title: Matt Sorum

text: After performing on Tori Amos' first record and synthpop band Y Kant Tori Read's sole album, Sorum joined the Cult in 1989 to tour in support of their fourth studio album, "Sonic Temple" (1989). During the tour, Sorum was spotted by Guns N' Roses guitarist Slash and subsequently replaced their drummer Steven Adler in 1990. Remaining in the band for seven years, Sorum recorded the albums, "Use Your Illusion I" (1991), "Use Your Illusion II" (1991), and ""The Spaghetti Incident?"" (1993), before departing in 1997 following an argument with Axl Rose.


title: Matt Sorum

text: In 1999, Sorum rejoined The Cult to perform on their reunion album, "Beyond Good and Evil" (2001), and its subsequent 2000/ 2001 tours, and subsequently co-founded the hard rock supergroup Velvet Revolver, alongside former Guns N' Roses bandmates, Slash and Duff McKagan. The band, which included guitarist Dave Kushner and Stone Temple Pilots frontman Scott Weiland, released two successful studio albums, "Contraband" (2004) and "Libertad" (2007), before entering an extended hiatus following Weiland's departure.


title: Matt Sorum

text: Sorum has been a permanent member of hard rock cover band Camp Freddy since 2003, alongside Jane's Addiction members Dave Navarro and Chris Chaney, and assisted in hosting its radio show and podcast on Indie 103.1. In 2012, Sorum founded a touring project, entitled Kings of Chaos, featuring members of Guns N' Roses, Deep Purple, Def Leppard, Aerosmith, ZZ Top, Cheap Trick and Slipknot.


title: Matt Sorum

text: Sorum was born Matthew William Sorum on November 19, 1960, in an unincorporated area of Orange County, California that later became the city of Mission Viejo. He started to play drums after watching Ringo Starr with The Beatles on The Ed Sullivan Show in 1964. Later he was mainly influenced by Ian Paice, Keith Moon, Neil Peart, Ginger Baker, John Bonham, Roger Taylor, Buddy Rich and Bill Ward.


title: Matt Sorum

text: At Mission Viejo High School Sorum was part of the jazz band, marching band, and wind ensemble. According to Sorum, he and his high school band, Prophecy, would play at The Starwood on amateur nights.


title: Matt Sorum

text: Sorum's work with Chateau produced a four-song set that was covered by local radio stations for a short time, but the music scene changed from grandiose rock to punk and alternative new wave music. Sorum left and went to Hollywood to play with a series of bands, including Population Five, with bassist Prescott Niles from The Knack, and Hawk, replacing Scott Travis, who went to play with Racer X and later Judas Priest. He then left on a tour around the country with a blues guitarist, playing nightclubs and bars.


title: Matt Sorum

text: In 1988, he was recruited to play on the debut album of Y Kant Tori Read, a band fronted by a then unknown Tori Amos. In the wake of that project, he joined The Cult as their live drummer for the 1989/1990 tour in support of "Sonic Temple".


title: Matt Sorum

text: In 1989, Slash saw Sorum live with The Cult on the Sonic Temple tour and, shortly after, Sorum joined Guns N' Roses as Steven Adler's replacement.


title: Matt Sorum

text: Sorum with Guns N' Roses can be heard on the 1990 cover of the Bob Dylan track "Knockin' on Heaven's Door", the albums "Use Your Illusion I", "Use Your Illusion II" (excluding the track "Civil War"), ""The Spaghetti Incident?"", the 1994 cover of The Rolling Stones track "Sympathy for the Devil" and the majority of "". Sorum featured fully on the lengthy Use Your Illusion Tour, drumming on all of the 194 shows, 9 legs and to over 7 million fans.


title: Matt Sorum

text: In 1994, Sorum formed Slash's Snakepit with Slash and Gilby Clarke and drummed on their debut album "It's Five O'Clock Somewhere". Sorum also lent his drumming skills in the theme song for the 1995 20th Century Fox film, "". That same year, Sorum formed the supergroup Neurotic Outsiders, which featured bandmate Duff McKagan. In 1996 they released their only album, the self-titled "Neurotic Outsiders". John Taylor (Duran Duran) and Steve Jones (Sex Pistols) also participated on this album, and toured behind it. Early performances featured guest spots by Simon Le Bon (Duran Duran), Slash, and Billy Idol.


title: Matt Sorum

text: In 1997, Sorum was fired from Guns N' Roses by Axl Rose after an argument with Rose over the inclusion of Paul Tobias in the band. Sorum claimed that Tobias made disparaging remarks about a Slash performance on TV, resulting in him blowing up at Tobias. Slash had recently left the band, and Sorum told Axl “without Slash there is no Guns N’ Roses”, to which Rose asked if he was going to quit the band. Sorum said no, then Rose fired him.


title: Matt Sorum

text: In April 2006, nine years after leaving Guns N' Roses, Sorum re-established his friendship with the band's lead singer Axl Rose.


title: Matt Sorum

text: In 1998, he released his first and only drum instructional video (Drum Licks and Tricks from the Rock n Roll Jungle) demonstrating his techniques. In 1999, Matt joined The Cult once again and featured on their album, Beyond Good And Evil, which he spent most of 2001 touring in support of.


title: Matt Sorum

text: In 1999, Sorum reunited with Slash and McKagan to promote a concert for the independent film Soundman (written and directed by Steven Ho) at the Slamdance Film Festival. Sorum had composed the film with Lanny Cordola and Michael Stearns. Realizing that they still had chemistry together, they formed a new band called Velvet Revolver with former Stone Temple Pilots frontman Scott Weiland and rhythm guitarist Dave Kushner. After the 2004 release of their debut album "Contraband", they embarked on a worldwide tour that continued through December 2005. In August 2005, Sorum broke his wrist in a boating accident, stalling the tour temporarily. While recovering from the wrist injury the drummer Brian Tichy and Mark Schulman filled in for him. In 2005, the band was nominated for three Grammys, Rock Album of the Year, Rock Song, and Hard Rock Performance for their Contraband single Slither which won their first and only Grammy.


title: Matt Sorum

text: After taking some time off in 2006, Sorum and the rest of the band returned to the studio in December to record "Libertad", Velvet Revolver's second album, which was released on July 3, 2007. Sorum toured with Velvet Revolver until singer Weiland parted ways with the band on April 1, 2008.


title: Matt Sorum

text: In 1994, Sorum was one of many guest drummers on the album, "". Playing with the Buddy Rich Big Band, Sorum was able to display his skill and finesse as a jazz drummer.


title: Matt Sorum

text: Sorum released his first solo album, "Hollywood Zen", in 2003. Available through his website, it was a musical statement about his life, touring, relationships, etc. In the same year, Sorum began playing with the newly formed Camp Freddy.


title: Matt Sorum

text: Sorum has endorsed Zildjian cymbals, featured in numerous sweepstakes with Zildjian, and lent his talents to Submersible Music's DrumCore software.


title: Matt Sorum

text: In 2006, Sorum began guest recording in his studio with a new project, called Circus Diablo. That year, he launched a clothing line; "SorumNoce".


title: Matt Sorum

text: Sorum was featured in episode 54 of TV's LA Ink originally airing on August 27, 2009. In it, Kat Von D. tattoos a portrait of his wife Ace on his leg.


title: Matt Sorum

text: Matt filled in on Motörhead's 2009 US tour, while drummer Mikkey Dee took part in Kändisdjungeln, a Swedish version of I'm a Celebrity...Get Me Out of Here!. "I can retire now," Sorum joked. "When they let me off in Kansas, I might open my own corn farm and just wear my Motörhead jacket. 'This is it, I'm done!' Axl calls and it's like, 'Aw, fuck that – I played with "Motörhead!""


title: Matt Sorum

text: After performing together at the "Giving 2010" benefit event on May 3, 2010, Sorum formed the cover band "Carnival of Dogs" with Tracii Guns (L.A. Guns, formerly of Brides of Destruction), Franky Perez (Solo, Scars on Broadway, DKFXP) and Phil Soussan (previously played with Ozzy Osbourne, Billy Idol and Vince Neil).


title: Matt Sorum

text: He made an appearance in an episode of FSN Sport Science, when a test was undertaken to determine if a professional basketball point guard had faster hands than a drummer.


title: Matt Sorum

text: In 2010 and 2011 Sorum appeared on the reality show "Rock 'n Roll Fantasy Camp." He appeared as one of the counselors guiding a new band in a music competition.


title: Matt Sorum

text: In 2012, Matt Sorum, and Ace Harper, formed the band Diamond Baby and are both featured in the music video, "The Last Rockstar" with actresses Jane Lynch, Juliette Lewis, and the late Verne Troyer." In 2012, Sorum and Jane Lynch created Adopt the Arts to save the arts from being eliminated from Los Angeles elementary schools.


title: Matt Sorum

text: In 2014, he worked with Animals Asia and adopted a moon bear that had been on a Chinese bear-bile farm, when her bile was extracted for traditional medicine. He hoped to draw attention to the abuse that bears suffer on the farms in China and Vietnam. He has since become an ambassador for the cause.


title: Matt Sorum

text: Sorum is also an auxiliary member of the Cooper-fronted rock supergroup Hollywood Vampires, appearing on the band's eponymous 2015 debut studio album and playing drums at the band's high-profile Rock in Rio show on September 24, 2015, as well as preceding warm-up shows at The Roxy on September 16 and 17. Sorum played with the Hollywood Vampires during their February 2016 Grammy Award Performance.


title: Matt Sorum

text: In 2018, at iconic conference and festival SXSW, Matt Sorum, who is the former drummer of Guns N' Roses, unveiled Artbit, a distributed-ledger platform that enables both artists and fans to share and monetise artistic talent from anywhere across the globe. Artbit addresses the issue of little monetary return for emerging artists in our digitally-led music industry. Upon launch Artbit users will be able to produce live shows and performances through the platform, linking locations to any of Artbit's virtual stages.


title: Matt Sorum

text: On October 12, 2013 Matt married his longtime girlfriend Ace Harper in Palm Springs, California. Their daughter, Lou Ellington Sorum, was born on June 11th, 2021.


title: Tender Is the Flesh

text: Tender is the Flesh is a dystopian novel by Argentine author Agustina Bazterrica. The novel was originally published in Spanish in 2017 and translated by Sarah Moses into English in 2020. "Tender is the Flesh" portrays a society in which a virus has contaminated all animal meat. Because of the lack of animal flesh, cannibalism becomes legal. Marcos, a human meat supplier, is conflicted by this new society, and tortured by his own personal losses.


