History of ray optics and wave optics | Physical or wave optics and geometrical or ray optics| What was Euclid's, Newton's and huygens view on optics.

Introduction

Optics is divided into 2 more fields, 

1. Physical optics

2. Geometrical optics

 

Physical optics

Physical optics also called wave optics, is the branch of optics that studies phenomenas like  diffraction, 

Credit:- quantummechanics.ucsd.edu

polarization,

Credit:- Encyclopedia Britannica

interference 

interference pattern because of slits

because of which considering a beam of light as a particle is invalid here. This usage tends not to include effects such as quantum noise in optical communication, which is studied in the sub-branch of coherence theory.

Geometrical optics

Unlike physical optics where light is described by waves but, here in geometrical optics light is described by rays. Geometrical optics is not applicable for optical effects such as diffraction and interference, because diffraction and interference are some  phenomenon which cannot be explained by rays or geometrical optics. Although, there is a link between ray optics and wave optics. The theory connecting ray optics and wave optics is "Fermat's principle" also called the principle of least time or Fermat's principle of least time. It says, between any two points, light will take the quickest path not shortest. A path that can be traveled in the least time no matter if it's the longest. 

History 

In ancient India, the philosophical schools of Samkhya and Vaisheshika, from around the 6th–5th century BC, developed theories on light. The Vaisheshika school gives an atomic theory of the physical world on the non-atomic ground of ether, space and time. Then it came to Ibn al-Haytham, also the father of optics, who gave us law of refraction and invented the pinhole camera. His work is concerned with how curved mirrors and lenses bend and focus light. (To know more how they do so read this:- all about reflection and refraction)

The word optics is derived from the Greek term τα ὀπτικά meaning 'appearance, look'. 

Optics was significantly reformed by the developments in the medieval Islamic world, and passed on to advanced level in the early modern Europe.

Now let's jump forward in time around 300 BC. The ancient Greek mathematician, geometer and logician. Also known as the "father of geometry", he is chiefly known for his  Elements treatise, a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid. 

Euclid, credit:- Encyclopedia Britannica

He assumed some self-evident axioms.

1. That rectilinear rays proceeding from the eye diverge indefinitely.

2. That the figure contained by a set of visual rays is a cone of which the vertex is at the eye and the base at the surface of the objects seen.

3. That those things are seen upon which visual rays fall and those things are not seen upon which visual rays do not fall. This is also known as emission theory.

4. That things seen under a larger angle appear larger, those under a smaller angle appear smaller, and those under equal angles appear equal.

5. That things seen by higher visual rays appear higher, and things seen by lower visual rays appear lower.

6. That, similarly, things seen by rays further to the right appear further to the right, and things seen by rays further to the left appear further to the left.

7. That things seen under more angles are seen more clearly.

 Galileo Galilei, Credit:- Justus Sustermans • Public domain

It was  "Galileo Galilei" who invented the first telescope by adjusting the focal length and in such a way that it increased its magnification. By which later, he observe the moons of the Jupiter do not revolved around the earth but actually they revolved around Jupiter, which clearly disobeyed geocentric theory. Then came sir Isaac Newton who wrote in his book Opticks in which he wrote about the reflection, refraction and dispersion of light. He said that light is a beam of particles which letter put him on a debate with "Christiaan Huygens", the one who said that light is a wave. Unlike Newton's corpuscular theory. Huygens said that light is as an irregular series of shock waves which proceeds with very great, but finite velocity through the ether, similar to sound waves. Famous principle known today as the "Huygens–Fresnel principle" said, that each point of a wavefront is itself the origin of a secondary spherical wave. 

Further, Isaac Newton discovered the refraction of light, that a prism could spread white light into a spectrum of colours (VIBGYOR), and that a second prism could then merge the multicoloured spectrum into white light. He also showed that the coloured light does not change its properties by separating out a coloured beam and shining it on various objects. Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves. Which is also known as Newton's theory of color. By which later, he concluded that due to the phenomenon of dispersion, refracting telescope will not give a clear vision and invented a reflecting telescope. Newton said that light is made of particles or corpuscles and were refracted by accelerating toward the denser medium, but he had to associate them with waves to explain the diffraction of light.

