the direction the wave is traveling. These wavelets add constructively in the direction the wave is traveling, and they cancel at points behind the traveling wavefront.
Isaac Newton, in his book Opticks (1704), had proposed that we consider light as consisting of a stream of particles (corpuscles) and treat them as rays. His experiments and thinking about the wavelength properties of light ray will be a focus of a later chapter. Newton relied on the idea of light as rays to explain properties such as reflection and abosrption and color. He was aware of Grimaldi’s observations, and he even repeated them (Citation). But he attempted to explain them by theorizing about physical properties of the rays.
Despite the clear demonstrations of diffraction, for a century Newton’s corpuscular theory was widely accepted. Perhaps this was because scientists held Newton in very high esteem; after all, scientists are people and they are moved by emotions like anyone else. Thomas Young’s (1804) double slit experiments, demonstrating interference between two separated light sources and demonstrated at the Royal Society, brought the wave theory back into prominence . Young’s demonstration started with a single point source that illuminated two different slits
Because the two slits are illuminated by a common source, the wave theory would suggest that their wavefronts are coherent (in synchrony) with one another. The corpuscular theory, in contrast, would simply suggest that their are different particles headed to the two slits with no particular connection.
Young measured the image formed by the two slits, and he showed that it had a distinct spatial structure of light and dark bands. We can understand these bands as arising from the spatial summation of the coherent waves arising from the two slits. He understood this well, and the wave concept is illustrated in his original publication for the Royal Society.
As one might expect in science, there was resistance to the shift. It was the work of August Fresnel who provided a mathematical foundation for explaining Huygens’ principle as well as additional experimental evidence (see Jenkins and White discussion on this point). Accepting the idea that light was a wave paved the way for Maxwell’s unified theory of light, electric fields, and magnetic fields expressed in his famous equations describing the electromagnetic spectrum. These concepts and equations are the foundation of much physics and engineering. For more of the history, which is wonderful, click here.
Hindsight is much clearer than foresight, and in a way it is surprising that the wave theory was ignored for so long. Consider the simple experiment illustrated in Figure . The image shows a collimated source, perhaps created by a point source at some distance from a pinhole. According to the Newton’s corpuscular theory (rays), a person standing to the side would not see the light: the rays would continue straight and none would arrive to the viewer’s eyes (panel A). Yet a simple experiment reveals that the the pinhole light can be seen from the side, or indeed from many positions. The light emerging from the pinhole must be spreading in many directions (panel B). The pinhole reveals ‘secondary wave source’, just as Huygens theory said.
Ray tracing is a useful computer graphics for making images, and in some conditions when the aperture is large and a lens is inserted, the role of diffraction may not be a big factor. But for these small entrance pupils diffraction is a large effect.
The thin lens, thick lens and all that into Chapter 02 Optics. ## Diffraction: the phenomenon
There will be a historical discussion of Young, Huygens and Fresnel. And the business about the Poisson spot, I think, too. Formula. Lord Airy.
Here is a ChatGPT discussion of the history
More history in a ChatGPT, much copied below.
Light, like all electromagnetic waves, can interfere and spread when its path is restricted by physical boundaries.
Formally, diffraction can be described using the Huygens-Fresnel principle, which treats every point on a wavefront as a secondary source of spherical wavelets. As these wavelets propagate, they interfere with each other, producing the characteristic diffraction patterns. Diffraction is significant when the size of the aperture or obstacle is on the order of the wavelength of the light. The phenomenon is typically divided into Fresnel diffraction (near-field diffraction) and Fraunhofer diffraction (far-field diffraction), depending on the distance between the aperture and the observation point.
Diffraction is fundamental in engineering applications, especially in designing optical systems. It defines the diffraction limit of resolution in imaging systems, such as cameras and microscopes, and is exploited in technologies like diffraction gratings, which are used for spectral analysis by dispersing light based on wavelength. Understanding and managing diffraction effects is crucial in fields like telecommunications, laser optics, and antenna design.
