Refractive Index

By: 196 DAYS (Sonya Hu & Connor Squellati), Period 1BDate: May 01, 2015 May 11, 2015

Refractive IndexThe velocity of light is one of the most important of the fundamental constants of Nature. Its measurement by Foucault and Fizeau gave as the result a speed greater in air than in water, thus deciding in favor of the undulatory and against the corpuscular theory. Again, the comparison of the electrostatic and the electromagnetic units gives as an experimental result a value remarkably close to the velocity of light. Albert Abraham Michelson (Studies in Optics)(Snell Descartes Law)

TABLE OF CONTENTS Abstract (Sonya)..2 Introduction (Sonya)................3 History (Sonya)7 Context (Connor).9 Proof (Connor)...11 Conclusion (Sonya)....13 Bibliography (Sonya).14 Appendix I.16

ABSTRACT

The refractive index of a material is a numerical value that is expressed relatively to the speed of light within a vacuum. When light travels from a vacuum to a different transparent medium, such as water or glass, or, when light travels from medium to medium, the speed of light is adjusted in relation to the refractive index, or optical density, of the material. This report will analyze the reasons that refractive index occurs, the historical background in its discovery, the social context, or importance, of refractive index, and then will provide a generalized proof of the refractive index. It will analyze Snells Law in depth.

INTRODUCTIONIn 1676, Danish astronomer Olaus Roemer discovered that the speed of light, commonly denoted as c, is a universal physical constant that has a value of approximately 3.00108 meters per second. It was also established that the speed of a wave is equal to the wavelength times the frequency, which can be expressed by the following equation:

However, the speed that Roemer established was only true when light traveled within a vacuum. When light that was traveling in a vacuum enters a different transparent medium, the speed of the light is reduced in proportion to the refractive index of this new medium. Refraction is the bending of the path of a light wave as it passes through one material to another.[footnoteRef:1] It occurs at the boundary and is caused by a change in the speed of the light wave upon crossing the boundary. The tendency of a ray of light to bend one direction or another is dependent upon whether the light wave speeds up or slows down upon crossing.[footnoteRef:2] The refractive index of a material is a numerical value that is expressed relatively to the speed of light within a vacuum. In a vacuum, the refractive index (represented by the symbol n) is equal to 1.0000. In other materials, the refractive index can be expressed by the following equation: [1: The Physics Classroom. The Physics Classroom [Internet]. n.c.: The Physics Classroom; c1996-2015. Optical Density and Light Speed; n.d. [cited 2015 May 04]; [about 4 pages]. Available from: http://www.physicsclassroom.com/class/refrn/Lesson-1/Optical-Density-and-Light-Speed] [2: ibid]

It can be better explained by Figure 1, which was also shown on the cover page:

Figure 1Figure 1 depicts the refractive index via what is commonly known as Snells Law. Although it labels the areas above and under the center axis air and water, it does not have to be those two mediums; it can be any. It may be better and easier to understand to label the upper part vacuum and the lower medium. i represents the angle of incidence of a ray in a cacuum, and r represents the angle of refraction. This allows the refractive index n to be defined by the following equation:

Similar to any other wave, the speed of a light wave is dependent on the properties of the medium through which it travels. However, in the case of a light wave, or electromagnetic wave, as it is otherwise known, is dependent upon the optical density of that material. However, the optical density is, by all means, not the same as the physical density of a material. The physical density refers to the mass to volume ration, whereas the optical density refers to the sluggish tendency of the atoms of a material to maintain the absorbed energy of an electromagnetic wave in the form of vibrating electrons before reemitting it as a new electromagnetic disturbance.[footnoteRef:3] The more optically dense a medium is, the slower that a wave will travel through that material. The index of refraction, or refractive index, of a material is one indicator of the optical density that a material has. [3: The Physics Classroom. The Physics Classroom [Internet]. n.c.: The Physics Classroom; c1996-2015. Optical Density and Light Speed; n.d. [cited 2015 May 04]; [about 4 pages]. Available from: http://www.physicsclassroom.com/class/refrn/Lesson-1/Optical-Density-and-Light-Speed]