Issac Newton and Christian Huygens

Diffractive optics 

The effects of diffraction were observed and characterized by Francesco Maria Grimaldi, the results of Grimaldi's observations were published after she died in 1665.

 2 years later after the death of Francesco Maria Grimaldi, came "Thomas Young" who proved that light is a wave by famous double slit experiment. Augustin-Jean Fresne gave great support to the wave theory of light by Christiaan Huygens by publishing his definitive studies and calculations of diffraction.

Max plank, Unknown authorUnknown author, credited to Transocean Berlin (see imprint in the lower right corner) • Public domain

Then it all passed on to the famous and greater scientist of all time "Max plank". In 1900, Max plank proposed that the energy observed or emitted by atoms or molecules is quantized. He hypothysized the radiant electromagnetic energy E = nhv , where n is = to 1,2,3.......

This hypothesis correctly explained the intensity versus wavelength graph for black body radiation. In short he said, the exchange of energy between light and matter only occurred in discrete amounts he called quanta.

Now came Einstein, introduced us to photoelectric effect. It appeared that the only possible explanation for the effect was the quantization of light itself. The understanding of the interaction between light and matter following from these developments not only formed the basis of quantum optics but also were crucial for the development of quantum mechanics.

This changed with the invention of the maser  and laser. Laser science, research into principles, design and application of these devices became an important field, and the quantum mechanics underlying the laser's principles was studied now with more emphasis on the properties of light, and the name quantum optics became customary. The work of Dirac in quantum field theory, George Sudarshan, Roy J. Glauber, and Leonard Mandel applied quantum theory to the electromagnetic field. This led to the discovery of the coherent state as a quantum description of laser light and hence, concluded that some states of light could not be described with classical waves. The applications to Solid state research such as "Raman spectroscopy" specially used to determine vibrational modes of molecules. Other remarkable results are the demonstration of quantum entanglement, quantum teleportation, and quantum logic gates. 

Huygens–Fresnel principle

It states that each point on a given wavefront is a source of secondary wavelets or secondary disturbances. Hence, sum of these spherical wavelets forms a new wavefront. In short, this principle is used for problems of wave propagation both in diffraction and reflection. He never explained why secondary waves travelled only in the forward direction . Fresnel concluded that, with his own principle of interference could explain both the rectilinear propagation of light and diffraction effects too. These assumptions have led to predictions that proved many experimental observations, including the agro also called Poisson spot or Fresnel spot. Over the years, scientists accepted wave theory of light over the corpuscular theory. 

After reading this you might think is this principle that good that everyone accepted it?  No, Melvin Schwartz argued that the Huygens' principle is an accurate microscopic representation of reality. He said, "Huygens principle actually does give the right answer but for the wrong reasons". This can be reflected in the following facts,

1. The microscopic mechanics to create photons and of emission, in general, is essentially acceleration of Electrons.

2. The original analysis of Huygens included amplitudes only it does not include neither phases, neither waves propagating at different speeds (due to diffraction within continuous media) and therefore does not take into account interference.

3. The Huygens analysis also does not include polarization for light which imply a vector potential, where instead sound waves can be described with a scalar potential and there is no unique and natural translation between the two.

4. In the Huygens description there is no explanation of why we choose only the forward going (i.e. Retarded wave) or forward envelope of wave fronts, versus the backward propagating Advance wave (i.e. backward envelope.)

5. In the Fresnel approximation there is a concept of non-local behavior due to the sum of spherical waves with different phases that comes from the different points of the wave front, and non-local theories are subject of many debates (e.g. not being Lorentz Covariant) and of active research.

6. The Fresnel approximation can be interpreted in a quantum probabilistic manner but is unclear how much this sum of states (i.e. wavelets on the wavefront) is a complete list of states that are meaningful physically or represents more of an approximation on a generic basis like in the LCAO method.

Later, Feynman defines the generalized form of hygens principle saying  "Actually Huygens’ principle is not correct in optics. It is replaced by Kirchoff’s modification which requires that both the amplitude and its derivative must be known on the adjacent surface. This is a consequence of the fact that the wave equation in optics is second order in the time. The wave equation of quantum mechanics is first order in the time; therefore, Huygens’ principle is correct for matter waves, action replacing time."