The evolution of the understanding of light from a particle-based model to a wave-based model is a fascinating story that spans several centuries. Here’s a brief history highlighting key contributors like Newton, Young, Huygens, and Fresnel:
Isaac Newton (1642–1727)
In the 17th century, Isaac Newton advocated the corpuscular theory of light, proposing that light consisted of tiny particles or “corpuscles.” He based this theory on observations such as the rectilinear propagation of light (light traveling in straight lines) and phenomena like reflection and refraction. Newton’s reputation and the success of his mathematical laws of motion helped make the particle theory dominant during his time.
Christiaan Huygens (1629–1695)
Around the same period, Dutch physicist Christiaan Huygens proposed a wave theory of light in 1678, which he detailed in his book Traité de la lumière (1690). Huygens suggested that light behaves as a wave, explaining reflection and refraction through what is now known as Huygens’ Principle. This principle posits that every point on a wavefront acts as a source of secondary wavelets, and the new wavefront is the envelope of these wavelets. However, because Newton’s corpuscular theory was more widely accepted, Huygens’ wave theory was largely overlooked.
Thomas Young (1773–1829)
In 1801, English polymath Thomas Young conducted the famous double-slit experiment, which strongly supported the wave theory of light. In this experiment, light passing through two closely spaced slits produced an interference pattern of bright and dark fringes on a screen. This phenomenon could not be explained by the particle theory but was easily explained by the superposition of waves—light waves from each slit interfered constructively (producing bright fringes) or destructively (producing dark fringes).
Young’s experiment was a major blow to the particle theory and revived interest in Huygens’ wave theory.
Augustin-Jean Fresnel (1788–1827)
Building on Huygens’ and Young’s work, French physicist Augustin-Jean Fresnel developed a comprehensive mathematical wave theory of light in the early 19th century. Fresnel provided a detailed analysis of wave interference, diffraction, and polarization, showing how light behaves as a transverse wave (with vibrations perpendicular to the direction of propagation). His work resolved many of the remaining questions about the behavior of light and solidified the wave theory as the dominant model.
One of Fresnel’s key achievements was explaining the phenomenon of diffraction, especially with his use of Fresnel integrals to predict how light waves bend around obstacles. Fresnel’s work, combined with the empirical success of his wave-based predictions, definitively displaced Newton’s particle theory.
The story of Fresnel, Poisson, and the so-called Poisson’s spot (or the Arago spot) is a famous and ironic episode in the history of physics, illustrating the power of scientific prediction and experimental validation.
Background: Fresnel’s Wave Theory of Light
In the early 19th century, Augustin-Jean Fresnel was developing and advocating a comprehensive wave theory of light. Fresnel’s work built on the wave theory of Christiaan Huygens and the interference experiments of Thomas Young. However, Fresnel faced stiff opposition from proponents of the particle theory of light, which was still widely accepted due to Newton’s authority.
In 1818, Fresnel submitted a paper on light diffraction to a competition held by the French Academy of Sciences. His theory relied on light behaving as a wave, and it successfully explained how light bends around obstacles and interferes to produce diffraction patterns. Among the judges reviewing his theory was Siméon Denis Poisson, a prominent French physicist and a strong supporter of the particle theory of light.
Poisson’s Challenge
Poisson sought to disprove Fresnel’s wave theory by identifying what he thought was an absurd consequence of it. Using Fresnel’s mathematical model, Poisson calculated the behavior of light when it encounters a small circular object, such as a disk, blocking its path.
According to Fresnel’s wave theory, light waves would bend around the edges of the disk and interfere constructively at the center of the shadow. Poisson pointed out that Fresnel’s theory predicted a bright spot at the very center of the shadow cast by the disk, where one would intuitively expect complete darkness. To Poisson, this seemed so absurd and counterintuitive that he believed it demonstrated the inadequacy of the wave theory of light.
