Light

Refraction

Refraction is the bending of light rays when passing through a surface between one transparent material and another. It is described by Snell's Law:

${\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}\ .}$

where θ₁ is the angle between the ray and the surface normal in the first medium, θ₂ is the angle between the ray and the surface normal in the second medium and n₁ and n₂ are the indices of refraction, n = 1 in a vacuum and n > 1 in a transparent substance.

When a beam of light crosses the boundary between a vacuum and another medium, or between two different media, the wavelength of the light changes, but the frequency remains constant. If the beam of light is not orthogonal (or rather normal) to the boundary, the change in wavelength results in a change in the direction of the beam. This change of direction is known as refraction.

The refractive quality of lenses is frequently used to manipulate light in order to change the apparent size of images. Magnifying glasses, spectacles, contact lenses, microscopes and refracting telescopes are all examples of this manipulation.

Classical Greece and Hellenism

In the fifth century BC, Empedocles postulated that everything was composed of four elements; fire, air, earth and water. He believed that goddess Aphrodite made the human eye out of the four elements and that she lit the fire in the eye which shone out from the eye making sight possible. If this were true, then one could see during the night just as well as during the day, so Empedocles postulated an interaction between rays from the eyes and rays from a source such as the sun.^[31]

In about 300 BC, Euclid wrote Optica, in which he studied the properties of light. Euclid postulated that light travelled in straight lines and he described the laws of reflection and studied them mathematically. He questioned that sight is the result of a beam from the eye, for he asks how one sees the stars immediately, if one closes one's eyes, then opens them at night. If the beam from the eye travels infinitely fast this is not a problem.^[32]

In 55 BC, Lucretius, a Roman who carried on the ideas of earlier Greek atomists, wrote that "The light & heat of the sun; these are composed of minute atoms which, when they are shoved off, lose no time in shooting right across the interspace of air in the direction imparted by the shove." (from On the nature of the Universe). Despite being similar to later particle theories, Lucretius's views were not generally accepted. Ptolemy (c. second century) wrote about the refraction of light in his book Optics.^[33]

Classical India

In ancient India, the Hindu schools of Samkhya and Vaisheshika, from around the early centuries AD developed theories on light. According to the Samkhya school, light is one of the five fundamental "subtle" elements (tanmatra) out of which emerge the gross elements. The atomicity of these elements is not specifically mentioned and it appears that they were actually taken to be continuous.^[34] The Vishnu Purana refers to sunlight as "the seven rays of the sun".^[34]

The Indian Buddhists, such as Dignāga in the fifth century and Dharmakirti in the seventh century, developed a type of atomism that is a philosophy about reality being composed of atomic entities that are momentary flashes of light or energy. They viewed light as being an atomic entity equivalent to energy.^[34]

Descartes

René Descartes (1596–1650) held that light was a mechanical property of the luminous body, rejecting the "forms" of Ibn al-Haytham and Witelo as well as the "species" of Roger Bacon, Robert Grosseteste and Johannes Kepler.^[35] In 1637 he published a theory of the refraction of light that assumed, incorrectly, that light travelled faster in a denser medium than in a less dense medium. Descartes arrived at this conclusion by analogy with the behaviour of sound waves.^{[citation needed]} Although Descartes was incorrect about the relative speeds, he was correct in assuming that light behaved like a wave and in concluding that refraction could be explained by the speed of light in different media.

Descartes is not the first to use the mechanical analogies but because he clearly asserts that light is only a mechanical property of the luminous body and the transmitting medium, Descartes's theory of light is regarded as the start of modern physical optics.^[35]

Particle theory

Pierre Gassendi (1592–1655), an atomist, proposed a particle theory of light which was published posthumously in the 1660s. Isaac Newton studied Gassendi's work at an early age and preferred his view to Descartes's theory of the plenum. He stated in his Hypothesis of Light of 1675 that light was composed of corpuscles (particles of matter) which were emitted in all directions from a source. One of Newton's arguments against the wave nature of light was that waves were known to bend around obstacles, while light travelled only in straight lines. He did, however, explain the phenomenon of the diffraction of light (which had been observed by Francesco Grimaldi) by allowing that a light particle could create a localised wave in the aether.

