In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is thus the inverse of the spatial frequency. Wavelength is determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. Wavelength is designated by the Greek letter lambda; the term wavelength is sometimes applied to modulated waves, to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids. Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency of the wave: waves with higher frequencies have shorter wavelengths, lower frequencies have longer wavelengths. Wavelength depends on the medium. Examples of wave-like phenomena are sound waves, water waves and periodic electrical signals in a conductor.
A sound wave is a variation in air pressure, while in light and other electromagnetic radiation the strength of the electric and the magnetic field vary. Water waves are variations in the height of a body of water. In a crystal lattice vibration, atomic positions vary. Wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. For example, in sinusoidal waves over deep water a particle near the water's surface moves in a circle of the same diameter as the wave height, unrelated to wavelength; the range of wavelengths or frequencies for wave phenomena is called a spectrum. The name originated with the visible light spectrum but now can be applied to the entire electromagnetic spectrum as well as to a sound spectrum or vibration spectrum. In linear media, any wave pattern can be described in terms of the independent propagation of sinusoidal components; the wavelength λ of a sinusoidal waveform traveling at constant speed v is given by λ = v f, where v is called the phase speed of the wave and f is the wave's frequency.
In a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear. In the case of electromagnetic radiation—such as light—in free space, the phase speed is the speed of light, about 3×108 m/s, thus the wavelength of a 100 MHz electromagnetic wave is about: 3×108 m/s divided by 108 Hz = 3 metres. The wavelength of visible light ranges from deep red 700 nm, to violet 400 nm. For sound waves in air, the speed of sound is 343 m/s; the wavelengths of sound frequencies audible to the human ear are thus between 17 m and 17 mm, respectively. Note that the wavelengths in audible sound are much longer than those in visible light. A standing wave is an undulatory motion. A sinusoidal standing wave includes stationary points of no motion, called nodes, the wavelength is twice the distance between nodes; the upper figure shows three standing waves in a box. The walls of the box are considered to require the wave to have nodes at the walls of the box determining which wavelengths are allowed.
For example, for an electromagnetic wave, if the box has ideal metal walls, the condition for nodes at the walls results because the metal walls cannot support a tangential electric field, forcing the wave to have zero amplitude at the wall. The stationary wave can be viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities. Wavelength and wave velocity are related just as for a traveling wave. For example, the speed of light can be determined from observation of standing waves in a metal box containing an ideal vacuum. Traveling sinusoidal waves are represented mathematically in terms of their velocity v, frequency f and wavelength λ as: y = A cos = A cos where y is the value of the wave at any position x and time t, A is the amplitude of the wave, they are commonly expressed in terms of wavenumber k and angular frequency ω as: y = A cos = A cos in which wavelength and wavenumber are related to velocity and frequency as: k = 2 π λ = 2 π f v = ω
Spectroscopy is the study of the interaction between matter and electromagnetic radiation. Spectroscopy originated through the study of visible light dispersed according to its wavelength, by a prism; the concept was expanded to include any interaction with radiative energy as a function of its wavelength or frequency, predominantly in the electromagnetic spectrum, though matter waves and acoustic waves can be considered forms of radiative energy. Spectroscopic data are represented by an emission spectrum, a plot of the response of interest as a function of wavelength or frequency. Spectroscopy in the electromagnetic spectrum, is a fundamental exploratory tool in the fields of physics and astronomy, allowing the composition, physical structure and electronic structure of matter to be investigated at atomic scale, molecular scale, macro scale, over astronomical distances. Important applications arise from biomedical spectroscopy in the areas of tissue analysis and medical imaging. Spectroscopy and spectrography are terms used to refer to the measurement of radiation intensity as a function of wavelength and are used to describe experimental spectroscopic methods.
Spectral measurement devices are referred to as spectrometers, spectrophotometers, spectrographs or spectral analyzers. Daily observations of color can be related to spectroscopy. Neon lighting is a direct application of atomic spectroscopy. Neon and other noble gases have characteristic emission frequencies. Neon lamps use collision of electrons with the gas to excite these emissions. Inks and paints include chemical compounds selected for their spectral characteristics in order to generate specific colors and hues. A encountered molecular spectrum is that of nitrogen dioxide. Gaseous nitrogen dioxide has a characteristic red absorption feature, this gives air polluted with nitrogen dioxide a reddish-brown color. Rayleigh scattering is a spectroscopic scattering phenomenon. Spectroscopic studies were central to the development of quantum mechanics and included Max Planck's explanation of blackbody radiation, Albert Einstein's explanation of the photoelectric effect and Niels Bohr's explanation of atomic structure and spectra.
