Snell's law

Snell's law 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, in experimental optics to find the refractive index of a material; the law is satisfied in metamaterials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index. Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media, or equivalent to the reciprocal of the ratio of the indices of refraction: sin ⁡ θ 2 sin ⁡ θ 1 = v 2 v 1 = n 1 n 2 with each θ as the angle measured from the normal of the boundary, v as the velocity of light in the respective medium, n as the refractive index of the respective medium; the law follows from Fermat's principle of least time, which in turn follows from the propagation of light as waves.

Ptolemy, in Alexandria, had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law as a result of fudging his data to fit theory. Alhazen, in his Book of Optics, came closer to discovering the law of refraction, though he did not take this step; the law named after Snell was first described by the Persian scientist Ibn Sahl at the Baghdad court in 984. In the manuscript On Burning Mirrors and Lenses, Sahl used the law to derive lens shapes that focus light with no geometric aberrations; the law was rediscovered by Thomas Harriot in 1602, who however did not publish his results although he had corresponded with Kepler on this subject. In 1621, the Dutch astronomer Willebrord Snellius —Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. René Descartes independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay Dioptrics, used it to solve a range of optical problems.

Rejecting Descartes' solution, Pierre de Fermat arrived at the same solution based on his principle of least time. Descartes assumed the speed of light was infinite, yet in his derivation of Snell's law he assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e. the speed of light is finite, his derivation depended upon the speed of light being slower in a denser medium. Fermat's derivation utilized his invention of adequality, a mathematical procedure equivalent to differential calculus, for finding maxima and tangents. In his influential mathematics book Geometry, Descartes solves a problem, worked on by Apollonius of Perga and Pappus of Alexandria. Given n lines L and a point P on each line, find the locus of points Q such that the lengths of the line segments QP satisfy certain conditions. For example, when n = 4, given the lines a, b, c, d and a point A on a, B on b, so on, find the locus of points Q such that the product QA*QB equals the product QC*QD.

When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose in optics from Snell's law. According to Dijksterhuis, "In De natura lucis et proprietate Isaac Vossius said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation. In French, Snell's Law is called "la loi de Descartes" or "loi de Snell-Descartes." In his 1678 Traité de la Lumière, Christiaan Huygens showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the Huygens–Fresnel principle. With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, Bloembergen showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.

In 2008 and 2011, plasmonic metasurfaces were demonstrated to change the reflection and refraction directions of light beam. Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction; the indices of refraction of the media, labeled n 1, n 2 and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum. As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one; these angles are measured with respect to the normal line, represented perpendicular to the boundary


WJZ-TV, virtual and VHF digital channel 13, is a CBS owned-and-operated television station licensed to Baltimore, United States. The station is owned by the CBS Television Stations subsidiary of ViacomCBS. WJZ-TV's studios and offices are located on Television Hill in the Woodberry section of Baltimore, adjacent to the transmission tower it shares with several other Baltimore broadcast outlets. On cable, the station is available on Comcast Xfinity channel 23. On Verizon FiOS, DirecTV and Dish Network and in most outlying areas of the market, it is carried on channel 13. Baltimore's third television station started on November 1, 1948 as WAAM; the station was owned by Radio-Television of Baltimore Inc. whose principals were Baltimore businessmen and brothers and Herman Cohen. Channel 13 was an ABC affiliate, the network's fifth outlet to be located on the East Coast; until 1956, it carried an additional primary affiliation with the DuMont Television Network. On the station's second day of operations, WAAM broadcast the 1948 presidential election returns and various entertainment shows, remaining on the air for 23 consecutive hours.

Channel 13 has been housed in the same studio facility, located near Druid Hill Park on what was known as Malden Hill, since the station's inception. As a DuMont affiliate, WAAM originated many Baltimore Colts games for the network's National Football League coverage; the Westinghouse Electric Corporation purchased WAAM from the Cohen brothers in May 1957. Westinghouse took control of the station in August of that year, changed its callsign to WJZ-TV the following month; the WJZ call letters had resided on ABC's flagship radio/television combination in New York City, which changed its calls to WABC-AM-FM-TV in 1953. However, Westinghouse's history with that set of call letters went back further, as it was the original owner of WJZ radio, the flagship station of NBC's Blue Network, which would become ABC. All of Baltimore's television stations at the time had short transmission towers in the medium's early years. In 1959, the three stations—WJZ-TV, WBAL-TV and WMAR-TV —formed a joint venture to build the world's first three-pronged candelabra tower.

