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Double Refraction
Birefringence, also called double refraction, is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are described as birefringent or birefractive. The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress. Birefringence is responsible for the phenomenon of double refraction whereby a ray of light, when incident upon a birefringent material, is split by polarization into two rays taking slightly different paths. This effect was first described by Danish scientist Rasmus Bartholin in 1669, who observed it in Iceland spar (calcite) crystals which have one of the strongest birefringences. In the 19th century Augustin-Jean Fresnel described the phenomenon in terms of polarization, understanding l ...
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Crystal On Graph Paper
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their Geometry, geometrical shape, consisting of flat face (geometry), faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification. The word ''crystal'' derives from the Ancient Greek word (), meaning both "ice" and "Quartz#Varieties (according to color), rock crystal", from (), "icy cold, frost". Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Polycrystals inclu ...
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Calcite And Polarizing Filter
Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate (CaCO3). It is a very common mineral, particularly as a component of limestone. Calcite defines hardness 3 on the Mohs scale of mineral hardness, based on scratch hardness comparison. Large calcite crystals are used in optical equipment, and limestone composed mostly of calcite has numerous uses. Other polymorphs of calcium carbonate are the minerals aragonite and vaterite. Aragonite will change to calcite over timescales of days or less at temperatures exceeding 300 °C, and vaterite is even less stable. Etymology Calcite is derived from the German , a term from the 19th century that came from the Latin word for lime, (genitive ) with the suffix ''-ite'' used to name minerals. It is thus a doublet of the word ''chalk''. When applied by archaeologists and stone trade professionals, the term alabaster is used not just as in geology and mineralogy, where it is reserved for a variety of g ...
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Wollaston Prism
A Wollaston prism is an optical device, invented by William Hyde Wollaston, that manipulates polarized light. It separates light into two separate linearly polarized outgoing beams with orthogonal polarization. The two beams are polarized according to the optical axis of the two right angle prisms. The Wollaston prism consists of two orthogonal prisms of birefringent material—typically a uniaxial material such as calcite Calcite is a Carbonate minerals, carbonate mineral and the most stable Polymorphism (materials science), polymorph of calcium carbonate (CaCO3). It is a very common mineral, particularly as a component of limestone. Calcite defines hardness 3 on .... These prisms are cemented together on their base (traditionally with Canada balsam) to form two right triangle prisms with perpendicular optic axes. Outgoing light beams diverge from the prism as ordinary and extraordinary rays due to the differences in the indexes of refraction, with the angle of divergence ...
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Snell's Law
Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in meta-materials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index. The law states that, for a given pair of media, the ratio of the sines of angle of incidence \left(\theta_1 \right) and angle of refraction \left(\theta_2\right) is equal to the refractive index of the second medium with regard to the first (n_) which is equal to the ratio of the refractive indices \left(\tfrac\right) of the two media, or e ...
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Polarization (waves)
, or , is a property of transverse waves which specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. One example of a polarized transverse wave is vibrations traveling along a taut string, for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves ( shear waves) in solids. An electromagnetic wave such as light consists of a coupled oscillating el ...
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Spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface (mathematics), surface obtained by Surface of revolution, rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The ball (gridiron football), American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M's, M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation of the Earth, rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattening, flattened in the direction of its axis of rotation. For that reason, in cartography and geode ...
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Circular Polarization
In electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to the direction of the wave. In electrodynamics, the strength and direction of an electric field is defined by its electric field vector. In the case of a circularly polarized wave, the tip of the electric field vector, at a given point in space, relates to the phase of the light as it travels through time and space. At any instant of time, the electric field vector of the wave indicates a point on a helix oriented along the direction of propagation. A circularly polarized wave can rotate in one of two possible senses: ''right-handed circular polarization (RHCP)'' in which the electric field vector rotates in a right-hand sense with respect to the direction of propagation, and ''left-handed circular polarization (LHCP)'' in which the vecto ...
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Waveplate
A waveplate or retarder is an optics, optical device that alters the Polarization (waves), polarization state of a light wave travelling through it. Two common types of waveplates are the ''half-wave plate'', which rotates the polarization direction of linear polarization, linearly polarized light, and the ''quarter-wave plate'', which converts between different elliptical polarizations (such as the special case of converting from linearly polarized light to circular polarization, circularly polarized light and vice versa.) Waveplates are constructed out of a birefringence, birefringent material (such as quartz or mica, or even plastic), for which the index of refraction is different for light that is linearly polarized along one or the other of two certain perpendicular crystal axes. The behavior of a waveplate (that is, whether it is a half-wave plate, a quarter-wave plate, etc.) depends on the thickness of the crystal, the wavelength of light, and the variation of the index of ...
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Wave Vector
In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), and its direction is perpendicular to the wavefront. In isotropic media, this is also the direction of wave propagation. A closely related vector is the angular wave vector (or angular wavevector), with a typical unit being radian per metre. The wave vector and angular wave vector are related by a fixed constant of proportionality, 2 radians per cycle. It is common in several fields of physics to refer to the angular wave vector simply as the ''wave vector'', in contrast to, for example, crystallography. It is also common to use the symbol for whichever is in use. In the context of special relativity, a '' wave four-vector'' can be defined, combining the (angular) wave vector and (angular) frequency. Definition The terms ...
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Poynting Vector
In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or '' power flow'' of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m2); kg/s3 in SI base units. It is named after its discoverer John Henry Poynting who first derived it in 1884. Nikolay Umov is also credited with formulating the concept. Oliver Heaviside also discovered it independently in the more general form that recognises the freedom of adding the curl of an arbitrary vector field to the definition. The Poynting vector is used throughout electromagnetics in conjunction with Poynting's theorem, the continuity equation expressing conservation of electromagnetic energy, to calculate the power flow in electromagnetic fields. Definition In Poynting's original paper and in most textbooks, the Poynting vector \mathbf is defined as the cross product \mathbf = \mathbf \time ...
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Fresnel Equations
The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media. They were deduced by French engineer and physicist Augustin-Jean Fresnel () who was the first to understand that light is a transverse wave, when no one realized that the waves were electric and magnetic fields. For the first time, polarization could be understood quantitatively, as Fresnel's equations correctly predicted the differing behaviour of waves of the ''s'' and ''p'' polarizations incident upon a material interface. Overview When light strikes the interface between a medium with refractive index and a second medium with refractive index , both reflection and refraction of the light may occur. The Fresnel equations give the ratio of the ''reflected'' wave's electric field to the incident wave's electric field, and the ratio of the ''transmitted'' wave's electric f ...
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