title: Tender Is the Flesh

text: The novel opens by describing the process of slaughtering humans, who are then referred to as "head". The world has fallen into chaos after the "Transition", the term describing an event where a virus that infected animals was found to be deadly to humans, resulting in the mass slaughter and burning of animals, with the world's population forced either to go vegan, or eat each other. Soon cannibalism was institutionalized, industrialized and normalized, with humans bred for consumption known as "special meat". Scavengers, who cannot afford the special meat, consume any dead body available.


title: Tender Is the Flesh

text: Marcos works at one of these slaughterhouses in order to support his ailing father, who suffers from dementia. He describes his internal conflict with his job and the state of the world. Marcos' job involves being a middle man, the one who purchases the "head" and then sells the products. The owner of a breeding center explains the entire process of raising the "head". He notes things like First Generation Pure (FGP's), describing "head" born in the breeding center. The breeding center delivers Marcos a female FGP as a gift.


title: Tender Is the Flesh

text: More of Marcos' personal life is revealed as he talks to his wife Cecilia on the phone. The couple tried repeatedly and unsuccessfully to have a family. They had a son, Leo, who died while still a baby. After his son's death he and his wife separated. It is made clear that he is having an affair with a butcher in town. After their encounter, Marcos' sister Marisa and her family are introduced. She contributes nothing to their father's care. Marcos travels back home and in his interactions with the female FGP, he seems to see her as less of a product. He eventually appears to develop feelings for the FGP and begins having sex with her, which is regarded as one of the worst transgressions in society.


title: Tender Is the Flesh

text: In part two of the novel, significant time has passed. Marcos has named the female FGP Jasmine, due to her smell reminding Marcos of wild jasmine flowers. She has apparently been living in the house with him and is eight months pregnant.


title: Tender Is the Flesh

text: Marcos's elderly father dies, and Marcos scatters his ashes in the zoo his father brought him to as a child, now abandoned. Marisa insists on hosting a "farewell party" for their father, which Marcos reluctantly attends, leaving after discovering his sister's "domestic head."


title: Tender Is the Flesh

text: Marcos comes home to find Jasmine in labor with indications that the baby is in trouble. He calls his wife Cecilia, a professional nurse herself, to come and help. Jasmine gives birth to a boy with Cecilia's help. Marcos tells Cecilia that the baby is theirs now. Marcos knocks Jasmine out and begins bringing her to the barn to slaughter her. Cecilia protests, stating that Jasmine could have given them more children. Marcos closes by saying "She had the human look of a domesticated animal.”


title: Tender Is the Flesh

text: "Tender is the Flesh" was a winner of Argentina's Premio Clarin de Novela prize and was praised by several critics. "The New York Times Book Review"'s Daniel Kraus described the novel as "powerful" in displaying the monstrosities and desires of the hierarchical structure of capitalism. Kraus also identified that replacing pigs with humans completely alters the view within the novel of industrialized farming. Justine Jordan of "The Guardian" saw the landscape of the novel as similar to Argentine author Samanta Schweblin's novel "Fever Dream". Jordan described "Tender Is the Flesh" as "vampiric", "provocative" and "sorrowful". "Headstuff"s David Tierney highlighted the use of dark humor as complimenting the novel's darkness and horror. Tierney also identified the main weakness of the novel as Bazterrica babying the reader, with the book improving considerably when this restraint is relaxed.


title: Tender Is the Flesh

text: Scholars such as Megan Todd analyze various ways in which the novel serves as an allegory. Todd in particular described Bazterrica's novel as a metaphor for the politics of exploitation in neoliberal capitalism. Sebastian Williams argues that the novel challenges a traditional humanist conceptualization of Self (as an autonomous, discrete subject), especially regarding the permeable boundaries between the individual and their environment (i.e., what humans consume; the diseases humans contract). Williams also notes that Bazterrica foregrounds broader cultural anxieties about zoonotic diseases; disease is never simply a material fact, but is embedded in cultural narratives that define politics, ethics, and so forth.


title: Eenadu

text: Eenadu () is the largest circulated Telugu-language daily newspaper of India sold mostly in the states of Andhra Pradesh and Telangana. According to the Indian Readership Survey (IRS) Q2 2019, Eenadu ranks eighth among the most circulated Indian-language dailies with a total readership (TR) of 1,614,105. It was founded by Ramoji Rao in 1974.


title: Eenadu

text: "Eenadu" is a polysemic word which has two meanings in Telugu language "today/this day" and "this land".


title: Eenadu

text: Various editions of "Eenadu" exist throughout the Telugu-speaking region of India constituting the states of Andhra Pradesh, Telangana.


title: Eenadu

text: Eenadu newspaper is owned by Ushodaya Enterprises Private Limited, a part of Ramoji Group. As per the 2018 report of Media Ownership Monitor, Ramoji Rao and family own 97.56% stake in Ushodaya Enterprises. In terms of individual ownership, Ramoji Rao holds 42.26%, his eldest son Cherukuri Kiron holds 28.36%, and his daughter-in-law Cherukuri Vijayeswari (wife of the deceased younger son, Cherukuri Suman) holds 25.38% shares in Ushodaya Enterprises.


title: Eenadu

text: "Eenadu" was launched from Visakhapatnam on 10 August 1974 by Ramoji Rao, a businessman who had previously achieved success with Priya Pickles and Margadarsi Chitfunds. At that time, the "Andhra Prabha", owned by the Indian Express Group, was the leading regional newspaper.


title: Eenadu

text: Initially, the circulation of "Eenadu" was limited. When launched in the city of Visakhapatnam, it wasn't able to sell more than 3,000 copies a week. "Eenadu" found itself struggling to become a daily publication among publication. However, it was popular in certain regions and rivalry was still an issue. "Eenadu" hired a new set of directors to be part of its key decision and management group which drove it towards what it is today: the most highly circulated newspaper in the region.


title: Eenadu

text: "Eenadu" began with a print order of 4,000 copies, composed by hand and produced using a second-hand printing press. But by the time it was admitted into the Audit Bureau of Circulations in 1976, its circulation had already reached a readership of 48,000. By 1978, "Eenadu" surpassed "Andhra Prabha"s circulation and, by 1995, two other rivals "Andhra Patrika" and "Udayam" folded, leaving "Eenadu" with over seventy-five percent of the audited circulation of Telugu dailies.


title: Eenadu

text: When "Eenadu" expanded to Hyderabad in 1975, it divided the city into target areas, recruited delivery boys three months in advance and handed out the paper freely for a week. During the 1980s, technology enabled "Eenadu" to spread over larger areas beyond only the main cities. Earlier, it was difficult to manage even the three editions of the 1970s (the Visakhapatnam, Vijayawada and Hyderabad editions) because the only communication facilities available to the publication at the time were the telegram, telephone, and teleprinter, all of which had limited presence in rural Andhra Pradesh.


title: Eenadu

text: Support of the Telugu Desam Party (TDP) by "Eenadu" has been recorded since the party's foundation in 1982. This has been attributed to Ramoji Rao's disdain for the Congress government, to the point that he planned to create a regional party on his own accord, and a personal rapport he formed with party founder and leader N. T. Rama Rao, who he had first doubted but eventually saw political potential in. Another factor that has been cited is caste politics, with both "Eenadu" and the TDP being perceived as Kamma-oriented organisations and both Raos being Kammas themselves, although this view has been challenged. During the 1983 elections, the party and the paper formed a symbiotic relationship as "Eenadu" not only publicised, promoted and ran positive stories on Rama Rao's campaign, but also gave more direct support, such as utilising its network of journalists to inform and advise Rama Rao on local issues for his stops and designing party advertisements through Ramoji Rao's marketing agency. This coverage led to a massive increase in subscriptions, with "Eenadu" going from a circulation of 230,000 copies to 350,000 in the six months of Rama Rao's electoral campaign and becoming one of the state's most popular newspapers. The TDP would go on to successfully sweep the election, making Rama Rao the Chief Minister of Andhra Pradesh, and over half a million copies were printed of "Eenadu" to declare this victory. Reportedly, Ramoji Rao sent a bill to Rama Rao for 3 million (30 lakh) rupees for the assistance he had given to the campaign. In response, film personality Dasari Narayana Rao and industrialist Gireesh Kumar Sanghi would launch pro-Congress newspapers of their own and eventually become members of the Rajya Sabha on the Congress ticket.


title: Eenadu

text: When Rama Rao and his government faced crises and parliamentary revolts in the 1980s, "Eenadu" continually supported him and clamored for his restoration to power. Despite Rama Rao's growing unpopularity in the later part of the decade due to perceptions of failed promises, the paper refrained from criticising him before expressing some concerns about his leadership in response to his continued loss of public support and the Congress victory in the 1989 Andhra Pradesh Legislative Assembly election. In the 1990s, as fissures developed between Rama Rao and his son-in-law and prominent party leader Chandrababu Naidu, "Eenadu" ultimately took Naidu's side, publishing mocking portrayals of Rama Rao depicting him as being manipulated by his new wife Lakshmi Parvathi, and eventually played a key role in the internal party coup by supporting Naidu's power grab. This paved the way for Naidu to become the next Chief Minister and ensured a friendly relationship between the paper and his administration. During the reign of Congress governments, "Eenadu" went on the offensive and became their "chief critic"; both Y. S. Rajasekhara Reddy and his son Y. S. Jagan Mohan Reddy would "fight back" during their time in power. This took on multiple forms, from the 2004 investigation of Margadarsi for irregular financial practices to the launch of "Sakshi" in 2008 under Jagan Mohan Reddy's ownership as a "counter" to what his father, the CM at the time, claimed was "biased news" from traditionally TDP-supporting papers.


title: Eenadu

text: With the introduction of offset printing, photocomposing software and computers, "Eenadu" was able to launch editions in smaller towns like Tirupathi in 1982. From the 1980s, the news editor of "Eenadu" oversaw an enormous local-based news gathering and disseminating organization from his Hyderabad office.


title: Eenadu

text: By the end of the 1980s, there were six substantial Telugu dailies running, and the business was highly competitive. In 1989 "Eenadu" introduced "district dailies (tabloid edition)" to carry its presence not only into district towns like Rajamahendravaram, Karimnagar, Guntur and Adilabad, but also "taluka" towns like Suryapet and Tadepalligudem. Each publication center required forty engineers to run its printing presses. "Eenadu"s district dailies were based on market research asserting that heavy local content would generate new groups of readers and boost advertising revenue. Currently, the district dailies print local news specifically for each major location in the area, thereby negating the need for any separate local daily. Few special sections are published every day of the week. "Eenadu" later ventured into other markets such as finance and chit funds (e.g. Margadarsi chits), foods (Priya Foods), film production (Ushakiran Movies), film distribution (Mayuri Films), and television (ETV). All the businesses are organized under the Ramoji Group.