The Experiment by Arago
However, another judge on the committee, the physicist François Arago, took Poisson’s prediction as a challenge to be tested experimentally, rather than dismissing it outright. Arago set up an experiment to observe the shadow cast by a small opaque disk with a distant point source of light.
To Poisson’s surprise, a bright spot did indeed appear at the center of the shadow, just as Fresnel’s wave theory predicted. This bright spot became known as the Poisson spot (sometimes called the Arago spot in honor of Arago’s experimental confirmation).
The observation of Poisson’s spot was a significant vindication of Fresnel’s wave theory of light. It not only confirmed a counterintuitive prediction of the theory but also dealt a blow to the corpuscular (particle) theory of light, which could not explain the phenomenon.
This episode was crucial in solidifying the wave theory of light in the scientific community. Fresnel’s work, along with Arago’s experiment, helped shift the consensus away from Newton’s particle theory and towards the wave theory, which was later expanded upon by the electromagnetic theory of light by James Clerk Maxwell in the mid-19th century.
James Clerk Maxwell (1831–1879)
The understanding of light as a wave reached a new height with the work of Scottish physicist James Clerk Maxwell. In the 1860s, Maxwell formulated the electromagnetic theory of light, showing that light is an electromagnetic wave composed of oscillating electric and magnetic fields. This unified light with the broader field of electromagnetism and explained why light propagates as a wave, further cementing the wave theory in physics.
The Particle-Wave Duality (20th century)
Despite the triumph of the wave theory in the 19th century, the advent of quantum mechanics in the early 20th century revealed that light exhibits both wave-like and particle-like properties. Albert Einstein’s explanation of the photoelectric effect in 1905 showed that light also behaves as discrete packets of energy called photons, leading to the modern understanding of wave-particle duality.
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Huygens’ principle indeed states that every point on a wavefront acts as a source of secondary spherical wavelets, and the new wavefront is the envelope of these wavelets. These secondary waves propagate in all directions, not just in the forward direction. However, the resulting wavefront that we observe is usually the forward-propagating part because of the constructive interference in the forward direction.
To clarify:
Huygens’ Principle: Each point on a wavefront acts as a source of secondary spherical wavelets. These wavelets spread out in all directions (including backward), but typically, we only consider the forward-moving wavefront when calculating how waves propagate. Fresnel’s Contribution: Fresnel extended Huygens’ idea by incorporating interference. He showed that wavelets from different points can interfere constructively in the forward direction and destructively in other directions (such as backward), which is why the backward propagation is generally not observed.
In summary, while the secondary waves propagate in all directions (including backward), due to interference effects, only the forward-moving wavefront is usually significant.
Yes, the key to understanding why the backward-propagating waves interfere destructively lies in the nature of wave interference and the contributions of secondary wavelets over time.
When considering a plane wave:
Secondary waves in all directions: Each point on the wavefront emits secondary spherical wavelets, which propagate in all directions, including backward. However, the forward-propagating secondary wavelets interfere constructively to form the next forward-moving wavefront. Destructive interference behind the wave: Behind the wavefront, the contributions from the secondary wavelets interfere destructively. This happens because, in the backward direction, the phases of these wavelets do not align as perfectly as they do in the forward direction. Each secondary wavelet is emitted at a different point in space and time, so the waves that propagate backward are out of phase with each other and tend to cancel out. Constructive interference in front: In the forward direction, the secondary wavelets are more in phase, as they all originate from the same plane wavefront moving forward. The new wavefront forms at the envelope of these wavelets, resulting in constructive interference. The contributions from past wavelets add coherently to build the next forward wavefront.
In this way, the forward direction experiences constructive interference because the secondary wavelets reinforce each other, while the backward direction experiences destructive interference due to phase mismatches. Fresnel’s explanation of interference provides the mathematical basis for this, where wavelets emitted earlier interact and interfere with those emitted later in such a way that only the forward-moving wavefront is significant.Yes, in a simulation based on Huygens’ principle, the amplitude of the secondary wavelet emitted from each point on the wavefront at a given moment in time would indeed depend on the sum of contributions from all wavefronts at that point at that specific time.
