In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light travels through the material. It is defined as n = c v, where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1/1.333 times as fast in vacuum as in water. Increasing refractive index corresponds to decreasing speed of light in the material; the refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, n1 sinθ1 = n2 sinθ2, where θ1 and θ2 are the angles of incidence and refraction of a ray crossing the interface between two media with refractive indices n1 and n2; the refractive indices determine the amount of light, reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity and Brewster's angle.. The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum.

This implies that vacuum has a refractive index of 1, that the frequency of the wave is not affected by the refractive index. As a result, the perceived color of the refracted light to a human eye which depends on the frequency is not affected by the refraction or the refractive index of the medium; the refractive index varies with wavelength, so white light will split into its constituent colors. This is called dispersion, it can be observed in prisms and rainbows, as chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex-valued refractive index; the imaginary part handles the attenuation, while the real part accounts for refraction. The concept of refractive index applies within the full electromagnetic spectrum, from X-rays to radio waves, it can be applied to wave phenomena such as sound. In this case the speed of sound is used instead of that of light, a reference medium other than vacuum must be chosen; the refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299792458 m/s, the phase velocity v of light in the medium, n = c v.

The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves. The definition above is sometimes referred to as the absolute refractive index or the absolute index of refraction to distinguish it from definitions where the speed of light in other reference media than vacuum is used. Air at a standardized pressure and temperature has been common as a reference medium. Thomas Young was the person who first used, invented, the name "index of refraction", in 1807. At the same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers; the ratio had the disadvantage of different appearances. Newton, who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396". Hauksbee, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9".

Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1. Young did not use a symbol for the index of refraction, in 1807. In the next years, others started using different symbols: n, m, µ; the symbol n prevailed. For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the adjacent table; these values are measured at the yellow doublet D-line of sodium, with a wavelength of 589 nanometers, as is conventionally done. Gases at atmospheric pressure have refractive indices close to 1 because of their low density. All solids and liquids have refractive indices above 1.3, with aerogel as the clear exception. Aerogel is a low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the other end of the range with a refractive index as high as 2.65. Most plastics have refractive indices in the range from 1.3 to 1.7, but some high-refractive-index polymers can have values as high as 1.76.

For infrared light refractive indices can be higher. Germanium is transparent in the wavelength region from 2 to 14 µm and has a refractive index of about 4. A type of new materials, called topological insulator, was found holding higher refractive index of up to 6 in near to mid infrared frequency range. Moreover, topological insulator material are transparent; these excellent properties make them a type of significant materials for infrared optics. According to the theory of relativity, no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be less than 1; the refractive index measures the phase velocity of light. The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, thereby give a refractive index below 1; this can occur close to resonance frequencies, for absorbing media, in plasmas, for X-rays. In the X-ray regime the refractive indices are lower than but cl

In Northern Ireland before the Troubles ended, low-level petty crime was not as common as in the rest of Ireland or the UK. Since the Good Friday Agreement was signed in 1998, there has been more low-level crimes being committed, although statistics show that some places in Northern Ireland have some of the lowest crime rates in Western Europe; the type of crime committed in Northern Ireland varies although robbery, racketeering, burglary, joyriding and assault are the main types. In recent times Tiger kidnapping has been used in robberies on banks and post offices. Over the three years 2011–14, the homicide rate in Northern Ireland was 0.9 per 100,000 inhabitants per year. This is a similar figure to the UK average, the murder rate in the Republic of Ireland, most Western European nations, a region which has among the lowest homicide rates globally. During The Troubles, homicide rates were higher: at their height in 1972 there were 479 deaths caused either by terrorism or Security Forces' action – around 31 per 100,000, similar to homicide rates in 2010s Colombia or South Africa.

During the period 1976–1993, most years saw 60–100 deaths related to The Troubles, or around 4.0–6.5/100,000 per annum. Although there are repeated terrorism-related attempts at murder, few succeed. Since the re-establishment of devolved government in 2007, two soldiers and one police officer were murdered in 2009, with a further police officer murdered in 2011. Other incidents have seen life-changing injuries to police officers caused by explosions. Since the historic signing of the Good Friday Agreement most large terrorist groups have since decommissioned their weapons or ceased military operations, these groups include the Provisional Irish Republican Army, Ulster Volunteer Force, Loyalist Volunteer Force, Ulster Defence Association, Irish National Liberation Army and some minor groups. Though the larger organisations have decommissioned and are complying with the terms of the 1998 Agreement there is still on the Republican side so called "Dissident republicans" who oppose the Agreement.

These elements are short of numbers but still pose a serious threat, the threat became clear in March 2009, when two Soldiers were killed in County Antrim while collecting a pizza just outside the barracks, the Real Irish Republican Army claimed responsibility for the shooting. Two days another group called the Continuity IRA shot dead a police officer in Craigavon, County Armagh; the officer was responding to a call from a lady in the area when he was shot in the back of the head by a sniper. More a large number of bombs have been discovered in counties Londonderry and Tyrone. Although none of the devices detonated the police and British Army said they were getting more "sophisticated", for instance in February 2008 the Army defused a 100 lb device in County Down September 2009 a 600 lb device was made safe; these groups do not have the same support as PIRA once had, nor the same weaponry but they are still capable of murder and bombings. On Friday 16 October 2009, at around 07:30 BST a car bomb exploded under the car of a police officer's wife in the large Unionist area of east Belfast and what is considered to be an area controlled by the Ulster Defence Association, the device was intended to kill her husband whom she drives to work but coincidentally was not present in the car at the time.