title: MØ

text: Karen Marie Aagaard Ørsted Andersen (; born 13 August 1988), known professionally as MØ (), is a Danish singer and songwriter. She signed a recording contract with Sony Music Entertainment in 2012, releasing her debut extended play, "Bikini Daze" (2013), and her debut studio album, "No Mythologies to Follow" (2014).


title: MØ

text: MØ collaborated with Australian rapper Iggy Azalea on the 2014 single "Beg for It", which peaked at number 27 on the US "Billboard" Hot 100, earning MØ her first entry on the chart. The following year, she co-wrote and provided vocals for the Major Lazer and DJ Snake collaboration "Lean On", which became an international success, charting at number one in several countries, number two in the United Kingdom, and number four in the United States. In 2016, MØ was featured on Snakehips's single "Don't Leave", and another Major Lazer single "Cold Water" with Canadian singer Justin Bieber, which debuted at number one on the UK Singles Chart and number two on the US "Billboard" Hot 100.


title: MØ

text: MØ earned her first commercially successful solo single with 2016's "Final Song". In 2017, she released her second extended play, "When I Was Young", followed by her second studio album, "Forever Neverland," in 2018. In 2022, MØ released her third studio album, "Motordrome", which was followed by a repackaging titled "Dødsdrom."


title: MØ

text: Karen Marie Aagaard Ørsted Andersen was born in Ubberud, near Odense, and she grew up in Ejlstrup on the island of Funen, Denmark. Her father, Frans Ørsted, is a psychologist, and her mother, Mette Ørsted, is a teacher. She has an older brother, Kasper, who is a doctor.


title: MØ

text: MØ was seven when she became interested in music thanks to the Spice Girls. As a teenager, she became interested in punk music and anti-fascist movements, listening to Black Flag, Nirvana, Smashing Pumpkins, Yeah Yeah Yeahs and especially Sonic Youth, saying she looked up to Kim Gordon as a "big hero and role model".


title: MØ

text: In 2006, MØ released a side project titled The Edmunds, which included tracks such as "Garbage King" and "Polly Get Your Gun". MØ also released several other side projects during 2008–10 including titles such as "A Piece of Music to F*ck to" and "The Rarities". The side-projects included songs that have been previously taken down due to an unknown reason, but has been re-released by a fan on YouTube.


title: MØ

text: MØ and her friend Josefine Struckmann Pedersen formed duo MOR in 2007, and released two EPs, "Fisse I Dit Fjæs"(""Pussy in Your Face"") and "Vanvidstimer"(""Madness Hours""), in 2009 and 2011, respectively. MOR disbanded on 7 September 2012, due to personal reasons.


title: MØ

text: In 2012, MØ began creating a cappella pop songs and began collaborating with producer Ronni Vindahl. On 14 January 2013, MØ released her debut single, "Glass". On 15 March 2013, she released "Pilgrim" with the B-side "Maiden". "Pilgrim" was recognised as P3s Uundgåelige (P3 Unavoidable), a label given to rising artists by Danish radio station DR P3, as it peaked at number eleven on the Danish Singles Chart. On 27 March 2013, she performed live on television at the Danish P3 Guld Awards.


title: MØ

text: On 7 June 2013, she released the single "Waste of Time". On 18 August 2013, it was confirmed through producer and DJ Avicii's manager Ash Pournouri that MØ had co-written and provided vocals on a track called "Dear Boy" which was later featured on Avicii's debut album, "True". On 30 August 2013, she released the single "XXX 88" MØ's first extended play, "Bikini Daze", was released on 18 October 2013. In October 2013, she supported AlunaGeorge on UK tour dates. The single "Don't Wanna Dance" debuted on BBC Radio 1 on 16 January 2014 as Zane Lowe's Hottest Record.


title: MØ

text: MØ's debut studio album, "No Mythologies to Follow", was released on 7 March 2014 and her album was inspired by the great Michael Jackson. On the review aggregate site Metacritic, the album has a Metascore of 77 out of 100 indicating ""generally favorable"" reviews. Music blog Pretty Much Amazing called the album "complex and euphoric", while "The Guardian" noted that "what MØ lacks in originality, she makes up for with warlike ardour". "No Mythologies to Follow" debuted at number 58 on the UK Albums Chart, selling 1,438 copies in its first week.


title: MØ

text: MØ began touring in Europe and the United States in support of the album, ending in June. On 2 June 2014, she made her US television debut on "Jimmy Kimmel Live!", where she performed the songs "Don't Wanna Dance" and "Pilgrim". "Walk This Way" was released on 16 June 2014 as a single from "No Mythologies to Follow". On 23 June, MØ announced additional United States and Canadian tour dates beginning in September. In November 2014, she won four awards at the Danish Music Awards: Danish Album of the Year, Danish Solo Artist of the Year, Danish Breakthrough Artist of the Year and Danish Music Video of the Year.


title: MØ

text: In 2014, MØ was featured on Australian rapper Iggy Azalea's song "Beg for It", which was released as the lead single from Azalea's reissue album, "Reclassified". Azalea and MØ performed the song for the first time on "Saturday Night Live" on 25 October. MØ was also featured on Elliphant's "One More", which was officially released as a single on 22 September 2014. The official music video was released a day later, 23 September. MØ also co-wrote the song "All My Love" by Major Lazer, featuring vocals from American singer and songwriter Ariana Grande.


title: MØ

text: MØ co-wrote and provided vocals for another Major Lazer song, "Lean On" with DJ Snake, which was released in March 2015. The single topped the charts globally in MØ's native Denmark, Australia, Finland, Ireland, the Netherlands and New Zealand, while reaching the top five in several countries, including France, Germany, Sweden, the United Kingdom and the United States. According to the IFPI, "Lean On" was the fifth best-selling song of 2015 worldwide, and one of the best-selling singles of all time, with global sales of 13.1 million. Spotify named it as the most streamed song of all time, and has over one billion streams globally as of June 2017. The music video for “Lean On” premiered on April 30, 2015, and became a viral success with over 2.5 billion views on YouTube, making it the sixteenth most viewed video on the site.


title: MØ

text: On 1 October 2015, it was announced that the first single from MØ's upcoming second studio album, "Kamikaze", produced by Diplo, would be released on 15 October 2015. On 14 October, the single made its world premiere on a BBC Radio 1 segment hosted by Annie Mac before the studio version was released the following day. "Kamikaze" charted in Denmark, the United Kingdom, Australia and Belgium. On 13 May 2016, "Final Song", the second single from MØ's second album, was released and also made its world premiere on the same radio segment hosted by Mac. The song was co-written with Swedish singer Noonie Bao and English singer MNEK. It became MØ's first top 40 single as a lead artist in the United Kingdom, with the song reaching number 14 on the UK Singles Chart. Additionally, the song reached the top 40 in more than 10 countries worldwide.


title: MØ

text: On 22 July 2016, Major Lazer released the single "Cold Water" which features Canadian singer Justin Bieber and MØ, marking the fourth time she has worked with Major Lazer. In the United States, "Cold Water" debuted at number two on the "Billboard" Hot 100, becoming MØ's second top 10 and her third top 40 single, It is also her highest-charting single in the United States. MØ is the highest-charting Danish act along with Jørgen Ingmann ("Apache") and Lukas Graham ("7 Years"), who all reached number two on the "Billboard" Hot 100. In the United Kingdom, "Cold Water" debuted at number one on the UK Singles Chart. The song became MØ's first number-one single, and she is only the fourth Danish act to reach number one in the UK. Additionally, it is the first time two Danish acts have reached number one in the same year (with the other being Lukas Graham's "7 Years").


title: MØ

text: On 17 September 2016, MØ announced the release of her new track titled "Drum" on Twitter. It had made special appearances in previous concerts and shows. The song was produced by American producer Bloodpop also co-written by English singer Charli XCX alongside Noonie Bao. In October 2016, the song's official audio was released.


title: MØ

text: On 6 January 2017, English electronic duo Snakehips premiered their new track "Don't Leave" which features vocals from MØ. The official lyric video was also released the same day, it has been said that it will be featured in Snakehips upcoming debut album. On 10 March 2017 she was featured on Charli XCX's "3AM (Pull Up)" taken from her mixtape, "Number 1 Angel". She was featured alongside Sophie on the song "9 (After Coachella)" by Cashmere Cat, which was the fifth single from his debut album, "9". On 21 April 2017 "Nights with You", the third single from her upcoming second studio album, was officially released worldwide after premiering on MistaJam's BBC Radio 1 show the previous day.


title: MØ

text: On 26 October 2017, MØ released her second extended play, titled "When I Was Young", as a surprise. The EP is composed of songs that MØ wrote over the course of four years since the release of "No Mythologies to Follow". On 30 October 2017, MØ announced a co-headlining North American tour with Cashmere Cat titled the "Meøw Tour" in support of the EP. The tour took place from January to April 2018. In 2017, MØ co-wrote and provided vocals on Diplo's song "Get It Right" for the album "Major Lazer Presents: Give Me Future". They both also performed the song on "The Jimmy Fallon Show" with an appearance from GoldLink.


title: MØ

text: In 2018, MØ collaborated with producer Jack Antonoff to provide vocals for the "Love, Simon" soundtrack with the song "Never Fall in Love". She also collaborated with Noah Cyrus on the song “We Are...” and was featured on Alma's "Heavy Rules Mixtape" with the song "Dance for Me".


title: MØ

text: On 19 October 2018, MØ released her second studio album, "Forever Neverland," by Columbia Records. The album was preceded by five singles: "Nostalgia", "Sun in Our Eyes" featuring Diplo, "Way Down", "Imaginary Friend",and "Blur" featuring Foster the People. The album also features collaborations with Charli XCX, What So Not, Two Feet and Empress Of. She revealed that other singles "Kamikaze", "Final Song" and "Nights with You" will only be available on the Japanese edition of the album.


title: MØ

text: In 2019, MØ performed her single "Blur" on "The Tonight Show Starring Jimmy Fallon," she co-wrote and provided vocals to the theme song for "Moominvalley", and was the support act for Panic! at the Disco's tour across the United Kingdom. MØ performed at 2019's Glastonbury Festival and Roskilde Festival. In October 2019, she released her debut mixtape, "MMMMØ - The Mix".