Here’s a breakdown of how this works:
Secondary Wave Emission: Each point on the wavefront acts as a source of secondary spherical wavelets. These wavelets propagate outward from that point, with an amplitude that depends on the wavefront at that moment in time. Amplitude of Secondary Waves: The amplitude of the secondary wavelet at any given point is influenced by the total wavefront at that point in time. This means that the sum of the wavefront amplitudes from surrounding points (both from previous wavefronts and those forming at the same time) will determine the local amplitude at that point. Superposition Principle: The key idea here is superposition. At each moment in time, the total wave at any given point is the sum of the contributions from all wavefronts that reach that point. These contributions include both the current wavefront and past wavefronts that have interacted through constructive or destructive interference. Wavelet Amplitude: When you calculate the secondary wavelet emitted from a point on the wavefront, its amplitude is proportional to the instantaneous sum of all the wavefronts at that point. This sum incorporates contributions from wavelets emitted by other points on the wavefront, leading to constructive interference in the forward direction and destructive interference in other directions. Mathematically: If ( E(x,t) ) represents the electric field (or another wave quantity) at a point ( x ) at time ( t ), then the total wave at that point is the sum of all contributions from earlier times, according to the superposition principle. The amplitude of the secondary wavelet at that point will be proportional to this total wave at time ( t ), i.e., ( A(x,t) E(x_i,t_i) ), where ( x_i ) and ( t_i ) are positions and times of other wavelets contributing to the point.
In essence, each point is emitting a spherical wavelet whose amplitude is determined by the instantaneous state of the wavefronts at that point, which is the sum of contributions from past and current wavefronts. This results in the propagation of the overall wave, with constructive interference ahead and destructive interference behind.
From Gemini, matches ChatGPT history
The Discovery of Interference and the Wave Theory of Light
The understanding of light as a wave phenomenon was a pivotal development in physics. This understanding emerged from a series of experiments and theoretical developments conducted over several centuries.
Early Ideas and Experiments Newton’s Corpuscular Theory: Isaac Newton proposed a corpuscular theory of light in his Opticks (1704), suggesting that light was composed of tiny particles. While this theory could explain phenomena like reflection and refraction, it struggled to account for diffraction and interference. Huygens’ Wave Theory Christian Huygens: In 1678, Christian Huygens proposed a wave theory of light. He suggested that light propagated through a medium called the “aether” as waves, similar to sound waves. Huygens’ principle, which states that each point on a wavefront can be considered as a secondary source of spherical waves, was a crucial tool in understanding wave propagation. Young’s Double-Slit Experiment Thomas Young: In 1801, Thomas Young conducted his famous double-slit experiment. He passed light through two narrow slits and observed the resulting pattern on a screen. The pattern showed alternating bright and dark fringes, which could only be explained by the interference of waves. This experiment provided strong evidence for the wave nature of light. Diffraction and the Wave Theory Diffraction: Diffraction is the bending of waves around obstacles or edges. It is a characteristic property of waves and was observed in light by Grimaldi in the 17th century. Young’s double-slit experiment also involved diffraction, as the light waves spread out from the slits. Fresnel’s Contributions: Augustin-Jean Fresnel, a French physicist, made significant contributions to the wave theory of light. He developed mathematical equations to describe diffraction and interference phenomena. Fresnel’s work helped to solidify the wave theory of light and provided a quantitative framework for understanding these phenomena. Further Developments Electromagnetic Theory: In the 19th century, James Clerk Maxwell developed the electromagnetic theory, which unified electricity, magnetism, and light. Maxwell’s equations predicted the existence of electromagnetic waves that traveled at the speed of light. These waves were later confirmed experimentally by Heinrich Hertz.