In order to better understand this concept, let us further analyze the mechanism by which a light wave is transported through a medium. This occurs by particle-to-particle interaction, quite similar to the method at which any other wave is transported. A light wave is produced by a vibrating electric charge, and, as previously stated, it travels at the speed of c in a vacuum. The Physics Classroom provides an explanation of the transportation of a light wave: When a wave impinges upon a particle of matter, the energy is absorbed and sets electrons within the atoms into vibrational motion. If the frequency of the electromagnetic wave does not match the resonant frequency of vibration of the electron, then the energy is reemitted in the form of an electromagnetic wave. This new electromagnetic wave has the same frequency of the electromagnetic wave has the same frequency as the original wave and it too will travel at a speed of c through the empty space between atoms. The newly emitted light wave continues to move through the interatomic space until it impinges upon a neighboring particle. The energy is absorbed by this new particle and sets the electrons of its atoms into vibration motion. And once more, if there is no match between the frequency of the electromagnetic wave and the resonant frequency of the electron, the energy is reemitted in the form of a new electromagnetic wave. The cycle of absorption and reemission continues as the energy is transported from particle to particle through the bulk of a medium. Every photon (bundle of electromagnetic energy) travels between the interatomic void at a speed of c; yet time delay involved in the process of being absorbed and reemitted by the atoms of the material lowers the net speed of transport from one end of the medium to the other. Subsequently, the net speed of an electromagnetic wave in any medium is somewhat less than its speed in a vacuum.[footnoteRef:4] [4: The Physics Classroom. The Physics Classroom [Internet]. n.c.: The Physics Classroom; c1996-2015. Optical Density and Light Speed; n.d. [cited 2015 May 04]; [about 4 pages]. Available from: http://www.physicsclassroom.com/class/refrn/Lesson-1/Optical-Density-and-Light-Speed]

The table below lists the refractive index values for a number of mediums:MaterialIndex of Refraction

Vacuum1

Air1.0003

Ice1.31

Water1.333

Ethyl Alcohol1.36

Plexiglas1.51

Crown Glass1.52

Light Flint Glass1.58

Dense Flint Glass1.66

Zircon1.923

Diamond2.417

Rutile2.907

Gallium phosphide3.50

HISTORYControversies concerning the refraction of light have been dotted throughout history. In 350 B.C., Greek scientist Euclid established that light travels in a straight line at a constant speed, which was later discovered to be approximately 3.00108 meters per second. Centuries later, Descartes, using analogies of moving balls, the walking stick of a blind man, and wine grapes being stomped on in a vat, formed the laws of reflection and refraction. He reasoned that the sines of the angles of incidents and refraction are proportional to the different ease of lights passage through the two media. This was written in his famous Discourse on Method and submitted for publication in 1637. However, Descartes was not the first to discover this law. Thomas Harriot discovered the concept of refraction in 1602, based on his observations in 1597 and 1598, but regrettably passed away before he could publish the concept. In 1621, Snel of the Netherlands rediscovered the law, but could not publish it before he was stuck with death in 1626. This was described by The Physics Hypertextbook, which states that although he discovered the law of refraction, a basis of modern geometric optics, in 1621, he did not publish it and only in 1703 did it become known when Huygens published Snell's law in Dioptrica. Snell also studied navigation and proposed the method of triangulation, which is the foundation of geodesy (the branch of mathematics dealing with the measurement of features on the earth). For some reason, the law named after the man is spelled incorrectly. Snel the man vs. Snell the law. This form of Snell's law was actually published by Ren Descartes (15961650) France in La Dioptrique (1637). Snell did discover the relationship but articulated it in a different way. Today it is the form used by Descartes that is called Snell's law.[footnoteRef:5] Therefore, the first to successfully publish the law was Descartes in 1637, which is why the law is known as Descartess Law in France. However, due to the widespread understanding that Snel was a precursor in the discovery of the law, in many other countries, the law is attributed to him. This law, Snels Law, is depicted in Figure 1 in the Introduction, as well as on the cover page, and is also known as the Descartes-Snel Law. [5: Glenn Elert, author. The Physics Hypertextbook [Internet]. n.c.: The Physics Hypertextbook. c1998-2015 [cited 2015 May 11]. Refraction; [about 9 pages]. Available from: http://physics.info/refraction/ ]