title: MØ

text: In an interview with "DIY" in July 2021, MØ confirmed that her third album, "Motordrome", would be released in 2022. It was later confirmed for release on 28 January 2022.


title: MØ

text: MØ said in an interview from Wonderland Magazine that her grandfather, Mogens Ørsted, who used to be an artist would sign his initials on his paintings. Therefore, she decided she wanted to do the same with the same initials within her own name. The word "mø" means "maiden" or "virgin to life" in Danish.


title: MØ

text: MØ's music has been classified as electronic, electropop, synth-pop, and indie pop, and has been described as "electro music with guts". "The Guardian" described her music stating; “her music, muscular and melodic, is a hybrid of bouncy EDM drops and scandipop on steroids”, and "NME" called her work a cross between Siouxsie Sioux and Janet Jackson. MØ has described her sound as "an organic yet dynamic mix of electro, indie-pop, soul and street vibes". She showcased different musical styles in her debut album, including indie pop, dream pop, dark pop, electronica and alternative R&B. Her second album, "Forever Neverland", was described as electropop and dance-pop, containing elements of tropical house, experimental, trip hop, alternative pop and dancehall. MØ's music has been compared to electropop artists Grimes and Twin Shadow, and her vocals to those of Lana Del Rey.


title: MØ

text: MØ's influences include the Spice Girls, Sonic Youth, Kim Gordon, Twin Shadow, Frank Ocean, Patti Smith, Björk, Thurston Moore, J Dilla, Dead Kennedys Yeah Yeah Yeahs, Little Dragon, Santigold, Karen O, Black Flag, Bonobo, Nico, Portishead, The Doors, The Smashing Pumpkins, The Clash, MS MR, Wu-Tang Clan, Grimes, SZA, and Lykke Li.


title: Shaddam IV

text: Shaddam IV of House Corrino is a fictional character in the "Dune" universe created by Frank Herbert. He is Padishah Emperor of the Known Universe in Herbert's 1965 novel "Dune". Shaddam's accession to the throne is chronicled in the "Prelude to Dune" prequel trilogy (1999–2001) by Brian Herbert and Kevin J. Anderson, and he later appears in the prequel series "Heroes of Dune" (2008–2009) and the "Caladan Trilogy" (2020–2022).


title: Shaddam IV

text: Born in year 10,134 A.G. (After Guild), Shaddam is the son of Elrood IX and the 81st member of House Corrino to occupy the Golden Lion Throne. Shaddam's closest friend is the assassin Count Hasimir Fenring, a cousin and childhood companion. Shaddam has five daughters—the Princesses Irulan, Chalice, Wensicia, Josifa, and Rugi—and no legal sons. His wife Anirul, a Bene Gesserit of Hidden Rank, died in 10,176 A.G.


title: Shaddam IV

text: Shaddam is described as "red-haired" by his daughter Irulan via epigraph in "Dune", and noted to be 72 years old yet looking no older than 35. He is portrayed by José Ferrer in the 1984 David Lynch film adaptation "Dune", by Giancarlo Giannini in the 2000 "Dune" miniseries and by Christopher Walken in the upcoming "". In the 1984 film, Shaddam is said to be over 200 years old, as the Guild representatives remind him of the importance of the spice melange, which extends life.


title: Shaddam IV

text: During the events of the original novel "Dune", Shaddam grants Duke Leto Atreides control of the harsh desert planet Arrakis, the only known source of the all-important spice. Though outwardly this seems like an opportunity for great wealth and power for House Atreides, Leto recognizes it as a trap; Shaddam feels threatened by Leto's rising popularity, and somehow intends to diminish or destroy him. Avoiding an overt attack, Shaddam instead uses the centuries-old feud between House Atreides and House Harkonnen to disguise his assault, enlisting the brilliant and power-hungry Baron Vladimir Harkonnen in his plan to trap and eliminate the Atreides. Shaddam's own power is secured by his fierce and seemingly unstoppable Sardaukar army; the Baron's ambush on Leto and his forces is bolstered by Sardaukar troops disguised as Harkonnens, and the Atreides are crushed. Leto is killed, but his Bene Gesserit concubine Lady Jessica and son Paul Atreides escape into the desert. They find sanctuary with a tribe of the planet's native Fremen.


title: Shaddam IV

text: Paul rises to power among the Fremen, whom he finds to be fierce fighters whose skills and numbers are underestimated by the Harkonnens. As the Fremen guerrilla "Muad'Dib", Paul soon manages to lead the Fremen in a widespread challenge to the Harkonnens' control of Arrakis. With the spice trade threatened, Shaddam arrives on Arrakis with his court and an escort of Sardaukar, intending to quickly end the disruption. However the Fremen, enhanced by Paul's training in Bene Gesserit martial arts, attack and manage to handily defeat the attendant Sardaukar forces. Making clear his ability and willingness to completely destroy all spice production should his terms not be met, Paul demands that Shaddam step down from the Imperial throne and install Paul in his place, with Irulan as Paul's consort. Shaddam has no choice but to concede, as an end to the spice supply would paralyze civilization across the entire universe. He is effectively exiled to his ancestral planet of Salusa Secundus, now a wasteland, prison planet, and training ground for the Sardaukar. According to "Appendix IV: The Almanak en-Ashraf (Selected Excerpts of the Noble Houses)" in "Dune", Shaddam dies in 10,202 A.G. after 68 years of life.


title: Shaddam IV

text: The author's son, Brian Herbert, noted that Shaddam's age in "Dune" is slightly inconsistent. Though described as 72 years old at one point in the novel, in the appendix his birth and death years are recorded as 10,134–10,202 A.G., making him 68 years old at the time of his death. In 2005, Brian Herbert described this inconsistency in Shaddam's age:


title: Shaddam IV

text: In the "Prelude to Dune" prequel trilogy (1999–2001), Shaddam is eager to succeed his father Elrood as Padishah Emperor, but despite his advanced age Elrood shows no signs of ill health. Shaddam finally tasks his longtime friend and minion Fenring to administer Elrood with an undetectable, slow-acting poison. Elrood finally dies in 10,156 A.G.; Shaddam had previously been complicit in the murder of his elder brother, the Crown Prince Fafnir, and had secretly administered contraceptives to his own mother, Habla, so she could not conceive another son to rival him. Shaddam secures his throne by paying the Spacing Guild with a supply of the spice and by arranging his own marriage to a Bene Gesserit. This union with the Lady Anirul Sadow-Tonkin results in five daughters, but no sons.


title: Shaddam IV

text: Shaddam is portrayed by José Ferrer in the 1984 David Lynch film adaptation "Dune", and by Giancarlo Giannini in the 2000 "Dune" miniseries. Giannini also dubbed himself in the Italian version of the miniseries. Shaddam does not appear in the 2021 film "Dune", which covers the first part of the book. The character will appear in the upcoming sequel film, "", portrayed by Christopher Walken.


title: IWI ACE

text: The IWI Galil ACE is a series of assault rifles and battle rifles originally developed and manufactured by Israel Weapon Industries (IWI). It is produced in three different calibers: 5.56×45mm NATO, 7.62×39mm and 7.62×51mm NATO. IWI USA also produced limited edition variants of the ACE in 5.45×39mm in 2020.


title: IWI ACE

text: The IWI Galil "ACE" series is based upon the original design of the IMI Galil, but instead utilizes a modern design to increase its accuracy and lower its weight, while maintaining the original Galil's ergonomics, ease of maintenance and reliability under battle conditions. In the design, emphasis was particularly placed on increasing the reliability and accuracy under adverse battlefield conditions.


title: IWI ACE

text: The firearm has been adopted as a service rifle in multiple counties, such as the Chilean Army and People's Army of Vietnam. The IWI Galil ACE is also manufactured under license by Indumil, FAMAE, RPC Fort and Z111 Factory.


title: IWI ACE

text: The original Galil was built with a machined solid steel billet action in order to increase the structural integrity and survivability of the weapon. Unfortunately this resulted in a weight of up to , depending on its variant, which was one of the primary criticisms from the Israel Defense Forces.


title: IWI ACE

text: The ACE has a significantly reduced weight. IWI redesigned the action to integrate the steel with polymer, which is much lighter than the fully steel receiver of the original Galil. While the upper receiver is machined steel and the receiver top features a MIL-STD-1913 Picatinny rail, polymer has been introduced to the lower receiver of the weapon to reduce the gun's weight.


title: IWI ACE

text: According to "American Rifleman": "Although this rifle is clearly based on the AK design, it demonstrated a superior level of accuracy potential compared to several of its cousins. The best single group of [5 rounds at 100 yards] of 0.83″ and five-group average of 0.98″ was produced using the Federal Premium 123-gr. [] Power-Shok soft-point load" (testing done using 7.62×39mm 16-inch barrelled variant).


title: IWI ACE

text: The gas tube, unlike the AK-47 system, is mounted on the rifle via a dovetailed slide machined on the receiver upper-front block. This avoids any movement of the gas block influencing barrel vibration, which would degrade accuracy.


title: IWI ACE

text: The rifle uses the Galil's long-stroke piston system. The long-stroke system is found in the M1 Garand, AK-47 (upon which the Galil's internal mechanism design borrowed heavily) and more recently in the IWI Tavor.


title: IWI ACE

text: The barrel is chrome-lined, cold hammer-forged, with a 1:7″ twist for 5.56×45mm NATO, 1:7.5″ for 5.45×39mm, 1:9.5″ for 7.62×39mm, and 1:12″ for 7.62×51mm NATO.


title: IWI ACE

text: The ACE adopts the Galil Sniper trigger instead of the original Galil trigger, in order to improve accuracy compared to the standard Galil. This is a two-stage trigger, which IWI have modelled on the two-stage trigger of the M1 Garand.


title: IWI ACE

text: According to "American Rifleman", the two-stage trigger is "clean and smooth with a 4 lb. 13 oz. [] trigger pull according to a Lyman digital trigger gauge".


title: IWI ACE

text: Another addition by IWI to the original Galil is the last round bolt catch (for variants of the ACE in 5.56×45mm NATO only). The bolt hold-open feature is a common request of military customers, to reduce reloading times during combat.


title: IWI ACE

text: The ACE has a fully adjustable iron sights with tritium front post and two dot tritium rear aperture. It also features a Picatinny rail for mounting various optical sight.


title: IWI ACE

text: The standard buttstock found on the ACE is a six-position telescopic stock that can be fitted with an optional cheek-piece to improve the sighting of the weapon when using an optical sight. An optional right folding version of the standard buttstock is also available.