Newton's theory could be used to predict the reflection of light, but could only explain refraction by incorrectly assuming that light accelerated upon entering a denser medium because the gravitational pull was greater. Newton published the final version of his theory in his Opticks of 1704. His reputation helped the particle theory of light to hold sway during the eighteenth century. The particle theory of light led Pierre-Simon Laplace to argue that a body could be so massive that light could not escape from it. In other words, it would become what is now called a black hole. Laplace withdrew his suggestion later, after a wave theory of light became firmly established as the model for light (as has been explained, neither a particle or wave theory is fully correct). A translation of Newton's essay on light appears in The large scale structure of space-time, by Stephen Hawking and George F. R. Ellis.

The fact that light could be polarized was for the first time qualitatively explained by Newton using the particle theory. Étienne-Louis Malus in 1810 created a mathematical particle theory of polarization. Jean-Baptiste Biot in 1812 showed that this theory explained all known phenomena of light polarization. At that time the polarization was considered as the proof of the particle theory.

Wave theory

To explain the origin of colours, Robert Hooke (1635–1703) developed a "pulse theory" and compared the spreading of light to that of waves in water in his 1665 work Micrographia ("Observation IX"). In 1672 Hooke suggested that light's vibrations could be perpendicular to the direction of propagation. Christiaan Huygens (1629–1695) worked out a mathematical wave theory of light in 1678 and published it in his Treatise on Light in 1690. He proposed that light was emitted in all directions as a series of waves in a medium called the luminiferous aether. As waves are not affected by gravity, it was assumed that they slowed down upon entering a denser medium.^[36]

The wave theory predicted that light waves could interfere with each other like sound waves (as noted around 1800 by Thomas Young). Young showed by means of a diffraction experiment that light behaved as waves. He also proposed that different colours were caused by different wavelengths of light and explained colour vision in terms of three-coloured receptors in the eye. Another supporter of the wave theory was Leonhard Euler. He argued in Nova theoria lucis et colorum (1746) that diffraction could more easily be explained by a wave theory. In 1816 André-Marie Ampère gave Augustin-Jean Fresnel an idea that the polarization of light can be explained by the wave theory if light were a transverse wave.^[37]

Later, Fresnel independently worked out his own wave theory of light and presented it to the Académie des Sciences in 1817. Siméon Denis Poisson added to Fresnel's mathematical work to produce a convincing argument in favor of the wave theory, helping to overturn Newton's corpuscular theory.^{[dubious – discuss]} By the year 1821, Fresnel was able to show via mathematical methods that polarization could be explained by the wave theory of light if and only if light was entirely transverse, with no longitudinal vibration whatsoever.^{[citation needed]}

The weakness of the wave theory was that light waves, like sound waves, would need a medium for transmission. The existence of the hypothetical substance luminiferous aether proposed by Huygens in 1678 was cast into strong doubt in the late nineteenth century by the Michelson–Morley experiment.

Newton's corpuscular theory implied that light would travel faster in a denser medium, while the wave theory of Huygens and others implied the opposite. At that time, the speed of light could not be measured accurately enough to decide which theory was correct. The first to make a sufficiently accurate measurement was Léon Foucault, in 1850.^[38] His result supported the wave theory, and the classical particle theory was finally abandoned (only to partly re-emerge in the twentieth century as photons in quantum theory).

Electromagnetic theory

In 1845, Michael Faraday discovered that the plane of polarization of linearly polarized light is rotated when the light rays travel along the magnetic field direction in the presence of a transparent dielectric, an effect now known as Faraday rotation.^[39] This was the first evidence that light was related to electromagnetism. In 1846 he speculated that light might be some form of disturbance propagating along magnetic field lines.^[39] Faraday proposed in 1847 that light was a high-frequency electromagnetic vibration, which could propagate even in the absence of a medium such as the ether.^[40]

Faraday's work inspired James Clerk Maxwell to study electromagnetic radiation and light. Maxwell discovered that self-propagating electromagnetic waves would travel through space at a constant speed, which happened to be equal to the previously measured speed of light. From this, Maxwell concluded that light was a form of electromagnetic radiation: he first stated this result in 1862 in On Physical Lines of Force. In 1873, he published A Treatise on Electricity and Magnetism, which contained a full mathematical description of the behavior of electric and magnetic fields, still known as Maxwell's equations. Soon after, Heinrich Hertz confirmed Maxwell's theory experimentally by generating and detecting radio waves in the laboratory and demonstrating that these waves behaved exactly like visible light, exhibiting properties such as reflection, refraction, diffraction and interference. Maxwell's theory and Hertz's experiments led directly to the development of modern radio, radar, television, electromagnetic imaging and wireless communications.