The discovery of interference and the development of the wave theory of light marked a turning point in our understanding of the nature of light. While Newton’s corpuscular theory had dominated for over a century, the experimental evidence provided by Young and others, combined with the theoretical work of Huygens, Fresnel, and Maxwell, established the wave nature of light as the prevailing paradigm.
You’re absolutely right—Francesco Maria Grimaldi is credited with the first recorded observations of diffraction of light. He performed experiments in the 1660s and described how light bends around obstacles and produces fringes, a phenomenon he called diffraction. Grimaldi’s observations were published posthumously in his work Physico-Mathesis de Lumine, Coloribus, et Iride (1665), where he carefully documented this bending of light.
Did Huygens Demonstrate Diffraction?
Christiaan Huygens did not experimentally demonstrate diffraction himself. In fact, his work focused more on explaining phenomena like reflection, refraction, and double refraction in terms of his wavefront theory. His theory, especially through the use of the concept of secondary wavelets, laid the groundwork for understanding diffraction later on, but Huygens did not provide a detailed analysis or experimental evidence of diffraction.
Huygens’ wave theory was primarily focused on explaining how light behaves when passing through different media, and he successfully derived Snell’s law for refraction using his principle of secondary wavelets. He did not directly address diffraction in his major works like Traité de la lumière (1690), and it is unlikely that he had a fully developed explanation for the phenomenon at the time.
Did Huygens Know About Grimaldi?
Huygens most likely knew about Grimaldi’s work. Grimaldi’s book Physico-Mathesis de Lumine was published in 1665, and the ideas spread across Europe. Huygens was an active member of the scientific community and would have been aware of contemporary developments in optics. Additionally, Huygens’ treatise on light was published in 1690, long after Grimaldi’s discoveries had become known.
However, even though Huygens probably knew about Grimaldi’s experiments with diffraction, he did not integrate diffraction into his wave theory in a detailed way. It wasn’t until the early 19th century, with the work of Thomas Young and Augustin-Jean Fresnel, that diffraction was fully explained within the framework of wave theory.
Summary of Contributions: Grimaldi (1665): First experimentally observed and documented diffraction. Huygens (1690): Proposed the wave theory of light and explained reflection and refraction using the concept of wavefronts and secondary wavelets but did not experimentally demonstrate diffraction. Young and Fresnel (19th century): Developed a complete explanation of diffraction and interference, which solidified the wave theory of light.
So, while Huygens was aware of Grimaldi’s work, diffraction was not a central part of his own contributions to optics.
Grimaldi’s work
Francesco Maria Grimaldi, an Italian Jesuit physicist, made crucial early contributions to the study of light and diffraction. His observations, published posthumously in his book “Physico-mathesis de lumine, coloribus, et iride” (Physical-Mathematical Treatise on Light, Colors, and the Rainbow) in 1665, were the first recorded observations of diffraction, a phenomenon that he named and described in detail. Grimaldi’s work laid the groundwork for future developments in wave theory, even though the concept of light as a wave was not fully developed in his time.
Here are the key experimental observations and findings about light and diffraction that Grimaldi described in his book:
- Discovery and Naming of Diffraction: Grimaldi coined the term “diffraction” (from the Latin “diffringere,” meaning “to break apart”) to describe the bending of light when it passes near the edges of an obstacle or through a small aperture. He noticed that light, instead of traveling in perfectly straight lines as expected by classical geometric optics, would spread out when passing through small slits or near obstacles. He observed that the light deviated from its rectilinear path, producing a pattern of light and shadow that couldn’t be explained by simple reflection or refraction.
- Light Spreads Beyond Geometric Shadows: One of Grimaldi’s most important observations was that light, after passing through a small aperture or around an obstacle, spread into the regions that should have been in shadow according to the rules of geometric optics. He conducted experiments where light was passed through a narrow slit or around the edge of an opaque object, and he noticed that some light appeared beyond the expected boundary of the shadow, indicating a bending or spreading of light into the geometrical shadow region. This contradicted the purely rectilinear propagation of light that was assumed by Newton’s corpuscular theory, which would predict sharp shadows with no light in the geometrical shadow region.