title: IWI ACE

text: The forearm consists of MIL-STD-1913 Picatinny rails on the bottom and both sides for mounting accessories such as aiming optics. The side forearm rails have central grooves to provide routing channels for electric wiring used by pressure switch activated accessories. The forearm comes with quick detachable polymer covering panels that can be mounted to protect the rails when a side or bottom rail has no accessories mounted to it. The gas tube above the barrel also has a Picatinny rail mounted on top that is aligned with the rail mounted on the cover over the receiver.


title: IWI ACE

text: IWI US offers a semi-automatic only version of the Galil ACE, including all three different calibres.


title: IWI ACE

text: In October 2020, IWI USA began production of an "extremely limited edition" 5.45×39mm variant of the Galil ACE, available with a 16-inch (40.64 cm) or 8.3 inch (21.08 cm) barrel, producing a total of 545 rifles in each size. They are compatible with AK-74 magazines.


title: Total internal reflection

text: Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected back into the first ("internal") medium. It occurs when the second medium has a higher wave speed (i.e., lower refractive index) than the first, and the waves are incident at a sufficiently oblique angle on the interface. For example, the water-to-air surface in a typical fish tank, when viewed obliquely from below, reflects the underwater scene like a mirror with no loss of brightness (Fig.1).


title: Total internal reflection

text: TIR occurs not only with electromagnetic waves such as light and microwaves, but also with other types of waves, including sound and water waves. If the waves are capable of forming a narrow beam (Fig.2), the reflection tends to be described in terms of "rays" rather than waves; in a medium whose properties are independent of direction, such as air, water or glass, the "rays" are perpendicular to the associated wavefronts.


title: Total internal reflection

text: Refraction is generally accompanied by "partial" reflection. When waves are refracted from a medium of lower propagation speed (higher refractive index) to a medium of higher speed—e.g., from water to air—the "angle of refraction" (between the outgoing ray and the surface normal) is greater than the "angle of incidence" (between the incoming ray and the normal). As the angle of incidence approaches a certain threshold, called the "critical angle", the angle of refraction approaches 90°, at which the refracted ray becomes parallel to the boundary surface. As the angle of incidence increases beyond the critical angle, the conditions of refraction can no longer be satisfied, so there is no refracted ray, and the partial reflection becomes total. For visible light, the critical angle is about 49° for incidence from water to air, and about 42° for incidence from common glass to air.


title: Total internal reflection

text: Details of the mechanism of TIR give rise to more subtle phenomena. While total reflection, by definition, involves no continuing flow of power "across" the interface between the two media, the external medium carries a so-called "evanescent wave", which travels "along" the interface with an amplitude that falls off exponentially with distance from the interface. The "total" reflection is indeed total if the external medium is lossless (perfectly transparent), continuous, and of infinite extent, but can be conspicuously "less" than total if the evanescent wave is absorbed by a lossy external medium ("attenuated total reflectance"), or diverted by the outer boundary of the external medium or by objects embedded in that medium ("frustrated" TIR). Unlike "partial" reflection between transparent media, total internal reflection is accompanied by a non-trivial phase shift (not just zero or 180°) for each component of polarization (perpendicular or parallel to the plane of incidence), and the shifts vary with the angle of incidence. The explanation of this effect by Augustin-Jean Fresnel, in 1823, added to the evidence in favor of the wave theory of light.


title: Total internal reflection

text: The phase shifts are utilized by Fresnel's invention, the Fresnel rhomb, to modify polarization. The efficiency of the total internal reflection is exploited by optical fibers (used in telecommunications cables and in image-forming fiberscopes), and by reflective prisms, such as image-erecting Porro/roof prisms for monoculars and binoculars.


title: Total internal reflection

text: Although total internal reflection can occur with any kind of wave that can be said to have oblique incidence, including (e.g.) microwaves and sound waves, it is most familiar in the case of light waves.


title: Total internal reflection

text: Total internal reflection of light can be demonstrated using a semicircular-cylindrical block of common glass or acrylic glass. In Fig.3, a "ray box" projects a narrow beam of light (a "ray") radially inward. The semicircular cross-section of the glass allows the incoming ray to remain perpendicular to the curved portion of the air/glass surface, and then hence to continue in a straight line towards the flat part of the surface, although its angle with the flat part varies.


title: Total internal reflection

text: Where the ray meets the flat glass-to-air interface, the angle between the ray and the normal (perpendicular) to the interface is called the "angle of incidence". If this angle is sufficiently small, the ray is "partly" reflected but mostly transmitted, and the transmitted portion is refracted away from the normal, so that the "angle of refraction" (between the refracted ray and the normal to the interface) is greater than the angle of incidence. For the moment, let us call the angle of incidence "θ" and the angle of refraction "θ" (where "t" is for "transmitted", reserving "r" for "reflected"). As "θ" increases and approaches a certain "critical angle", denoted by "θ" (or sometimes "θ"), the angle of refraction approaches 90° (that is, the refracted ray approaches a tangent to the interface), and the refracted ray becomes fainter while the reflected ray becomes brighter. As "θ" increases beyond "θ", the refracted ray disappears and only the reflected ray remains, so that all of the energy of the incident ray is reflected; this is total internal reflection (TIR). In brief:


title: Total internal reflection

text: The critical angle is the smallest angle of incidence that yields total reflection, or equivalently the largest angle for which a refracted ray exists. For light waves incident from an "internal" medium with a single refractive index , to an "external" medium with a single refractive index , the critical angle is given by formula_1 and is defined if . For some other types of waves, it is more convenient to think in terms of propagation velocities rather than refractive indices. The explanation of the critical angle in terms of velocities is more general and will therefore be discussed first.


title: Total internal reflection

text: When a wavefront is refracted from one medium to another, the incident (incoming) and refracted (outgoing) portions of the wavefront meet at a common line on the refracting surface (interface). Let this line, denoted by "L", move at velocity across the surface, where is measured normal to "L" (Fig.4). Let the incident and refracted wavefronts propagate with normal velocities formula_2 and formula_3 (respectively), and let them make the dihedral angles "θ" and "θ" (respectively) with the interface. From the geometry, formula_2 is the component of in the direction normal to the incident wave, so that formula_5 Similarly, formula_6 Solving each equation for and equating the results, we obtain the general law of refraction for waves:


title: Total internal reflection

text: But the dihedral angle between two planes is also the angle between their normals. So "θ" is the angle between the normal to the incident wavefront and the normal to the interface, while "θ" is the angle between the normal to the refracted wavefront and the normal to the interface; and Eq.() tells us that the sines of these angles are in the same ratio as the respective velocities.


title: Total internal reflection

text: This result has the form of "Snell's law", except that we have not yet said that the ratio of velocities is constant, nor identified "θ" and "θ" with the angles of incidence and refraction (called "θ" and "θ" above). However, if we now suppose that the properties of the media are "isotropic" (independent of direction), two further conclusions follow: first, the two velocities, and hence their ratio, are independent of their directions; and second, the wave-normal directions coincide with the "ray" directions, so that "θ" and "θ" coincide with the angles of incidence and refraction as defined above.


title: Total internal reflection

text: Obviously the angle of refraction cannot exceed 90°. In the limiting case, we put and in Eq.(), and solve for the critical angle:


title: Total internal reflection

text: In deriving this result, we retain the assumption of isotropic media in order to identify "θ" and "θ" with the angles of incidence and refraction.


title: Total internal reflection

text: For electromagnetic waves, and especially for light, it is customary to express the above results in terms of "refractive indices". The refractive index of a medium with normal velocity formula_2 is defined as formula_8 where "c" is the speed of light in a vacuum. Hence formula_9 Similarly, formula_10 Making these substitutions in Eqs.()and(), we obtain


title: Total internal reflection

text: Eq.() is the law of refraction for general media, in terms of refractive indices, provided that "θ" and "θ" are taken as the dihedral angles; but if the media are "isotropic", then and become independent of direction while "θ" and "θ" may be taken as the angles of incidence and refraction for the rays, and Eq.() follows. So, for isotropic media, Eqs.()and() together describe the behavior in Fig.5.


title: Total internal reflection

text: According to Eq.(), for incidence from water () to air (), we have , whereas for incidence from common glass or acrylic () to air (), we have .


title: Total internal reflection

text: The arcsin function yielding "θ" is defined only if formula_11 Hence, for isotropic media, total internal reflection cannot occur if the second medium has a higher refractive index (lower normal velocity) than the first. For example, there cannot be TIR for incidence from air to water; rather, the critical angle for incidence from water to air is the angle of refraction at grazing incidence from air to water (Fig.6).


title: Total internal reflection

text: The medium with the higher refractive index is commonly described as optically "denser", and the one with the lower refractive index as optically "rarer". Hence it is said that total internal reflection is possible for "dense-to-rare" incidence, but not for "rare-to-dense" incidence.


title: Total internal reflection

text: When standing beside an aquarium with one's eyes below the water level, one is likely to see fish or submerged objects reflected in the water-air surface (Fig.1). The brightness of the reflected image – just as bright as the "direct" view – can be startling.


title: Total internal reflection

text: A similar effect can be observed by opening one's eyes while swimming just below the water's surface. If the water is calm, the surface outside the critical angle (measured from the vertical) appears mirror-like, reflecting objects below. The region above the water cannot be seen except overhead, where the hemispherical field of view is compressed into a conical field known as "Snell's window", whose angular diameter is twice the critical angle (cf. Fig.6). The field of view above the water is theoretically 180° across, but seems less because as we look closer to the horizon, the vertical dimension is more strongly compressed by the refraction; e.g., by Eq.(), for air-to-water incident angles of 90°, 80°, and 70°, the corresponding angles of refraction are 48.6° ("θ" in Fig.6), 47.6°, and 44.8°, indicating that the image of a point 20° above the horizon is 3.8° from the edge of Snell's window while the image of a point 10° above the horizon is only 1° from the edge.


title: Total internal reflection

text: Fig.7, for example, is a photograph taken near the bottom of the shallow end of a swimming pool. What looks like a broad horizontal stripe on the right-hand wall consists of the lower edges of a row of orange tiles, and their reflections; this marks the water level, which can then be traced across the other wall. The swimmer has disturbed the surface above her, scrambling the lower half of her reflection, and distorting the reflection of the ladder (to the right). But most of the surface is still calm, giving a clear reflection of the tiled bottom of the pool. The space above the water is not visible except at the top of the frame, where the handles of the ladder are just discernible above the edge of Snell's window – within which the reflection of the bottom of the pool is only partial, but still noticeable in the photograph. One can even discern the color-fringing of the edge of Snell's window, due to variation of the refractive index, hence of the critical angle, with wavelength (see "Dispersion").