Spectroscopy is used in physical and analytical chemistry because atoms and molecules have unique spectra. As a result, these spectra can be used to detect and quantify information about the atoms and molecules. Spectroscopy is used in astronomy and remote sensing on Earth. Most research telescopes have spectrographs; the measured spectra are used to determine the chemical composition and physical properties of astronomical objects. One of the central concepts in spectroscopy is its corresponding resonant frequency. Resonances were first characterized in mechanical systems such as pendulums. Mechanical systems that vibrate or oscillate will experience large amplitude oscillations when they are driven at their resonant frequency. A plot of amplitude vs. excitation frequency will have a peak centered at the resonance frequency. This plot is one type of spectrum, with the peak referred to as a spectral line, most spectral lines have a similar appearance. In quantum mechanical systems, the analogous resonance is a coupling of two quantum mechanical stationary states of one system, such as an atom, via an oscillatory source of energy such as a photon.
The coupling of the two states is strongest when the energy of the source matches the energy difference between the two states. The energy of a photon is related to its frequency by E = h ν where h is Planck's constant, so a spectrum of the system response vs. photon frequency will peak at the resonant frequency or energy. Particles such as electrons and neutrons have a comparable relationship, the de Broglie relations, between their kinetic energy and their wavelength and frequency and therefore can excite resonant interactions. Spectra of atoms and molecules consist of a series of spectral lines, each one representing a resonance between two different quantum states; the explanation of these series, the spectral patterns associated with them, were one of the experimental enigmas that drove the development and acceptance of quantum mechanics. The hydrogen spectral series in particular was first explained by the Rutherford-Bohr quantum model of the hydrogen atom. In some cases spectral lines are well separated and distinguishable, but spectral lines can overlap and appear to be a single transition if the density of energy states is high enough.
Named series of lines include the principal, sharp and fundamental series. Spectroscopy is a sufficiently broad field that many sub-disciplines exist, each with numerous implementations of specific spectroscopic techniques; the various implementations and techniques can be classified in several ways. The types of spectroscopy are distinguished by the type of radiative energy involved in the interaction. In many applications, the spectrum is determined by measuring changes in the intensity or frequency of this energy; the types of radiative energy studied include: Electromagnetic radiation was the first source of energy used for spectroscopic studies. Techniques that employ electromagnetic radiation are classified by the wavelength region of the spectrum and include microwave, terahe
In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. At least two of the flat surfaces must have an angle between them; the exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, in colloquial use "prism" refers to this type; some types of optical prism are not in fact in the shape of geometric prisms. Prisms can be made from any material, transparent to the wavelengths for which they are designed. Typical materials include glass and fluorite. A dispersive prism can be used to break light up into its constituent spectral colors. Furthermore, prisms can be used to reflect light, or to split light into components with different polarizations. Light changes speed; this speed change causes the light to enter the new medium at a different angle. The degree of bending of the light's path depends on the angle that the incident beam of light makes with the surface, on the ratio between the refractive indices of the two media.
The refractive index of many materials varies with the wavelength or color of the light used, a phenomenon known as dispersion. This causes light of different colors to be refracted differently and to leave the prism at different angles, creating an effect similar to a rainbow; this can be used to separate a beam of white light into its constituent spectrum of colors. A similar separation happens with iridescent materials, such as a soap bubble. Prisms will disperse light over a much larger frequency bandwidth than diffraction gratings, making them useful for broad-spectrum spectroscopy. Furthermore, prisms do not suffer from complications arising from overlapping spectral orders, which all gratings have. Prisms are sometimes used for the internal reflection at the surfaces rather than for dispersion. If light inside the prism hits one of the surfaces at a sufficiently steep angle, total internal reflection occurs and all of the light is reflected; this makes a prism a useful substitute for a mirror in some situations.
Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using Snell's law at each interface. For the prism shown at right, the indicated angles are given by θ 0 ′ = arcsin θ 1 = α − θ 0 ′ θ 1 ′ = arcsin θ 2 = θ 1 ′ − α. All angles are positive in the direction shown in the image. For a prism in air n 0 = n 2 ≃ 1. Defining n = n 1, the deviation angle δ is given by δ = θ 0 + θ 2 = θ 0 + arcsin − α If the angle of incidence θ 0 and prism apex angle α are both small, sin θ ≈ θ and arcsin x ≈ x if the angles are expressed in radians; this allows the nonlinear equation in the deviation angle δ to be approximated by δ ≈ θ 0 − α + = θ 0 − α + n α − θ 0 = α
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an atom or molecule making a transition from a high energy state to a lower energy state. The photon energy of the emitted photon is equal to the energy difference between the two states. There are many possible electron transitions for each atom, each transition has a specific energy difference; this collection of different transitions, leading to different radiated wavelengths, make up an emission spectrum. Each element's emission spectrum is unique. Therefore, spectroscopy can be used to identify the elements in matter of unknown composition; the emission spectra of molecules can be used in chemical analysis of substances. In physics, emission is the process by which a higher energy quantum mechanical state of a particle becomes converted to a lower one through the emission of a photon, resulting in the production of light; the frequency of light emitted is a function of the energy of the transition.
Since energy must be conserved, the energy difference between the two states equals the energy carried off by the photon. The energy states of the transitions can lead to emissions over a large range of frequencies. For example, visible light is emitted by the coupling of electronic states in molecules. On the other hand, nuclear shell transitions can emit high energy gamma rays, while nuclear spin transitions emit low energy radio waves; the emittance of an object quantifies. This may be related to other properties of the object through the Stefan–Boltzmann law. For most substances, the amount of emission varies with the temperature and the spectroscopic composition of the object, leading to the appearance of color temperature and emission lines. Precise measurements at many wavelengths allow the identification of a substance via emission spectroscopy. Emission of radiation is described using semi-classical quantum mechanics: the particle's energy levels and spacings are determined from quantum mechanics, light is treated as an oscillating electric field that can drive a transition if it is in resonance with the system's natural frequency.
The quantum mechanics problem is treated using time-dependent perturbation theory and leads to the general result known as Fermi's golden rule. The description has been superseded by quantum electrodynamics, although the semi-classical version continues to be more useful in most practical computations; when the electrons in the atom are excited, for example by being heated, the additional energy pushes the electrons to higher energy orbitals. When the electrons fall back down and leave the excited state, energy is re-emitted in the form of a photon; the wavelength of the photon is determined by the difference in energy between the two states. These emitted photons form the element's spectrum; the fact that only certain colors appear in an element's atomic emission spectrum means that only certain frequencies of light are emitted. Each of these frequencies are related to energy by the formula: E photon = h ν,where E photon is the energy of the photon, ν is its frequency, h is Planck's constant.
This concludes. The principle of the atomic emission spectrum explains the varied colors in neon signs, as well as chemical flame test results; the frequencies of light that an atom can emit are dependent on states. When excited, an electron moves to orbital; when the electron falls back to its ground level the light is emitted. The above picture shows the visible light emission spectrum for hydrogen. If only a single atom of hydrogen were present only a single wavelength would be observed at a given instant. Several of the possible emissions are observed because the sample contains many hydrogen atoms that are in different initial energy states and reach different final energy states; these different combinations lead to simultaneous emissions at different wavelengths. As well as the electronic transitions discussed above, the energy of a molecule can change via rotational and vibronic transitions; these energy transitions lead to spaced groups of many different spectral lines, known as spectral bands.
Unresolved band spectra may appear as a spectral continuum. Light consists of electromagnetic radiation of different wavelengths. Therefore, when the elements or their compounds are heated either on a flame or by an electric arc they emit energy in the form of light. Analysis of this light, with the help of a spectroscope gives us a discontinuous spectrum. A spectroscope or a spectrometer is an instrument, used for separating the components of light, which have different wavelengths; the spectrum appears in a series of lines called the line spectrum. This line spectrum is called an atomic spectrum; each element has a different atomic spectrum. The production of line spectra by the atoms of an element indicate that an atom can radiate only a certain amount of energy; this leads to the conclusion that bound electrons cannot have just any amount of energy but only a certain amount of energy. The emission spectrum can be used to determine the composition of a material, since it is different for each element of the periodic table.
