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 plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane. Angles are formed by the intersection of two planes in Euclidean and other spaces; these are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is used to designate the measure of an angle or of a rotation; this measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation; the word angle comes from the Latin word angulus, meaning "corner".
Both are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow". Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, do not lie straight with respect to each other. According to Proclus an angle must be a relationship; the first concept was used by Eudemus. In mathematical expressions, it is common to use Greek letters to serve as variables standing for the size of some angle. Lower case Roman letters are used, as are upper case Roman letters in the context of polygons. See the figures in this article for examples. In geometric figures, angles may be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB and AC is denoted ∠BAC or B A C ^. Sometimes, where there is no risk of confusion, the angle may be referred to by its vertex. An angle denoted, say, ∠BAC might refer to any of four angles: the clockwise angle from B to C, the anticlockwise angle from B to C, the clockwise angle from C to B, or the anticlockwise angle from C to B, where the direction in which the angle is measured determines its sign.
However, in many geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant, no ambiguity arises. Otherwise, a convention may be adopted so that ∠BAC always refers to the anticlockwise angle from B to C, ∠CAB to the anticlockwise angle from C to B. An angle equal to 0° or not turned is called a zero angle. Angles smaller than a right angle are called acute angles. An angle equal to 1/4 turn is called a right angle. Two lines that form a right angle are said to be orthogonal, or perpendicular. Angles larger than a right angle and smaller than a straight angle are called obtuse angles. An angle equal to 1/2 turn is called a straight angle. Angles larger than a straight angle but less than 1 turn are called reflex angles. An angle equal to 1 turn is called complete angle, round angle or a perigon. Angles that are not right angles or a multiple of a right angle are called oblique angles; the names and measured units are shown in a table below: Angles that have the same measure are said to be equal or congruent.
An angle is not dependent upon the lengths of the sides of the angle. Two angles which share terminal sides, but differ in size by an integer multiple of a turn, are called coterminal angles. A reference angle is the acute version of any angle determined by subtracting or adding straight angle, to the results as necessary, until the magnitude of result is an acute angle, a value between 0 and 1/4 turn, 90°, or π/2 radians. For example, an angle of 30 degrees has a reference angle of 30 degrees, an angle of 150 degrees has a reference angle of 30 degrees. An angle of 750 degrees has a reference angle of 30 degrees; when two straight lines intersect at a point, four angles are formed. Pairwise these angles are named according to their location relative to each other. A pair of angles opposite each other, formed by two intersecting straight lines that form an "X"-like shape, are called vertical angles or opposite angles or vertically opposite angles, they are abbreviated as vert. opp. ∠s. The equality of vertically opposite angles is called the vertical angle theorem.
Eudemus of Rhodes attributed the proof to Thales of Miletus. The proposition showed that since both of a pair of vertical angles are supplementary to both of the adjacent angles, the vertical angles are equal in measure. According to a historical Note, w
Reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power, reflected at an interface; the reflectance spectrum or spectral reflectance curve is the plot of the reflectance as a function of wavelength. The hemispherical reflectance of a surface, denoted R, is defined as R = Φ e r Φ e i, where Φer is the radiant flux reflected by that surface; the spectral hemispherical reflectance in frequency and spectral hemispherical reflectance in wavelength of a surface, denoted Rν and Rλ are defined as R ν = Φ e, ν r Φ e, ν i, R λ = Φ e, λ r Φ e, λ i, where Φe,νr is the spectral radiant flux in frequency reflected by that surface. The directional reflectance of a surface, denoted RΩ, is defined as R Ω = L e, Ω r L e, Ω i, where Le,Ωr is the radiance reflected by that surface; the spectral directional reflectance in frequency and spectral directional reflectance in wavelength of a surface, denoted RΩ,ν and RΩ,λ are defined as R Ω, ν = L e, Ω, ν r L e, Ω, ν i, R Ω, λ = L e, Ω, λ r L e, Ω, λ i, where Le,Ω,νr is the spectral radiance in frequency reflected by that surface.