title: Total internal reflection

text: The critical angle influences the angles at which gemstones are cut. The round "brilliant" cut, for example, is designed to refract light incident on the front facets, reflect it twice by TIR off the back facets, and transmit it out again through the front facets, so that the stone looks bright. Diamond (Fig.8) is especially suitable for this treatment, because its high refractive index (about 2.42) and consequently small critical angle (about 24.5°) yield the desired behavior over a wide range of viewing angles. Cheaper materials that are similarly amenable to this treatment include cubic zirconia (index≈2.15) and moissanite (non-isotropic, hence doubly refractive, with an index ranging from about 2.65 to 2.69, depending on direction and polarization); both of these are therefore popular as diamond simulants.


title: Total internal reflection

text: Mathematically, waves are described in terms of time-varying fields, a "field" being a function of location in space. A propagating wave requires an "effort" field and a "flow" field, the latter being a vector (if we are working in two or three dimensions). The product of effort and flow is related to power (see "System equivalence"). For example, for sound waves in a non-viscous fluid, we might take the effort field as the pressure (a scalar), and the flow field as the fluid velocity (a vector). The product of these two is intensity (power per unit area). For electromagnetic waves, we shall take the effort field as the electric field and the flow field as the magnetizing field . Both of these are vectors, and their vector product is again the intensity (see "Poynting vector").


title: Total internal reflection

text: When a wave in (say) medium 1 is reflected off the interface between medium 1 and medium 2, the flow field in medium 1 is the vector sum of the flow fields due to the incident and reflected waves. If the reflection is oblique, the incident and reflected fields are not in opposite directions and therefore cannot cancel out at the interface; even if the reflection is total, either the normal component or the tangential component of the combined field (as a function of location and time) must be non-zero adjacent to the interface. Furthermore, the physical laws governing the fields will generally imply that one of the two components is "continuous" across the interface (that is, it does not suddenly change as we cross the interface); for example, for electromagnetic waves, one of the interface conditions is that the tangential component of is continuous if there is no surface current. Hence, even if the reflection is total, there must be some penetration of the flow field into medium 2; and this, in combination with the laws relating the effort and flow fields, implies that there will also be some penetration of the effort field. The same continuity condition implies that the variation ("waviness") of the field in medium 2 will be synchronized with that of the incident and reflected waves in medium 1.


title: Total internal reflection

text: But, if the reflection is total, the spatial penetration of the fields into medium 2 must be limited somehow, or else the total extent and hence the total energy of those fields would continue to increase, draining power from medium 1. Total reflection of a continuing wavetrain permits some energy to be stored in medium 2, but does not permit a "continuing" transfer of power from medium 1 to medium 2.


title: Total internal reflection

text: Thus, using mostly qualitative reasoning, we can conclude that total internal reflection must be accompanied by a wavelike field in the "external" medium, traveling along the interface in synchronism with the incident and reflected waves, but with some sort of limited spatial penetration into the "external" medium; such a field may be called an "evanescent wave".


title: Total internal reflection

text: Fig.9 shows the basic idea. The incident wave is assumed to be plane and sinusoidal. The reflected wave, for simplicity, is not shown. The evanescent wave travels to the right in lock-step with the incident and reflected waves, but its amplitude falls off with increasing distance from the interface.


title: Total internal reflection

text: If the internal reflection is to be total, there must be no diversion of the evanescent wave. Suppose, for example, that electromagnetic waves incident from glass (with a higher refractive index) to air (with a lower refractive index) at a certain angle of incidence are subject to TIR. And suppose that we have a third medium (often identical to the first) whose refractive index is sufficiently high that, if the third medium were to replace the second, we would get a standard transmitted wavetrain for the same angle of incidence. Then, if the third medium is brought within a distance of a few wavelengths from the surface of the first medium, where the evanescent wave has significant amplitude in the second medium, then the evanescent wave is effectively refracted into the third medium, giving non-zero transmission into the third medium, and therefore less than total reflection back into the first medium. As the amplitude of the evanescent wave decays across the air gap, the transmitted waves are attenuated, so that there is less transmission, and therefore more reflection, than there would be with no gap; but as long as there is "some" transmission, the reflection is less than total. This phenomenon is called "frustrated total internal reflection" (where "frustrated" negates "total"), abbreviated "frustrated TIR" or "FTIR".


title: Total internal reflection

text: Frustrated TIR can be observed by looking into the top of a glass of water held in one's hand (Fig.10). If the glass is held loosely, contact may not be sufficiently close and widespread to produce a noticeable effect. But if it is held more tightly, the ridges of one's fingerprints interact strongly with the evanescent waves, allowing the ridges to be seen through the otherwise totally reflecting glass-air surface.


title: Total internal reflection

text: The same effect can be demonstrated with microwaves, using paraffin wax as the "internal" medium (where the incident and reflected waves exist). In this case the permitted gap width might be (e.g.) 1cm or several cm, which is easily observable and adjustable.


title: Total internal reflection

text: The term "frustrated TIR" also applies to the case in which the evanescent wave is scattered by an object sufficiently close to the reflecting interface. This effect, together with the strong dependence of the amount of scattered light on the distance from the interface, is exploited in "total internal reflection microscopy".


title: Total internal reflection

text: The mechanism of FTIR is called "evanescent-wave coupling", and is a directly visible example of quantum tunneling. Due to the wave nature of matter, an electron has a non-zero probability of "tunneling" through a barrier, even if classical mechanics would say that its energy is insufficient. Similarly, due to the wave nature of light, a photon has a non-zero probability of crossing a gap, even if ray optics would say that its approach is too oblique.


title: Total internal reflection

text: Another reason why internal reflection may be less than total, even beyond the critical angle, is that the external medium may be "lossy" (less than perfectly transparent), in which case the external medium will absorb energy from the evanescent wave, so that the maintenance of the evanescent wave will draw power from the incident wave. The consequent less-than-total reflection is called "attenuated total reflectance" (ATR). This effect, and especially the frequency-dependence of the absorption, can be used to study the composition of an unknown external medium.


title: Total internal reflection

text: where is the (constant) complex amplitude vector,  is the imaginary unit,  is the wave vector (whose magnitude is the angular wavenumber),  is the position vector,  "ω" is the angular frequency,  is time, and it is understood that the "real part" of the expression is the physical field. The magnetizing field has the same form with the same and "ω". The value of the expression is unchanged if the position varies in a direction normal to ; hence "is normal to the wavefronts".


title: Total internal reflection

text: If "ℓ" is the component of in the direction of the field () can be written formula_12  If the argument of formula_13 is to be constant,  "ℓ" must increase at the velocity formula_14 known as the "phase velocity". This in turn is equal to formula_15 where is the phase velocity in the reference medium (taken as a vacuum) and is the local refractive index w.r.t. the reference medium. Solving for gives formula_16 i.e.


title: Total internal reflection

text: where is the wave vector for the transmitted wave (we assume isotropic media, but the transmitted wave is not "yet" assumed to be evanescent).


title: Total internal reflection

text: In Cartesian coordinates , let the region have refractive index and let the region have refractive index . Then the plane is the interface, and the axis is normal to the interface (Fig.11). Let and (in bold roman type) be the unit vectors in the and directions, respectively. Let the plane of incidence (containing the incident wave-normal and the normal to the interface) be the plane (the plane of the page), with the angle of incidence "θ" measured from towards . Let the angle of refraction, measured in the same sense, be "θ" ("t" for "transmitted", reserving "r" for "reflected").


title: Total internal reflection

text: In the case of TIR, the angle "θ" does not exist in the usual sense. But we can still interpret () for the transmitted (evanescent) wave, by allowing to be "complex". This becomes necessary when we write in terms of and thence in terms of using Snell's law:


title: Total internal reflection

text: where the undetermined sign is the opposite of that in (). For an "evanescent" transmitted wave – that is, one whose amplitude decays as increases – the undetermined sign in () must be "minus", so the undetermined sign in () must be "plus".


title: Total internal reflection

text: So the evanescent wave is a plane sinewave traveling in the direction, with an amplitude that decays exponentially in the direction (cf. Fig.9). It is evident that the energy stored in this wave likewise travels in the direction and does not cross the interface. Hence the Poynting vector generally has a component in the direction, but its component averages to zero (although its instantaneous component is not "identically" zero).


title: Total internal reflection

text: Eq.() indicates that the amplitude of the evanescent wave falls off by a factor as the coordinate (measured from the interface) increases by the distance formula_22 commonly called the "penetration depth" of the evanescent wave. Taking reciprocals of the first equation of (), we find that the penetration depth is


title: Total internal reflection

text: where "λ" is the wavelength in a vacuum, i.e. formula_24 Dividing the numerator and denominator by yields


title: Total internal reflection

text: where formula_26 is the wavelength in the second (external) medium. Hence we can plot in units of "λ", as a function of the angle of incidence, for various values of formula_27 (Fig.12). As "θ" decreases towards the critical angle, the denominator approaches zero, so that increases without limit – as is to be expected, because as soon as "θ" is "less" than critical, uniform plane waves are permitted in the external medium. As "θ" approaches 90° (grazing incidence), approaches a minimum


title: Total internal reflection

text: For incidence from water to air, or common glass to air, is not much different from . But is larger at smaller angles of incidence (Fig.12), and the amplitude may still be significant at distances of several times ; for example, because is just greater than 0.01, the evanescent wave amplitude within a distance of the interface is at least 1% of its value at the interface. Hence, speaking loosely, we tend to say that the evanescent wave amplitude is significant within "a few wavelengths" of the interface.


title: Total internal reflection

text: Between 1817 and 1823, Augustin-Jean Fresnel discovered that total internal reflection is accompanied by a non-trivial phase shift (that is, a phase shift that is not restricted to 0° or 180°), as the Fresnel reflection coefficient acquires a non-zero imaginary part. We shall now explain this effect for electromagnetic waves in the case of linear, homogeneous, isotropic, non-magnetic media. The phase shift turns out to be an "advance", which grows as the incidence angle increases beyond the critical angle, but which depends on the polarization of the incident wave.


title: Total internal reflection

text: In equations (), (), (), (), and (), we advance the phase by the angle "ϕ" if we replace by (that is, if we replace by ), with the result that the (complex) field is multiplied by . So a phase "advance" is equivalent to multiplication by a complex constant with a "negative" argument. This becomes more obvious when (e.g.) the field () is factored as formula_29 where the last factor contains the time-dependence.