After Descartes findings were published, Pierre de Fermat took it upon himself to rebuke Descartes findings, only to discover in 1664 that Descartes was correct. However, he believed that Descartess method of showing and providing proof of this law was flawed. In his final correspondence found in the Works in 1664, he wrote, the opinion of M. Descartes on the proportion of refractions is quite true his demonstration is quite false, and full of paralogisms![footnoteRef:6] [6: Larouchepac. Larouchepac [Internet]. Leesburg (VA): Lyndon LaRouche Political Action Committee; c2015. Fermats Work on Refraction: A History; n.d. [cited 2015 May 11]; [about 3 pages]. Available from:http://science.larouchepac.com/fermat/history.html]

CONTEXT

The concept of the refractive index as a whole has substantially encouraged and improved not only technology but also modern day industry. One tool created on the basis of the refractive index is the refractometer, a relatively inexpensive piece of test equipment used to determine the sugar content in a liquid. The refractometer developed a kind of revolution in the push for industrial advances. It aids in pharmaceutical drug diagnosis, veterinarian medicine, aquatic upkeep/improvement, gemology, farming/agriculture, and even beverage enhancement. When using the refractometer, one can tell different materials from each other (i.e., rock from soil) by the contrast in soluble liquids/loose solids. For example, in the scientific field of geology, the use of a refractometer helps identify specific metals in the ground and can even assist in the location of rare geodes or gems. But of all impacts, the refractometer mostly benefits farming and agriculture. It is an all-in-one tool that can be used to test the health of crops via plant sap or fruit/vegetable juices. Because the refractometer reacts differently to light depending on the amount of sugar present within the sap/juice, a measuring system known as BRIX helps measure the health and care of crops. The higher the level on the BRIX rating the better the crop condition is, while the lower the level indicates poor crop health. Some of the reasons for receiving a low BRIX rating can be the dilution of nutrients, an imbalance in the soil and/or mineral load, or a low calcium content. But with all advancements the discovery of the refractive index has brought, there is a minor controversy in the use of such physical detection. Although it is indirectly argued upon, the refractive index plays an important role in the Abraham-Minkowski Controversy. A physicist in 1908, Hermann Minkowski, was one of the first to finalize an idea describing the momentum transfer between matter and electromagnetic fields. However, one year later (1909), Max Abraham had achieved the same concept using the same tools/theories as Minkowski, but resulted in a completely different conclusion. The main difference between the twos results was that Minkowski believed that waves that travel through mediums at a slow rate have a lower momentum, later thought to be canonical momentum [Equation 1]. Abraham on the other hand believed that waves traveling through a medium at a slow rate has a higher momentum, later thought to be kinetic momentum [Equation 2]. The two ideas conflicted with each other even in modern day times. In either situation, if one theory were to be proven correct over another, it would ensure the development of a reactionless drive, a device that generates motion without propellant.