Constructed behind the WJZ-TV studios and opposite the original channel 13 tower, it was the tallest free standing television antenna in the United States at the time of its completion. The new tower improved channel 13's signal coverage in central Maryland, added new viewers in Pennsylvania, Washington, D. C. and Virginia. WJZ-TV nearly lost its ABC affiliation in 1977, when the network pursued WBAL-TV just as ABC became the most-watched broadcast network in the United States for the first time. However, WBAL-TV declined the ABC affiliation offer due to ABC's last-place network evening newscast offerings of the time, keeping ABC on channel 13. In June 1994, ABC agreed to an affiliation deal with the broadcasting division of the E. W. Scripps Company, which resulted in three of Scripps' television stations—WMAR-TV in Baltimore, WFTS-TV in Tampa and KNXV-TV in Phoenix—becoming ABC affiliates. ABC agreed to the deal as a condition of keeping its affiliation on Scripps' two biggest stations, WXYZ-TV in Detroit and WEWS in Cleveland.

Both stations had been courted by CBS, about to lose two of its longtime affiliates—WJBK and WJW—to Fox. One of the stations, tapped to switch was Baltimore's then-NBC affiliate, WMAR-TV. ABC was reluctant to include WMAR in the deal. However, not wanting to be relegated to UHF in two markets with few viable choices for a new affiliate, ABC opted to end its 46-year affiliation with channel 13 and move its affiliation to channel 2. Group W felt betrayed by ABC after so many years of loyalty, as channel 13 had been ABC's longest-tenured affiliate at the time; as a safeguard, it began to shop for an affiliation deal of its own. One month Westinghouse agreed to a long-term affiliation contract with CBS, resulting in WJZ-TV and its sister stations in Philadelphia and Boston switching to CBS; the affiliation switch, the second in Baltimore television history, occurred early on the morning of January 2, 1995. The last ABC prime time program to air on channel 13 was the made-for-TV movie A Dangerous Affair, broadcast at 9:00 p.m. Eastern Time on January 1, the final overall ABC program to air on channel 13 was the January 2 edition of ABC World News Now.

As a result, channel 13 became the third station in Baltimore to affiliate with CBS. The network had affiliated with WMAR-TV in 1948 before moving to WBAL-TV in 1981. Westinghouse bought CBS on November 24, 1995, making WJZ-TV a CBS owned-and-operated station. Notably, this marked the first time that CBS had wholly owned a station in the Baltimore/Washington corridor. WJZ-TV has used its current stylized "13" logo, using a font face exclusive to Group W, since 1967. In 2002, the CBS eye was added, in 2018, the station switched to a silver and gold-colored version with the WJZ call letters displayed below in squares; the station's digital signal is multiplexed: WJZ-TV shut d

GM Ecotec engine

The GM Ecotec engine known by its codename L850, is a family of all-aluminium inline-four engines, displacing between 1.4 and 2.5 litres. While these engines were based on the GM Family II engine, the architecture was re-engineered for the new Ecotec application produced since 2000; this engine family replaced the GM Family II engine, the GM 122 engine, the Saab H engine, the Quad 4 engine. It is manufactured in multiple locations, to include Spring Hill Manufacturing, in Spring Hill, Tennessee. The'Ecotec' name was adopted in 1994 for the new generation of Family II engines; the name was used for the Opel GM Family II engine, Family 1 and Family 0 ranges. GM intends this new Ecotec to become its global 4-cylinder, it has fully replaced their OHV I4 line; the Ecotec engine is a DOHC 4-valve design with a lost foam cast aluminum block and head, designed for displacements from 1.8 to 2.4 L. Development began in 1994, by an international team of engineers and technicians from Opel's International Technical Development Center in Rüsselsheim, Germany, GM Powertrain in Pontiac and Saab in Södertälje, Sweden.