- Interference Patterns: Grimaldi observed bright and dark bands near the edges of shadows, which indicated that light was not simply spreading out, but that it was also interacting in a complex way. These bands are now recognized as interference patterns, a phenomenon that would later be fully explained by wave theory. He noticed that the edges of shadows produced by diffracted light were not sharp but instead featured alternating bright and dark fringes, which suggested that light was somehow interfering with itself. These fringes were caused by the constructive and destructive interference of light waves—a concept that was not yet understood during Grimaldi’s time.
- Color Effects: Grimaldi also observed that light passing through small apertures or around obstacles could produce colored fringes near the edges of the illuminated regions, though his understanding of color was not fully developed. He noted that the diffraction fringes exhibited different colors under certain conditions, adding complexity to the phenomenon. He speculated that the colors could be linked to the interactions of light with the aperture or obstacle, although his explanation was incomplete by modern standards.
- Experiments with Apertures and Obstacles: Grimaldi performed a series of experiments using small holes, slits, and obstacles. In one such experiment, he allowed sunlight to pass through a very small hole in a screen and observed that the light formed an image of a circular or oval shape on the opposite wall. The resulting light pattern wasn’t a simple spot but rather exhibited a diffraction pattern, with light spreading out from the central beam. He also found that the size of the hole affected the degree of diffraction, with smaller holes producing more pronounced spreading. Similarly, he observed light bending around small objects (like needles or threads), where the light did not simply cast a shadow but instead produced fringes around the edges of the shadow.
- Wave-like Behavior: Though Grimaldi did not explicitly propose a wave theory of light, his observations strongly hinted at wave-like behavior. The bending of light around obstacles and the appearance of interference fringes were phenomena that could only be fully explained by a wave-based model, which came later with the work of Huygens and Fresnel.
- Interaction of Multiple Beams of Light: Grimaldi also experimented with multiple light sources and noticed that when two beams of light crossed each other, they did not “block” each other or collide as one might expect if light were composed of particles. This observation suggested that light was not behaving like solid particles and hinted at the possibility of light waves passing through one another without interaction. Grimaldi’s Legacy:
Grimaldi’s work on diffraction was ahead of its time. Although he did not propose a complete theoretical framework for his observations, his experiments were the first to systematically document diffraction, and they provided compelling evidence that light behaved in ways that couldn’t be fully explained by the prevailing corpuscular theory of light. His observations of light bending, producing fringes, and spreading into shadow regions would later be critical for the development of the wave theory of light.
Why Was Grimaldi’s Work Overlooked?
Despite the significance of Grimaldi’s experiments, his work did not gain immediate widespread recognition. There are several reasons for this:
Newton’s Dominance: Newton’s corpuscular theory of light, published a few decades later, became the dominant explanation for optical phenomena in the 18th century. Newton’s authority in the scientific world overshadowed alternative views, including Grimaldi’s diffraction experiments. Limited Dissemination: Grimaldi’s work was published posthumously and in Latin, which limited its immediate influence in the broader European scientific community. It took time for his results to be known and appreciated by other scientists. Incomplete Theoretical Framework: Grimaldi’s work lacked a comprehensive theoretical framework to explain diffraction. He observed and documented the phenomena, but the wave theory of light had not yet been fully developed, leaving his observations as empirical findings without a solid theoretical foundation. Conclusion:
Francesco Grimaldi’s book on optics documented some of the earliest and most accurate observations of diffraction, the spreading of light into shadow regions, and the appearance of interference fringes. These findings were crucial to the eventual development of the wave theory of light but were not fully appreciated in Grimaldi’s lifetime due to the dominance of Newton’s corpuscular theory and the incomplete theoretical understanding of light in his time. His work, however, laid the foundation for later breakthroughs by Huygens, Young, and Fresnel, who would use these phenomena to build the case for the wave nature of light.