title: Total internal reflection

text: To represent the polarization of the incident, reflected, or transmitted wave, the electric field adjacent to an interface can be resolved into two perpendicular components, known as the "s" and "p" components, which are parallel to the "surface" and the "plane" of incidence, respectively; in other words, the "s" and "p" components are respectively "square" and "parallel" to the plane of incidence.


title: Total internal reflection

text: For each component of polarization, the incident, reflected, or transmitted electric field in Eq.() has a certain direction, and can be represented by its (complex) scalar component in that direction. The reflection or transmission coefficient can then be defined as a "ratio" of complex components at the same point, or at infinitesimally separated points on opposite sides of the interface. But, in order to fix the "signs" of the coefficients, we must choose positive senses for the "directions". For the "s" components, the obvious choice is to say that the positive directions of the incident, reflected, and transmitted fields are all the same (e.g., the direction in Fig.11). For the "p" components, this article adopts the convention that the positive directions of the incident, reflected, and transmitted fields are inclined towards the same medium (that is, towards the same side of the interface, e.g. like the red arrows in Fig.11). But the reader should be warned that some books use a different convention for the "p" components, causing a different sign in the resulting formula for the reflection coefficient.


title: Total internal reflection

text: For the "s" polarization, let the reflection and transmission coefficients be and respectively. For the "p" polarization, let the corresponding coefficients be and . Then, for "linear, homogeneous, isotropic, non-magnetic" media, the coefficients are given by:


title: Total internal reflection

text: Now we suppose that the transmitted wave is evanescent. With the correct sign (+), substituting () into () gives


title: Total internal reflection

text: that is, is the index of the "internal" medium relative to the "external" one, or the index of the internal medium if the external one is a vacuum. So the magnitude of is 1, and the "argument" of is


title: Total internal reflection

text: Making the same substitution in (), we find that has the same denominator as with a positive real numerator (instead of a complex conjugate numerator) and therefore has "half" the argument of so that "the phase advance of the evanescent wave is half that of the reflected wave".


title: Total internal reflection

text: Making the same substitution in (), we again find that the phase advance of the evanescent wave is "half" that of the reflected wave.


title: Total internal reflection

text: Equations () and () apply when where "θ" is the angle of incidence and "θ" is the critical angle . These equations show that


title: Total internal reflection

text: For the reflection coefficients are given by equations () and (), and are "real", so that the phase shift is either 0° (if the coefficient is positive) or 180° (if the coefficient is negative).


title: Total internal reflection

text: which is positive for all angles of incidence with a transmitted ray (since ), giving a phase shift of zero.


title: Total internal reflection

text: which is negative for small angles (that is, near normal incidence), but changes sign at "Brewster's angle", where "θ" and "θ" are complementary. Thus the phase shift is 180° for small "θ" but switches to 0° at Brewster's angle. Combining the complementarity with Snell's law yields as Brewster's angle for dense-to-rare incidence.


title: Total internal reflection

text: Equations () and () are known as "Fresnel's sine law" and "Fresnel's tangent law". Both reduce to 0/0 at normal incidence, but yield the correct results in the limit as . That they have opposite signs as we approach normal incidence is an obvious disadvantage of the sign convention used in this article; the corresponding advantage is that they have the same signs at grazing incidence.


title: Total internal reflection

text: That completes the information needed to plot and for all angles of incidence. This is done in Fig.13, with in red and in blue, for three refractive indices. On the angle-of-incidence scale (horizontal axis), Brewster's angle is where (red) falls from 180° to 0°, and the critical angle is where both and (red and blue) start to rise again. To the left of the critical angle is the region of "partial" reflection, where both reflection coefficients are real (phase 0° or 180°) with magnitudes less than 1. To the right of the critical angle is the region of "total" reflection, where both reflection coefficients are complex with magnitudes equal to 1. In that region, the black curves show the phase advance of the "p" component relative to the "s" component:


title: Total internal reflection

text: It can be seen that a refractive index of 1.45 is not enough to give a 45° phase difference, whereas a refractive index of 1.5 is enough (by a slim margin) to give a 45° phase difference at two angles of incidence: about 50.2° and 53.3°.


title: Total internal reflection

text: This 45° relative shift is employed in Fresnel's invention, now known as the Fresnel rhomb, in which the angles of incidence are chosen such that the two internal reflections cause a total relative phase shift of 90° between the two polarizations of an incident wave. This device performs the same function as a birefringent quarter-wave plate, but is more achromatic (that is, the phase shift of the rhomb is less sensitive to wavelength). Either device may be used, for instance, to transform linear polarization to circular polarization (which Fresnel also discovered) and vice versa.


title: Total internal reflection

text: In Fig.13,  is computed by a final subtraction; but there are other ways of expressing it. Fresnel himself, in 1823, gave a formula for . Born and Wolf (1970, p.50) derive an expression for and find its maximum analytically.


title: Total internal reflection

text: For TIR of a beam with finite width, the variation in the phase shift with the angle of incidence gives rise to the "Goos–Hänchen effect", which is a lateral shift of the reflected beam within the plane of incidence. This effect applies to linear polarization in the "s" or "p" direction. The "Imbert–Fedorov effect" is an analogous effect for circular or elliptical polarization, and produces a shift perpendicular to the plane of incidence.


title: Total internal reflection

text: Optical fibers exploit total internal reflection to carry signals over long distances with little attenuation. They are used in telecommunication cables, and in image-forming fiberscopes such as colonoscopes.


title: Total internal reflection

text: In the catadioptric Fresnel lens, invented by Augustin-Jean Fresnel for use in lighthouses, the outer prisms use TIR to deflect light from the lamp through a greater angle than would be possible with purely refractive prisms, but with less absorption of light (and less risk of tarnishing) than with conventional mirrors.


title: Total internal reflection

text: Other reflecting prisms that use TIR include the following (with some overlap between the categories):


title: Total internal reflection

text: Polarizing prisms: Although the Fresnel rhomb, which converts between linear and elliptical polarization, is not birefringent (doubly refractive), there are other kinds of prisms that combine birefringence with TIR in such a way that light of a particular polarization is totally reflected while light of the orthogonal polarization is at least partly transmitted. Examples include the Nicol prism, Glan–Thompson prism, Glan–Foucault prism (or "Foucault prism"), and Glan–Taylor prism.


title: Total internal reflection

text: Rain sensors for automatic windscreen/windshield wipers have been implemented using the principle that total internal reflection will guide an infrared beam from a source to a detector if the outer surface of the windshield is dry, but any water drops on the surface will divert some of the light.


title: Total internal reflection

text: Edge-lit LED panels, used (e.g.) for backlighting of LCD computer monitors, exploit TIR to confine the LED light to the acrylic glass pane, except that some of the light is scattered by etchings on one side of the pane, giving an approximately uniform luminous emittance.


title: Total internal reflection

text: Total internal reflection microscopy (TIRM) uses the evanescent wave to illuminate small objects close to the reflecting interface. The consequent scattering of the evanescent wave (a form of frustrated TIR), makes the objects appear bright when viewed from the "external" side. In the "total internal reflection fluorescence microscope" (TIRFM), instead of relying on simple scattering, we choose an evanescent wavelength short enough to cause fluorescence (Fig.15). The high sensitivity of the illumination to the distance from the interface allows measurement of extremely small displacements and forces.


title: Total internal reflection

text: A beam-splitter cube uses frustrated TIR to divide the power of the incoming beam between the transmitted and reflected beams. The width of the air gap (or low-refractive-index gap) between the two prisms can be made adjustable, giving higher transmission and lower reflection for a narrower gap, or higher reflection and lower transmission for a wider gap.


title: Total internal reflection

text: Optical modulation can be accomplished by means of frustrated TIR with a rapidly variable gap. As the transmission coefficient is highly sensitive to the gap width (the function being approximately exponential until the gap is almost closed), this technique can achieve a large dynamic range.


title: Total internal reflection

text: Optical fingerprinting devices have used frustrated TIR to record images of persons' fingerprints without the use of ink (cf. Fig.11).


title: Total internal reflection

text: Gait analysis can be performed by using frustrated TIR with a high-speed camera, to capture and analyze footprints.


title: Total internal reflection

text: A gonioscope, used in optometry and ophthalmology for the diagnosis of glaucoma, "suppresses" TIR in order to look into the angle between the iris and the cornea. This view is usually blocked by TIR at the cornea-air interface. The gonioscope replaces the air with a higher-index medium, allowing transmission at oblique incidence, typically followed by reflection in a "mirror", which itself may be implemented using TIR.


title: Total internal reflection

text: Some multi-touch interactive tables and whiteboards utilise FTIR to detect fingers touching the screen. An infrared camera is placed behind the screen surface, which is edge-lit by infrared LEDs; when touching the surface FTIR causes some of the infrared light to escape the screen plane, and the camera sees this as bright areas. Computer vision software is then used to translate this into a series of coordinates and gestures.


title: Total internal reflection

text: The surprisingly comprehensive and largely correct explanations of the rainbow by Theodoric of Freiberg (written between 1304 and 1310) and Kamāl al-Dīn al-Fārisī (completed by 1309), although sometimes mentioned in connection with total internal reflection (TIR), are of dubious relevance because the internal reflection of sunlight in a spherical raindrop is "not" total. But, according to Carl Benjamin Boyer, Theodoric's treatise on the rainbow also classified optical phenomena under five causes, the last of which was "a total reflection at the boundary of two transparent media". Theodoric's work was forgotten until it was rediscovered by Giovanni Battista Venturi in 1814.


title: Total internal reflection

text: Theodoric having fallen into obscurity, the discovery of TIR was generally attributed to Johannes Kepler, who published his findings in his "Dioptrice" in 1611. Although Kepler failed to find the true law of refraction, he showed by experiment that for air-to-glass incidence, the incident and refracted rays rotated in the same sense about the point of incidence, and that as the angle of incidence varied through ±90°, the angle of refraction (as we now call it) varied through ±42°. He was also aware that the incident and refracted rays were interchangeable. But these observations did not cover the case of a ray incident from glass to air at an angle beyond 42°, and Kepler promptly concluded that such a ray could only be "reflected".


title: Total internal reflection

text: René Descartes rediscovered the law of refraction and published it in his "Dioptrique" of 1637. In the same work he mentioned the senses of rotation of the incident and refracted rays and the condition of TIR. But he neglected to discuss the limiting case, and consequently failed give an expression for the critical angle, although he could easily have done so.