Much of the development work on this project was carried out by Lotus Engineering, United Kingdom. The engine cast iron cylinder liners. Vibration is reduced with twin balance shafts; the first engine in the Ecotec Gen I line-up was Ecotec 2.2 L61, introduced in 2000. The current Ecotec line is manufactured in New York; this engine is known as B207 when used by Saab and Z20NET by Opel for use in the Vectra C and Signum. LK9 is a turbocharged 2.0 L— 1,998 cc —version of the L850 series Ecotec utilizing an all-new reinforced sand cast aluminum cylinder head and upgraded internal components. The engine features a five-bearing forged steel crankshaft, strengthened connecting rods, redesigned pistons, piston oil cooling jets, reprofiled camshafts and an integrated oil cooler; the exhaust valves are liquid sodium-cooled. All vehicles using this engine feature Saab's Trionic 8 engine management system as well as a revised valve train; the timing chain and timing gears are new, along with Saab's Direct Ignition system.

The reinforcements, intercooling, dual overhead camshaft, such were developed by GM Powertrain Sweden. It features stroke and a 9.5:1 compression ratio. Maximum power is 221 ft ⋅ lb of torque at 2500 rpm. Maximum boost is 12.3 psi. 2003–2014 Saab 9-3 - B207E, B207L, B207R 2003–2008 Opel Vectra - Z20NET 2003–2008 Opel Signum - Z20NET 2006–2010 Cadillac BLS - B207L, B207R The LSJ is a supercharged version of the LK9 Ecotec 2.0 L— 1,998 cc — with an Eaton M62 Roots-type supercharger and air-to-liquid intercooler. The LSJ shares many of its components with the LK9 such as: piston cooling jets, oil cooler, connecting rods, oil pan, sodium-filled exhaust valves and cylinder head, it is rated at 205 hp at 5600 rpm and 200 ft⋅lb at 4400 rpm with a compression ratio of 9.5:1 and a 6450 rpm redline. With the end of the Chevy Cobalt S/C SS and Saturn Ion Red Line, the LSJ was discontinued after 2007. In late 2005 Brammo Motorsports struck a deal with GM for the Supercharged 2.0 L Ecotec for their Ariel Atom.

The engine came in various ratings from 205 hp to 300 hp. The LSJ was on the Ward's 10 Best Engines list for 2006; this engine is used in: This engine is known as a Z22SE in other countries such as the United Kingdom and Europe. The basic Family II architecture was re-engineered in 2000 to become the Ecotec Gen I. Unlike its notably harsh predecessor, the engine was designed for smoothness. Dual in-block balance shafts were integral to the design, the power-steering pump was mounted directly to the cylinder head and driven by the intake camshaft, the water-pump housing was cast into the block, the A/C compressor and alternator were mounted directly on the block without brackets; the oil filter housing was cast into the block with a removable replaceable paper element. It did not use an EGR valve; the Ecotec line is manufactured in Tonawanda, New York and Kaiserslautern and was manufactured for Saturn in Spring Hill, Tennessee until Saturn's discontinuation. In North America this engine replaced both the Quad-4 and the GM 122 engines and first appeared in the 2000 Saturn L-Series.

The L61 is a 2.2 L -- 2,198 cc -- version with block. The engine is 665 millimetres in length, 642 millimetres in width, 655 millimetres in height and 139 kilograms; the Ecotec 2.2, model L61 first appeared in the 2000 Saturn LS1. There are a few variations to the standard L61; the 2003 Saturn L-Series has a high output version with higher compression and more aggressive camshaft. The 2004–2008 Chevrolet Malibu uses a version with electronic throttle control and a special unitized exhaust manifold and catalytic converter; the Malibu and Saturn versions use return-less fuel injection. The 2002 Saturn VUE was the first North American variant of the L61 to be equipped with electronic throttle control, whereas other applications did not arise until 2005 in the Saturn ION and Chevrolet Cobalt. For 2007, introduced an updated version of the L61 based on the Gen II