One example is astronomical spectroscopy: iden
Arthur Schopenhauer was a German philosopher. He is best known for his 1818 work The World as Will and Representation, wherein he characterizes the phenomenal world as the product of a blind and insatiable metaphysical will. Proceeding from the transcendental idealism of Immanuel Kant, Schopenhauer developed an atheistic metaphysical and ethical system, described as an exemplary manifestation of philosophical pessimism, rejecting the contemporaneous post-Kantian philosophies of German idealism. Schopenhauer was among the first thinkers in Western philosophy to share and affirm significant tenets of Eastern philosophy, having arrived at similar conclusions as the result of his own philosophical work. Though his work failed to garner substantial attention during his life, Schopenhauer has had a posthumous impact across various disciplines, including philosophy and science, his writing on aesthetics and psychology influenced thinkers and artists throughout the 19th and 20th centuries. Those who cited his influence include Friedrich Nietzsche, Richard Wagner, Leo Tolstoy, Ludwig Wittgenstein, Erwin Schrödinger, Otto Rank, Gustav Mahler, Joseph Campbell, Albert Einstein, Carl Jung, Thomas Mann, Émile Zola, George Bernard Shaw, Jorge Luis Borges and Samuel Beckett.
Schopenhauer was born on 22 February 1788, in the city of Danzig on Heiligegeistgasse, the son of Johanna Schopenhauer and Heinrich Floris Schopenhauer, both descendants of wealthy German-Dutch patrician families. Neither of them were religious,; when Danzig became part of Prussia in 1793, Heinrich moved to Hamburg—a free city with a republican constitution, protected by Britain and Holland against Prussian aggression—although his firm continued trading in Danzig where most of their extended families remained. Adele, Arthur's only sibling was born on 12 July 1797. In 1797 Arthur was sent to Le Havre to live for two years with the family of his father's business associate, Grégoire de Blésimaire, he seemed to enjoy his stay there, learned to speak French fluently and started a friendship with Jean Anthime Grégoire de Blésimaire, his peer, which lasted for a large part of their lives. As early as 1799, Arthur started playing the flute. In 1803 he joined his parents on their long tour of Holland, France, Switzerland and Prussia.
Heinrich gave his son a choice – he could stay at home and start preparations for university education, or he could travel with them and continue his merchant education. Arthur deeply regretted his choice because he found his merchant training tedious, he spent twelve weeks of the tour attending a school in Wimbledon where he was unhappy and appalled by strict but intellectually shallow Anglican religiosity, which he continued to criticize in life despite his general Anglophilia. He was under pressure from his father who became critical of his educational results. Heinrich became so fussy that his wife started to doubt his mental health. In 1805, Heinrich died by drowning in a canal by their home in Hamburg. Although it was possible that his death was accidental, his wife and son believed that it was suicide because he was prone to unsociable behavior and depression which became pronounced in his last months of life. Arthur showed similar moodiness since his youth and acknowledged that he inherited it from his father.
His mother Johanna was described as vivacious and sociable. Despite the hardships, Schopenhauer seemed to like his father and mentioned him always in a positive light. Heinrich Schopenhauer left the family with a significant inheritance, split in three among Johanna and the children. Arthur Schopenhauer was entitled to control of his part, he invested it conservatively in government bonds and earned annual interest, more than double the salary of a university professor. Arthur spent two years as a merchant in honor of his dead father, because of his own doubts about being too old to start a life of a scholar. Most of his prior education was practical merchant training and he had some trouble with learning Latin, a prerequisite for any academic career, his mother moved, with her daughter Adele, to Weimar—then the centre of German literature—to enjoy social life among writers and artists. Arthur and his mother were not on good terms. In one letter to him she wrote, "You are unbearable and burdensome, hard to live with.