title: Total internal reflection

text: Christiaan Huygens, in his "Treatise on Light" (1690), paid much attention to the threshold at which the incident ray is "unable to penetrate into the other transparent substance". Although he gave neither a name nor an algebraic expression for the critical angle, he gave numerical examples for glass-to-air and water-to-air incidence, noted the large change in the angle of refraction for a small change in the angle of incidence near the critical angle, and cited this as the cause of the rapid increase in brightness of the reflected ray as the refracted ray approaches the tangent to the interface. Huygens' insight is confirmed by modern theory: in Eqs.() and () above, there is nothing to say that the reflection coefficients increase exceptionally steeply as "θ" approaches 90°, except that, according to Snell's law, "θ" itself is an increasingly steep function of "θ".


title: Total internal reflection

text: Huygens offered an explanation of TIR within the same framework as his explanations of the laws of rectilinear propagation, reflection, ordinary refraction, and even the extraordinary refraction of "Iceland crystal" (calcite). That framework rested on two premises: first, every point crossed by a propagating wavefront becomes a source of secondary wavefronts ("Huygens' principle"); and second, given an initial wavefront, any subsequent position of the wavefront is the envelope (common tangent surface) of all the secondary wavefronts emitted from the initial position. All cases of reflection or refraction by a surface are then explained simply by considering the secondary waves emitted from that surface. In the case of refraction from a medium of slower propagation to a medium of faster propagation, there is a certain obliquity of incidence beyond which it is impossible for the secondary wavefronts to form a common tangent in the second medium; this is what we now call the critical angle. As the incident wavefront approaches this critical obliquity, the refracted wavefront becomes concentrated against the refracting surface, augmenting the secondary waves that produce the reflection back into the first medium.


title: Total internal reflection

text: Huygens' system even accommodated "partial" reflection at the interface between different media, albeit vaguely, by analogy with the laws of collisions between particles of different sizes. However, as long as the wave theory continued to assume longitudinal waves, it had no chance of accommodating polarization, hence no chance of explaining the polarization-dependence of extraordinary refraction, or of the partial reflection coefficient, or of the phase shift in TIR.


title: Total internal reflection

text: Isaac Newton rejected the wave explanation of rectilinear propagation, believing that if light consisted of waves, it would "bend and spread every way" into the shadows. His corpuscular theory of light explained rectilinear propagation more simply, and it accounted for the ordinary laws of refraction and reflection, including TIR, on the hypothesis that the corpuscles of light were subject to a force acting perpendicular to the interface. In this model, for dense-to-rare incidence, the force was an attraction back towards the denser medium, and the critical angle was the angle of incidence at which the normal velocity of the approaching corpuscle was just enough to reach the far side of the force field; at more oblique incidence, the corpuscle would be turned back. Newton gave what amounts to a formula for the critical angle, albeit in words: "as the Sines are which measure the Refraction, so is the Sine of Incidence at which the total Reflexion begins, to the Radius of the Circle".


title: Total internal reflection

text: Newton went beyond Huygens in two ways. First, not surprisingly, Newton pointed out the relationship between TIR and "dispersion": when a beam of white light approaches a glass-to-air interface at increasing obliquity, the most strongly-refracted rays (violet) are the first to be "taken out" by "total Reflexion", followed by the less-refracted rays. Second, he observed that total reflection could be "frustrated" (as we now say) by laying together two prisms, one plane and the other slightly convex; and he explained this simply by noting that the corpuscles would be attracted not only to the first prism, but also to the second.


title: Total internal reflection

text: In two other ways, however, Newton's system was less coherent. First, his explanation of "partial" reflection depended not only on the supposed forces of attraction between corpuscles and media, but also on the more nebulous hypothesis of "Fits of easy Reflexion" and "Fits of easy Transmission". Second, although his corpuscles could conceivably have "sides" or "poles", whose orientations could conceivably determine whether the corpuscles suffered ordinary or extraordinary refraction in "Island-Crystal", his geometric description of the extraordinary refraction was theoretically unsupported and empirically inaccurate.


title: Total internal reflection

text: William Hyde Wollaston, in the first of a pair of papers read to the Royal Society of London in 1802, reported his invention of a refractometer based on the critical angle of incidence from an internal medium of known "refractive power" (refractive index) to an external medium whose index was to be measured. With this device, Wollaston measured the "refractive powers" of numerous materials, some of which were too opaque to permit direct measurement of an angle of refraction. Translations of his papers were published in France in 1803, and apparently came to the attention of Pierre-Simon Laplace.


title: Total internal reflection

text: According to Laplace's elaboration of Newton's theory of refraction, a corpuscle incident on a plane interface between two homogeneous isotropic media was subject to a force field that was symmetrical about the interface. If both media were transparent, total reflection would occur if the corpuscle were turned back before it exited the field in the second medium. But if the second medium were opaque, reflection would not be total unless the corpuscle were turned back before it left the "first" medium; this required a larger critical angle than the one given by Snell's law, and consequently impugned the validity of Wollaston's method for opaque media. Laplace combined the two cases into a single formula for the relative refractive index in terms of the critical angle (minimum angle of incidence for TIR). The formula contained a parameter which took one value for a transparent external medium and another value for an opaque external medium. Laplace's theory further predicted a relationship between refractive index and density for a given substance.


title: Total internal reflection

text: In 1807, Laplace's theory was tested experimentally by his protégé, Étienne-Louis Malus. Taking Laplace's formula for the refractive index as given, and using it to measure the refractive index of bees' wax in the liquid (transparent) state and the solid (opaque) state at various temperatures (hence various densities), Malus verified Laplace's relationship between refractive index and density.


title: Total internal reflection

text: But Laplace's theory implied that if the angle of incidence exceeded his modified critical angle, the reflection would be total even if the external medium was absorbent. Clearly this was wrong: in Eqs.() above, there is no threshold value of the angle "θ" beyond which "κ" becomes infinite; so the penetration depth of the evanescent wave (1/"κ") is always non-zero, and the external medium, if it is at all lossy, will attenuate the reflection. As to why Malus apparently observed such an angle for opaque wax, we must infer that there was a certain angle beyond which the attenuation of the reflection was so small that ATR was visually indistinguishable from TIR.


title: Total internal reflection

text: Fresnel came to the study of total internal reflection through his research on polarization. In 1811, François Arago discovered that polarized light was apparently "depolarized" in an orientation-dependent and color-dependent manner when passed through a slice of doubly-refractive crystal: the emerging light showed colors when viewed through an analyzer (second polarizer). "Chromatic polarization", as this phenomenon came to be called, was more thoroughly investigated in 1812 by Jean-Baptiste Biot. In 1813, Biot established that one case studied by Arago, namely quartz cut perpendicular to its optic axis, was actually a gradual rotation of the plane of polarization with distance.


title: Total internal reflection

text: In 1816, Fresnel offered his first attempt at a "wave-based" theory of chromatic polarization. Without (yet) explicitly invoking transverse waves, his theory treated the light as consisting of two perpendicularly polarized components. In 1817 he noticed that plane-polarized light seemed to be partly depolarized by total internal reflection, if initially polarized at an acute angle to the plane of incidence. By including total internal reflection in a chromatic-polarization experiment, he found that the apparently depolarized light was a mixture of components polarized parallel and perpendicular to the plane of incidence, and that the total reflection introduced a phase difference between them. Choosing an appropriate angle of incidence (not yet exactly specified) gave a phase difference of 1/8 of a cycle. Two such reflections from the "parallel faces" of "two coupled prisms" gave a phase difference of 1/4 of a cycle. In that case, if the light was initially polarized at 45° to the plane of incidence and reflection, it appeared to be "completely" depolarized after the two reflections. These findings were reported in a memoir submitted and read to the French Academy of Sciences in November 1817.


title: Total internal reflection

text: In 1821, Fresnel derived formulae equivalent to his sine and tangent laws Eqs.() and (), above by modeling light waves as transverse elastic waves with vibrations perpendicular to what had previously been called the plane of polarization. Using old experimental data, he promptly confirmed that the equations correctly predicted the direction of polarization of the reflected beam when the incident beam was polarized at 45° to the plane of incidence, for light incident from air onto glass or water. The experimental confirmation was reported in a "postscript" to the work in which Fresnel expounded his mature theory of chromatic polarization, introducing transverse waves. Details of the derivation were given later, in a memoir read to the academy in January 1823. The derivation combined conservation of energy with continuity of the "tangential" vibration at the interface, but failed to allow for any condition on the "normal" component of vibration.


title: Total internal reflection

text: Meanwhile, in a memoir submitted in December 1822, Fresnel coined the terms "linear polarization", "circular polarization", and "elliptical polarization". For "circular" polarization, the two perpendicular components were a quarter-cycle (±90°) out of phase.


title: Total internal reflection

text: The new terminology was useful in the memoir of January 1823, containing the detailed derivations of the sine and tangent laws: in that same memoir, Fresnel found that for angles of incidence greater than the critical angle, the resulting reflection coefficients were complex with unit magnitude. Noting that the magnitude represented the amplitude ratio as usual, he guessed that the argument represented the phase shift, and verified the hypothesis by experiment. The verification involved


title: Total internal reflection

text: This procedure was necessary because, with the technology of the time, one could not measure the "s" and "p" phase-shifts directly, and one could not measure an arbitrary degree of ellipticality of polarization, such as might be caused by the difference between the phase shifts. But one could verify that the polarization was "circular", because the brightness of the light was then insensitive to the orientation of the analyzer.


title: Total internal reflection

text: For glass with a refractive index of 1.51, Fresnel calculated that a 45° phase difference between the two reflection coefficients (hence a 90° difference after two reflections) required an angle of incidence of 48°37' or 54°37'. He cut a rhomb to the latter angle and found that it performed as expected. Thus the specification of the Fresnel rhomb was completed. Similarly, Fresnel calculated and verified the angle of incidence that would give a 90° phase difference after "three" reflections at the same angle, and "four" reflections at the same angle. In each case there were two solutions, and in each case he reported that the larger angle of incidence gave an accurate circular polarization (for an initial linear polarization at 45° to the plane of reflection). For the case of three reflections he also tested the smaller angle, but found that it gave some coloration due to the proximity of the critical angle and its slight dependence on wavelength. (Compare Fig.13 above, which shows that the phase difference is more sensitive to the refractive index for smaller angles of incidence.)


title: Total internal reflection

text: For added confidence, Fresnel predicted and verified that four total internal reflections at 68°27' would give an accurate circular polarization if two of the reflections had water as the external medium while the other two had air, but not if the reflecting surfaces were all wet or all dry.