For homogeneous and semi-infinite materials, reflectivity is the same as reflectance. Reflectivity is the square of the magnitude of the Fresnel reflection coefficient, the ratio of the reflected to incident electric field. For layered and finite media, according to the CIE, reflectivity is distinguished from reflectance by the fact that reflectivity is a value that applies to thick reflecting objects; when reflection occurs from thin layers of material, internal reflection effects can cause the reflectance to vary with surface thickness. Reflectivity is the limit value of reflectance. Another way to interpret this is that the reflectance is the fraction of electromagnetic power reflected from a specific sample, while reflectivity is a property of the material itself, which would be measured on a perfect machine if the material filled half of all space. Given that reflectance is a directional property, most surfaces can be divided into those that give specular reflection and those that give diffuse reflection: for specular surfaces, such as glass or polished metal, reflectance will be nearly zero at all angles except at the appropriate reflected angle.
Such surfaces are said to be Lambertian. Most real objects have some mixture of specular reflective properties. Reflection occurs when light moves from a medium with one index of refraction into a second medium with a different index of refraction. Specular reflection from a body of water is calculated by the Fresnel equat
The pupil is a hole located in the center of the iris of the eye that allows light to strike the retina. It appears black because light rays entering the pupil are either absorbed by the tissues inside the eye directly, or absorbed after diffuse reflections within the eye that miss exiting the narrow pupil. In humans the pupil is round, but other species, such as some cats, have vertical slit pupils, goats have horizontally oriented pupils, some catfish have annular types. In optical terms, the anatomical pupil is the eye's aperture and the iris is the aperture stop; the image of the pupil as seen from outside the eye is the entrance pupil, which does not correspond to the location and size of the physical pupil because it is magnified by the cornea. On the inner edge lies a prominent structure, the collarette, marking the junction of the embryonic pupillary membrane covering the embryonic pupil; the pupil is a hole located in the centre of the iris of the eye that allows light to strike the retina.
It appears black because light rays entering the pupil are either absorbed by the tissues inside the eye directly, or absorbed after diffuse reflections within the eye that miss exiting the narrow pupil. The iris is a contractile structure, consisting of smooth muscle, surrounding the pupil. Light enters the eye through the pupil, the iris regulates the amount of light by controlling the size of the pupil; this is known as the pupillary light reflex. The iris contains two groups of smooth muscles; when the sphincter pupillae contract, the iris constricts the size of the pupil. The dilator pupillae, innervated by sympathetic nerves from the superior cervical ganglion, cause the pupil to dilate when they contract; these muscles are sometimes referred to as intrinsic eye muscles. The sensory pathway is linked with its counterpart in the other eye by a partial crossover of each eye's fibers; this causes the effect in one eye to carry over to the other. The pupil gets narrower in light; when narrow, the diameter is 2 to 4 millimeters.
In the dark it will be the same at first, but will approach the maximum distance for a wide pupil 3 to 8 mm. In any human age group there is however considerable variation in maximal pupil size. For example, at the peak age of 15, the dark-adapted pupil can vary from 4 mm to 9 mm with different individuals. After 25 years of age the average pupil size decreases, though not at a steady rate. At this stage the pupils do not remain still, therefore may lead to oscillation, which may intensify and become known as hippus; the constriction of the pupil and near vision are tied. In bright light, the pupils constrict to prevent aberrations of light rays and thus attain their expected acuity; when bright light is shone on the eye, light sensitive cells in the retina, including rod and cone photoreceptors and melanopsin ganglion cells, will send signals to the oculomotor nerve the parasympathetic part coming from the Edinger-Westphal nucleus, which terminates on the circular iris sphincter muscle. When this muscle contracts, it reduces the size of the pupil.