The woman escaped with minor injuries. The Real IRA claimed responsibility for this incident. Between 2007 and 2009, there were on average in Northern Ireland around seven or more Hoax Bomb Alerts each week, but some alerts are genuine, they are so common that there is a permanent Bomb Disposal team of the British Army stationed in Northern Ireland. The main areas are County Down, County Antrim and Belfast. Due to the threat posed to the society in Northern Ireland, all objects have to be treated with suspect care and controlled explosions are common place in some areas. On 14 October 2009, the Police Service of Northern Ireland got a call stating that a 600 lb bomb had been left in a van abandoned on a bridge in a village in County Tyrone, the Army carried out a controlled explosion on the device which turned out to be a hoax. A British newspaper published an article that said, "Republican bomb alerts total 750 in two years", an average of 7.21 a week or just over one a day. Until racism did not pose a substantial problem Northern Ireland but due to new countries joining the European Union and the freedom of movement of people within the union, there has been an influx of people from countries such as, Poland and surrounding areas.

In June 2009, attacks on such people increased to the stage that around 100 Roma gypsies from Romania had to be moved to safer houses because their windows had been smashed and racist graffiti dubbed on their houses in a Loyalist area of south Belfast. The theft of Automated Teller Machines in recent years is on the rise, it is not known if the paramilitary groups are the main perpetrators or just organised crime groups; the theft of such a machine in Northern Ireland involves pulling the ATM from the wall with a large digger putting it in a waiting vehicle. The BBC reported on 21 October 2009 that three such incidents had occurred in one week, all involving a digger. In November 2009 after a'smash and grab' incident in Dungannon, County Tyrone the Irish News newspaper released an article that revealed that there has been 13 such incidents since March 2009 in Northern Ireland

Alice Caroline Kipling was one of the MacDonald sisters, four Scottish women of the Victorian era, notable for their contribution to the arts and their marriages to well-known men. A writer and poet, she was the mother of the author Rudyard Kipling. Alice Kipling was born as Alice Caroline MacDonald in Sheffield, England in 1837, the first of the four daughters of Reverend George Browne MacDonald, a Wesleyan Methodist minister, Hannah Jones. In her youth Alice MacDonald wrote sonnets, she was described as: "...slender, pale complexion, dark brown hair and grey eyes, with black lashes and delicately pencilled eyebrows. In those eyes lay the chief fascination of her face. So expressive were they that they seemed to deepen or pale in colour according to passing emotion.. it was impossible to predict how she would act at any given point. There was a certain fascination in this, fascinating she was..." John Lockwood Kipling and Alice MacDonald met in 1863 and courted at Rudyard Lake in Rudyard, England.

They married in St Mary Abbots Church, Kensington on 18 March 1865 and moved to India the same year. They had been so moved by the beauty of the Rudyard Lake area that when their first child was born they named him after it. Two of Alice's sisters married artists: Georgiana was married to the painter Edward Burne-Jones, her sister Agnes to Edward Poynter. Kipling's most famous relative was his first cousin, Stanley Baldwin, Conservative Prime Minister three times in the 1920s and'30s, he was her husband Alfred Baldwin. Harry Ricketts in his biography of Rudyard Kipling wrote of Alice that she: "...was lively and talented. She wrote and published poems, arranged songs and sewed and knew how to run a household, her racy, gossipy letters captured acquaintances and social situations in phrases that flickered between mischief and malice. Frederic, her younger brother, thought her'keen and versatile' beyond anyone he had known. She'saw things at a glance', he recalled,'and dispatched them in a word'.

Her poems showed another side, revealing a deep strain of melancholy..." In January 1865, John Lockwood Kipling was made Architectural Sculptor and Professor of Modelling at the School of Art and Industry in Bombay. Alice became the mother of Rudyard Kipling on 31 December 1865. In Simla, Lord Dufferin once said, "Dullness and Mrs Kipling cannot exist in the same room." Alice Kipling and John Lockwood Kipling remained in India for many years, including during the period when their children were being educated in England. Alice Kipling published much less of her writing than did her sisters, but some of her poems were published in collections including Quartette and in Hand in Hand: Verses by a Mother and a Daughter, the latter a collaboration with her daughter Alice Fleming, she died in November 1910, three days after suffering a heart attack and is buried beside her husband in the churchyard of St John the Baptist in Tisbury in Wiltshire, England. Alice Kipling features in the 2002 biography A Circle of Sisters: Alice Kipling, Georgiana Burne-Jones, Agnes Poynter and Louisa Baldwin by Judith Flanders.

Portraits of Alice Kipling on the