PROOFIn order to prove that the speed of light travels at different speeds in different mediums, thus proving that the refractive index is valid, Snells Law would need to be analyzed and simplified to a single equation, the refractive index equation. First, directly from Snells Law, the concept of refracted light (through two separate mediums in respect to dielectric indices),would need a four quadrant grid to best express refraction. Quadrant I would be Medium 1, Quadrant II would be Incident Ray (Overall Value of N1), Quadrant III would be Medium 2, and Quadrant IV would be Refracted Ray (Overall Value of N2). Two parallel lines should be drawn, the leftmost at approximately y = -x. When the leftmost line reaches the origin (0,0), it continues through Quadrant IV at an angle between the x-axis and y-axis (2) smaller than the angle in Quadrant II between the x-axis and y-axis (aprrox. 45, 1). The rightmost line would continue until the x-axis where it passes through Quadrant IV parallel to the leftmost line in Quadrant IV. Based on what is already drawn, two right triangle can be made, sharing one side with each other along the positive x-axis (PQB, PAB) [Refer to Figure 1]. Because segment PQ must happen in the real-world at the same time as segment AB, the equation N1 sin1 = N2 sin2 (foundation of Snells Law). This can be further simplified into N1N2 = sin2 sin1. The sin1 and sin2 can further be expressed by the speed of incident (v2) and speed of recracted (v1), leaving the equation N1N2 = v2 v1. The relationship between the refractive index 1 over the refractive index 2 (N1/N2) is equivalent to one-half of the two indices, represented as Nt (the combined/total value of the refractive indices of v2/v1). The equation now stands as Nt = v2 v1. Because we are proving that the speed of light travels differently per medium via refractive index and v2 is the speed of incident, the experimentational equivalent of the speed of incident is the speed of light (v2 = c). The final equation stands as Nt = c v1, proving the refractive index equation, thus proving validity and success. Refer to Appendix I for a formal, mathematical proof of Snells Law.

CONCLUSIONTo conclude, despite the various controversies surrounding the refractive index throughout history, the concept was cemented by Descartes, and established through Snells Law. Although the concept is seemingly pointless to know, and appears to just be another addition to the endless of archive of information, despite not having any modern-day impact, that is, in fact, not the case. The index of refraction has encouraged and improved modern-day technology and industry; an example of which is the refractometer.

BIBLIOGRAPHYGlenn Elert, author. The Physics Hypertextbook [Internet]. n.c.: The Physics Hypertextbook. c1998-2015 [cited 2015 May 11]. Refraction; [about 9 pages]. Available from: http://physics.info/refraction/

Michael W. Davidson. Optical Microscopy Primer [Internet]. Molecular Expressions; c2014. Speed of Light in Transparent Materials; 2014 [cited 2015 May 4]; [about 3 pages]. Available from: http://micro.magnet.fsu.edu/primer/java/speedoflight/

Kevin Brown. Reflections on Relativity. Lulu [Internet]. Lulu; c2015. 3.3 De Mora Luminis; 2015 [cited 2015 May 4]; [about 9 pages]. Available from: http://mathpages.com/rr/s3-03/3-03.htm

Larouchepac. Larouchepac [Internet]. Leesburg (VA): Lyndon LaRouche Political Action Committee; c2015. Fermats Work on Refraction: A History; n.d. [cited 2015 May 11]; [about 3 pages]. Available from: http://science.larouchepac.com/fermat/history.html

Physics 2000. Physics 2000 [Internet]. Colorado.edu; c2015. Speed of Light; n.d. [cited 2015 May 04]; [about 4 pages]. Available from: http://www.colorado.edu/physics/2000/waves_particles/lightspeed-1.html

The Physics Classroom. The Physics Classroom [Internet]. n.c.: The Physics Classroom; c1996-2015. Optical Density and Light Speed; n.d. [cited 2015 May 04]; [about 4 pages]. Available from: http://www.physicsclassroom.com/class/refrn/Lesson-1/Optical-Density-and-Light-Speed

The Editors of Encyclopaedia Britannica. Encyclopaedia Britannica [Internet]. Encyclopaedia Britannica; c2015. Refractive Index; 2014 [cited 2015 May 4]; [about 1 page]. Available from: http://www.britannica.com/EBchecked/topic/495677/refractive-index

APPENDIX I16 | Page