Arthur left his mother, though she died 24 years they never met again. Some of negative opinions of the philosopher about women may be rooted in his troubled relationship with his mother. Arthur lived in Hamburg with his friend Jean Anthime, studying to become a merchant. After quitting his merchant apprenticeship, with some encouragement from his mother, he dedicated himself to studies at the Gotha gymnasium in Saxe-Gotha-Altenburg, but he enjoyed social life among local nobility spending large amounts of money which caused concern to his frugal
The human eye is an organ which reacts to light and pressure. As a sense organ, the mammalian eye allows vision. Human eyes help to provide a three dimensional, moving image coloured in daylight. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth; the human eye can differentiate between about 10 million colors and is capable of detecting a single photon. Similar to the eyes of other mammals, the human eye's non-image-forming photosensitive ganglion cells in the retina receive light signals which affect adjustment of the size of the pupil and suppression of the hormone melatonin and entrainment of the body clock; the eye is not shaped like a perfect sphere, rather it is a fused two-piece unit, composed of the anterior segment and the posterior segment. The anterior segment is made up of the cornea and lens; the cornea is transparent and more curved, is linked to the larger posterior segment, composed of the vitreous, retina and the outer white shell called the sclera.
The cornea is about 11.5 mm in diameter, 1/2 mm in thickness near its center. The posterior chamber constitutes the remaining five-sixths; the cornea and sclera are connected by an area termed the limbus. The iris is the pigmented circular structure concentrically surrounding the center of the eye, the pupil, which appears to be black; the size of the pupil, which controls the amount of light entering the eye, is adjusted by the iris' dilator and sphincter muscles. Light energy enters the eye through the cornea, through the pupil and through the lens; the lens shape is controlled by the ciliary muscle. Photons of light falling on the light-sensitive cells of the retina are converted into electrical signals that are transmitted to the brain by the optic nerve and interpreted as sight and vision. Dimensions differ among adults by only one or two millimetres, remarkably consistent across different ethnicities; the vertical measure less than the horizontal, is about 24 mm. The transverse size of a human adult eye is 24.2 mm and the sagittal size is 23.7 mm with no significant difference between sexes and age groups.
Strong correlation has been found between the width of the orbit. The typical adult eye has an anterior to posterior diameter of 24 millimetres, a volume of six cubic centimetres, a mass of 7.5 grams.. The eyeball grows increasing from about 16–17 millimetres at birth to 22.5–23 mm by three years of age. By age 12, the eye attains its full size; the eye is made up of layers, enclosing various anatomical structures. The outermost layer, known as the fibrous tunic, is composed of the sclera; the middle layer, known as the vascular tunic or uvea, consists of the choroid, ciliary body, pigmented epithelium and iris. The innermost is the retina, which gets its oxygenation from the blood vessels of the choroid as well as the retinal vessels; the spaces of the eye are filled with the aqueous humour anteriorly, between the cornea and lens, the vitreous body, a jelly-like substance, behind the lens, filling the entire posterior cavity. The aqueous humour is a clear watery fluid, contained in two areas: the anterior chamber between the cornea and the iris, the posterior chamber between the iris and the lens.
The lens is suspended to the ciliary body by the suspensory ligament, made up of hundreds of fine transparent fibers which transmit muscular forces to change the shape of the lens for accommodation. The vitreous body is a clear substance composed of water and proteins, which give it a jelly-like and sticky composition; the approximate field of view of an individual human eye varies by facial anatomy, but is 30° superior, 45° nasal, 70° inferior, 100° temporal. For both eyes combined visual field is 200 ° horizontal, it is 13700 square degrees for binocular vision. When viewed at large angles from the side, the iris and pupil may still be visible by the viewer, indicating the person has peripheral vision possible at that angle. About 15° temporal and 1.5° below the horizontal is the blind spot created by the optic nerve nasally, 7.5° high and 5.5° wide. The retina has a static contrast ratio of around 100:1; as soon as the eye moves to acquire a target, it re-adjusts its exposure by adjusting the iris, which adjusts the size of the pupil.