This is the pupillary light reflex, an important test of brainstem function. Furthermore, the pupil will dilate. If the drug pilocarpine is administered, the pupils will constrict and accommodation is increased due to the parasympathetic action on the circular muscle fibers, atropine will cause paralysis of accommodation and dilation of the pupil. Certain drugs cause constriction such as opioids. Other drugs, such as atropine, LSD, MDMA, psilocybin mushrooms and amphetamines may cause pupil dilation; the sphincter muscle has a parasympathetic innervation, the dilator has a sympathetic innervation. In pupillary constriction induced by pilocarpine, not only is the sphincter nerve supply activated but that of the dilator is inhibited; the reverse is true, so control of pupil size is controlled by differences in contraction intensity of each muscle. Another term for the constriction of the pupil is miosis. Substances that cause miosis are described as miotic. Dilation of the pupil is mydriasis. Dilation can be caused by mydriatic substances such as an eye drop solution containing tropicamide.
A condition called bene dilitatism occurs when the optic nerves are damaged. This condition is typified by chronically widened pupils due to the decreased ability of the optic nerves to respond to light. In normal lighting, people afflicted with this condition have dilated pupils, bright lighting can cause pain. At the other end of the spectrum, people with this condition have trouble seeing in darkness, it is necessary for these people to be careful when driving at night due to their inability to see objects in their full perspective. This condition is not otherwise dangerous; the size of the pupil can be a symptom of an underlying disease. Dilation of the pupil is known as mydriasis and contraction as miosis. Not all variations in size are indicative of disease however. In addition to dilation and contraction caused by light and darkness, it has been shown that solving simple multiplication problems affects the size of the pupil; the simple act of recollection can dilate the size of the pupil, however when the brain is required to process at a rate above its maximum capacity, the pupils contract.
There is evidence that pupil size is related to the extent of positive or negative emotional arousal experienced by a person. Not all animals
Etendue or étendue is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product in Gaussian optics. From the source point of view, it is the product of the area of the source and the solid angle that the system's entrance pupil subtends as seen from the source. Equivalently, from the system point of view, the etendue equals the area of the entrance pupil times the solid angle the source subtends as seen from the pupil; these definitions must be applied for infinitesimally small "elements" of area and solid angle, which must be summed over both the source and the diaphragm as shown below. Etendue may be considered to be a volume in phase space. Etendue is important because it never decreases in any optical system where optical power is conserved. A perfect optical system produces an image with the same etendue as the source; the etendue is related to the Lagrange invariant and the optical invariant, which share the property of being constant in an ideal optical system.
The radiance of an optical system is equal to the derivative of the radiant flux with respect to the etendue. The term étendue comes from the French étendue géométrique, meaning "geometrical extent". Other names for this property are acceptance, light grasp, light-gathering or -collecting power, optical extent, geometric extent, the AΩ product. Throughput and AΩ product are used in radiometry and radiative transfer where it is related to the view factor, it is a central concept in nonimaging optics. An infinitesimal surface element, dS, with normal nS is immersed in a medium of refractive index n; the surface is crossed by light confined to a solid angle, dΩ, at an angle θ with the normal nS. The area of dS projected in the direction of the light propagation is dS cos θ; the etendue of this light crossing dS is defined as d G = n 2 d S cos θ d Ω. Because angles, solid angles, refractive indices are dimensionless quantities, etendue has units of area; as shown below, etendue is conserved as light travels through free space and at refractions or reflections.
It is also conserved as light travels through optical systems where it undergoes perfect reflections or refractions. However, if light was to hit, say, a diffuser, its solid angle would increase, increasing the etendue. Etendue can remain constant or it can increase as light propagates through an optic, but it cannot decrease; this is a direct result of increasing entropy, which only can be reverted if a priori knowledge is used to reconstruct a phase-matched wave-front such as with phase conjugated mirrors. Conservation of etendue can be derived in different contexts, such as from optical first principles, from Hamiltonian optics or from the second law of thermodynamics. Consider a light source Σ, a light detector S, both of which are extended surfaces, which are separated by a medium of refractive index n, transparent. To compute the etendue of the system, one must consider the contribution of each point on the surface of the light source as they cast rays to each point on the receiver. According to the definition above, the etendue of the light crossing dΣ towards dS is given by: d G Σ = n 2 d Σ cos θ Σ d Ω Σ = n 2 d Σ cos θ Σ d S cos θ S d 2 where dΩΣ is the solid angle defined by area dS at area dΣ.