In the quantum theory, photons are seen as wave packets of the waves described in the classical theory of Maxwell. The quantum theory was needed to explain effects even with visual light that Maxwell's classical theory could not (such as spectral lines).

Quantum theory

In 1900 Max Planck, attempting to explain black-body radiation, suggested that although light was a wave, these waves could gain or lose energy only in finite amounts related to their frequency. Planck called these "lumps" of light energy "quanta" (from a Latin word for "how much"). In 1905, Albert Einstein used the idea of light quanta to explain the photoelectric effect and suggested that these light quanta had a "real" existence. In 1923 Arthur Holly Compton showed that the wavelength shift seen when low intensity X-rays scattered from electrons (so called Compton scattering) could be explained by a particle-theory of X-rays, but not a wave theory. In 1926 Gilbert N. Lewis named these light quanta particles photons.^[41]

Eventually quantum mechanics came to picture light as (in some sense) both a particle and a wave, and (in another sense) as a phenomenon which is neither a particle nor a wave (which actually are macroscopic phenomena, such as baseballs or ocean waves). Instead, under some approximations light can be described sometimes with mathematics appropriate to one type of macroscopic metaphor (particles) and sometimes another macroscopic metaphor (waves).

As in the case for radio waves and the X-rays involved in Compton scattering, physicists have noted that electromagnetic radiation tends to behave more like a classical wave at lower frequencies, but more like a classical particle at higher frequencies, but never completely loses all qualities of one or the other. Visible light, which occupies a middle ground in frequency, can easily be shown in experiments to be describable using either a wave or particle model, or sometimes both.

In 1924–1925, Satyendra Nath Bose showed that light followed different statistics from that of classical particles. With Einstein, they generalized this result for a whole set of integer spin particles called bosons (after Bose) that follow Bose–Einstein statistics. The photon is a massless boson of spin 1.

In 1927, Paul Dirac quantized the electromagnetic field. Pascual Jordan and Vladimir Fock generalized this process to treat many-body systems as excitations of quantum fields, a process with the misnomer of second quantization. And at the end of the 1940s a full theory of quantum electrodynamics was developed using quantum fields based on the works of Julian Schwinger, Richard Feynman, Freeman Dyson, and Shinichiro Tomonaga.

Quantum optics

John R. Klauder, George Sudarshan, Roy J. Glauber, and Leonard Mandel applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics of light (see degree of coherence). This led to the introduction of the coherent state as a concept which addressed variations between laser light, thermal light, exotic squeezed states, etc. as it became understood that light cannot be fully described just referring to the electromagnetic fields describing the waves in the classical picture. In 1977, H. Jeff Kimble et al. demonstrated a single atom emitting one photon at a time, further compelling evidence that light consists of photons. Previously unknown quantum states of light with characteristics unlike classical states, such as squeezed light were subsequently discovered.

Development of short and ultrashort laser pulses—created by Q switching and modelocking techniques—opened the way to the study of what became known as ultrafast processes. Applications for solid state research (e.g. Raman spectroscopy) were found, and mechanical forces of light on matter were studied. The latter led to levitating and positioning clouds of atoms or even small biological samples in an optical trap or optical tweezers by laser beam. This, along with Doppler cooling and Sisyphus cooling, was the crucial technology needed to achieve the celebrated Bose–Einstein condensation.

Other remarkable results are the demonstration of quantum entanglement, quantum teleportation, and quantum logic gates. The latter are of much interest in quantum information theory, a subject which partly emerged from quantum optics, partly from theoretical computer science.