Initial dark adaptation takes place in four seconds of profound, uninterrupted darkness. The process is nonlinear and multifaceted, so an interruption by light exposure requires restarting the dark adaptation process over again. Full adaptation is dependent on good blood flow; the human eye can detect a luminance range of 1014, or one hundred trillion, from 10−6 cd/m2, or one millionth of a candela per square meter to 108 cd/m2 or one hundred million candelas per square meter. This range does not include looking at the midday lightning discharge. At the low end o
In astronomy, stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum exhibiting the rainbow of colors interspersed with spectral lines; each line indicates a particular chemical element or molecule, with the line strength indicating the abundance of that element. The strengths of the different spectral lines vary due to the temperature of the photosphere, although in some cases there are true abundance differences; the spectral class of a star is a short code summarizing the ionization state, giving an objective measure of the photosphere's temperature. Most stars are classified under the Morgan-Keenan system using the letters O, B, A, F, G, K, M, a sequence from the hottest to the coolest; each letter class is subdivided using a numeric digit with 0 being hottest and 9 being coolest. The sequence has been expanded with classes for other stars and star-like objects that do not fit in the classical system, such as class D for white dwarfs and classes S and C for carbon stars.
In the MK system, a luminosity class is added to the spectral class using Roman numerals. This is based on the width of certain absorption lines in the star's spectrum, which vary with the density of the atmosphere and so distinguish giant stars from dwarfs. Luminosity class 0 or Ia+ is used for hypergiants, class I for supergiants, class II for bright giants, class III for regular giants, class IV for sub-giants, class V for main-sequence stars, class sd for sub-dwarfs, class D for white dwarfs; the full spectral class for the Sun is G2V, indicating a main-sequence star with a temperature around 5,800 K. The conventional color description takes into account only the peak of the stellar spectrum. In actuality, stars radiate in all parts of the spectrum; because all spectral colors combined appear white, the actual apparent colors the human eye would observe are far lighter than the conventional color descriptions would suggest. This characteristic of'lightness' indicates that the simplified assignment of colors within the spectrum can be misleading.
Excluding color-contrast illusions in dim light, there are indigo, or violet stars. Red dwarfs are a deep shade of orange, brown dwarfs do not appear brown, but hypothetically would appear dim grey to a nearby observer; the modern classification system is known as the Morgan–Keenan classification. Each star is assigned a spectral class from the older Harvard spectral classification and a luminosity class using Roman numerals as explained below, forming the star's spectral type. Other modern stellar classification systems, such as the UBV system, are based on color indexes—the measured differences in three or more color magnitudes; those numbers are given labels such as "U-V" or "B-V", which represent the colors passed by two standard filters. The Harvard system is a one-dimensional classification scheme by astronomer Annie Jump Cannon, who re-ordered and simplified a prior alphabetical system. Stars are grouped according to their spectral characteristics by single letters of the alphabet, optionally with numeric subdivisions.
Main-sequence stars vary in surface temperature from 2,000 to 50,000 K, whereas more-evolved stars can have temperatures above 100,000 K. Physically, the classes indicate the temperature of the star's atmosphere and are listed from hottest to coldest; the spectral classes O through M, as well as other more specialized classes discussed are subdivided by Arabic numerals, where 0 denotes the hottest stars of a given class. For example, A0 denotes A9 denotes the coolest ones. Fractional numbers are allowed; the Sun is classified as G2. Conventional color descriptions are traditional in astronomy, represent colors relative to the mean color of an A class star, considered to be white; the apparent color descriptions are what the observer would see if trying to describe the stars under a dark sky without aid to the eye, or with binoculars. However, most stars in the sky, except the brightest ones, appear white or bluish white to the unaided eye because they are too dim for color vision to work. Red supergiants are cooler and redder than dwarfs of the same spectral type, stars with particular spectral features such as carbon stars may be far redder than any black body.
The fact that the Harvard classification of a star indicated its surface or photospheric temperature was not understood until after its development, though by the time the first Hertzsprung–Russell diagram was formulated, this was suspected to be true. In the 1920s, the Indian physicist Meghnad Saha derived a theory of ionization by extending well-known ideas in physical chemistry pertaining to the dissociation of molecules to the ionization of atoms. First he applied it to the solar chromosphere to stellar spectra. Harvard astronomer Cecilia Payne demonstrated that the O-B-A-F-G-K-M spectral sequence is a sequence in temperature; because the classification sequence predates our understanding that it is a temperature sequence, the placement of a spectrum into a given subtype, such as B3 or A7, depends upon estimates of the strengths of absorption features in stellar spectra. As a result, these subtypes are not evenly divided into any sort of mathematically representable intervals; the Yerkes spectral classification called the MKK system from the authors' initial