The etendue of the light crossing dS coming from dΣ is given by: d G S = n 2 d S cos θ S d Ω S = n 2 d S cos θ S d Σ cos θ Σ d 2, where dΩS is the solid angle defined by area dΣ. These expressions result in d G Σ = d G S, showing that etendue is conserved as light propagates in free space; the etendue of the whole system is then: G = ∫ Σ ∫ S d G. If both surfaces dΣ and dS are immersed in air, n = 1 and the expression above for the etendue may be written as d G = d Σ cos θ Σ d S cos θ S d 2 = π
Luminescence is spontaneous emission of light by a substance not resulting from heat. It can be caused by electrical energy, subatomic motions or stress on a crystal; this distinguishes luminescence from incandescence, light emitted by a substance as a result of heating. Radioactivity was thought of as a form of "radio-luminescence", although it is today considered to be separate since it involves more than electromagnetic radiation; the dials, hands and signs of aviation and navigational instruments and markings are coated with luminescent materials in a process known as "luminising". The following are types of luminescence: Chemiluminescence, the emission of light as a result of a chemical reaction Bioluminescence, a result of biochemical reactions in a living organism Electrochemiluminescence, a result of an electrochemical reaction Lyoluminescence, a result of dissolving a solid in a liquid solvent Candoluminescence, is light emitted by certain materials at elevated temperatures, which differs from the blackbody emission expected at the temperature in question.
Crystalloluminescence, produced during crystallization Electroluminescence, a result of an electric current passed through a substance Cathodoluminescence, a result of a luminescent material being struck by electrons Mechanoluminescence, a result of a mechanical action on a solid Triboluminescence, generated when bonds in a material are broken when that material is scratched, crushed, or rubbed Fractoluminescence, generated when bonds in certain crystals are broken by fractures Piezoluminescence, produced by the action of pressure on certain solids Sonoluminescence, a result of imploding bubbles in a liquid when excited by sound Photoluminescence, a result of absorption of photons Fluorescence, photoluminescence as a result of singlet–singlet electronic relaxation Phosphorescence, photoluminescence as a result of triplet–singlet electronic relaxation Raman emission, photoluminescence as a result of inelastic light scattering, Radioluminescence, a result of bombardment by ionizing radiation Thermoluminescence, the re-emission of absorbed energy when a substance is heatedCryoluminescence, the emission of light when an object is cooled Light-emitting diodes emit light via electro-luminescence.
Phosphors, materials that emit light when irradiated by higher-energy electromagnetic radiation or particle radiation Phosphor thermometry, measuring temperature using phosphorescence Thermoluminescence dating Thermoluminescent dosimeter Non-disruptive observation of processes within a cell. Luminescence occurs in some minerals when they are exposed to low-powered sources of ultraviolet or infrared electromagnetic radiation, at atmospheric pressure and atmospheric temperatures; this property of these minerals can be used during the process of mineral identification at rock outcrops in the field, or in the laboratory. List of light sources Fluorophores.org A database of luminescent dyes
Laser safety is the safe design and implementation of lasers to minimize the risk of laser accidents those involving eye injuries. Since relatively small amounts of laser light can lead to permanent eye injuries, the sale and usage of lasers is subject to government regulations. Moderate and high-power lasers are hazardous because they can burn the retina of the eye, or the skin. To control the risk of injury, various specifications, for example 21 Code of Federal Regulations Part 1040 in the US and IEC 60825 internationally, define "classes" of laser depending on their power and wavelength; these regulations impose upon manufacturers required safety measures, such as labeling lasers with specific warnings, wearing laser safety goggles when operating lasers. Consensus standards, such as American National Standards Institute Z136, provide users with control measures for laser hazards, as well as various tables helpful in calculating maximum permissible exposure limits and accessible exposures limits.
Thermal effects are the predominant cause of laser radiation injury, but photo-chemical effects can be of concern for specific wavelengths of laser radiation. Moderately powered lasers can cause injury to the eye. High power lasers can burn the skin; some lasers are so powerful that the diffuse reflection from a surface can be hazardous to the eye. The coherence and low divergence angle of laser light, aided by focusing from the lens of an eye, can cause laser radiation to be concentrated into an small spot on the retina. A transient increase of only 10 °C can destroy retinal photoreceptor cells. If the laser is sufficiently powerful, permanent damage can occur within a fraction of a second faster than the blink of an eye. Sufficiently powerful lasers in the visible to near infrared range will penetrate the eyeball and may cause heating of the retina, whereas exposure to laser radiation with wavelengths less than 400 nm and greater than 1400 nm are absorbed by the cornea and lens, leading to the development of cataracts or burn injuries.
Infrared lasers are hazardous, since the body's protective glare aversion response referred to as the "blink reflex," is triggered only by visible light. For example, some people exposed to high power Nd:YAG laser emitting invisible 1064 nm radiation may not feel pain or notice immediate damage to their eyesight. A pop or click noise emanating from the eyeball may be the only indication that retinal damage has occurred i.e. the retina was heated to over 100 °C resulting in localized explosive boiling accompanied by the immediate creation of a permanent blind spot. Lasers can cause damage in biological tissues, both to the eye and to the skin, due to several mechanisms. Thermal damage, or burn, occurs when tissues are heated to the point where denaturation of proteins occurs. Another mechanism is photochemical damage. Photochemical damage occurs with short-wavelength light and can be accumulated over the course of hours. Laser pulses shorter than about 1 μs can cause a rapid rise in temperature, resulting in explosive boiling of water.
The shock wave from the explosion can subsequently cause damage far away from the point of impact. Ultrashort pulses can exhibit self-focusing in the transparent parts of the eye, leading to an increase of the damage potential compared to longer pulses with the same energy. Photoionization proved to be the main mechanism of radiation damage at the use of titanium-sapphire laser; the eye focuses near-infrared light onto the retina. A laser beam can be focused to an intensity on the retina which may be up to 200,000 times higher than at the point where the laser beam enters the eye. Most of the light is absorbed by melanin pigments in the pigment epithelium just behind the photoreceptors, causes burns in the retina. Ultraviolet light with wavelengths shorter than 400 nm tends to be absorbed by lens and 300 nm in the cornea, where it can produce injuries at low powers due to photochemical damage. Infrared light causes thermal damage to the retina at near-infrared wavelengths and to more frontal parts of the eye at longer wavelengths.
The table below summarizes the various medical conditions caused by lasers at different wavelengths, not including injuries due to pulsed lasers. The skin is much less sensitive to laser light than the eye, but excessive exposure to ultraviolet light from any source can cause short- and long-term effects similar to sunburn, while visible and infrared wavelengths are harmful due to thermal damage. FAA researchers compiled a database of more than 400 reported incidents occurring between 1990 and 2004 in which pilots have been startled, temporarily blinded, or disoriented by laser exposure; this information led to an inquiry in the US Congress. Exposure to hand-held laser light under such circumstances may seem trivial given the brevity of exposure, the large distances involved and beam spread of up to several metres. However, laser exposure may create dangerous conditions such as flash blindness. If this occurs during a critical moment in aircraft operation, the aircraft may be endangered. In addition, some 18% to 35% of the population possess the autosomal dominant genetic trait, photic sneeze, that causes the affected individual to experience an involuntary sneezing fit when exposed to a sudden flash of light.
The maximum permissible exposure is the highest power or energy density of a light source, considered safe, i.e. that has a negligible probability for creating damage. It is about 10% of the dose that has a 50% chance of