Optics is the branch of physics that studies the behaviour and properties of light , including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible , ultraviolet , and infrared light. Light is a type of electromagnetic radiation , and other forms of electromagnetic radiation such as X-rays , microwaves , and radio waves exhibit similar properties.
143-397: A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction . A simple lens consists of a single piece of transparent material , while a compound lens consists of several simple lenses ( elements ), usually arranged along a common axis . Lenses are made from materials such as glass or plastic and are ground , polished , or molded to
286-502: A reticle graduated to allow measuring distances in the focal plane. The other (and older) type has simple crosshairs and a micrometer mechanism for moving the subject relative to the microscope. Very small, portable microscopes have found some usage in places where a laboratory microscope would be a burden. At very high magnifications with transmitted light, point objects are seen as fuzzy discs surrounded by diffraction rings. These are called Airy disks . The resolving power of
429-408: A 1758 patent. Developments in transatlantic commerce were the impetus for the construction of modern lighthouses in the 18th century, which utilize a combination of elevated sightlines, lighting sources, and lenses to provide navigational aid overseas. With maximal distance of visibility needed in lighthouses, conventional convex lenses would need to be significantly sized which would negatively affect
572-586: A 3-D effect. A camera is typically used to capture the image ( micrograph ). The sample can be lit in a variety of ways. Transparent objects can be lit from below and solid objects can be lit with light coming through ( bright field ) or around ( dark field ) the objective lens. Polarised light may be used to determine crystal orientation of metallic objects. Phase-contrast imaging can be used to increase image contrast by highlighting small details of differing refractive index. A range of objective lenses with different magnification are usually provided mounted on
715-405: A biconcave or plano-concave lens in a lower-index medium, a collimated beam of light passing through the lens is diverged (spread); the lens is thus called a negative or diverging lens. The beam, after passing through the lens, appears to emanate from a particular point on the axis in front of the lens. For a thin lens in air, the distance from this point to the lens is the focal length, though it
858-430: A broad band, or extremely low reflectivity at a single wavelength. Constructive interference in thin films can create a strong reflection of light in a range of wavelengths, which can be narrow or broad depending on the design of the coating. These films are used to make dielectric mirrors , interference filters , heat reflectors , and filters for colour separation in colour television cameras. This interference effect
1001-619: A changing index of refraction; this principle allows for lenses and the focusing of light. The simplest case of refraction occurs when there is an interface between a uniform medium with index of refraction n 1 and another medium with index of refraction n 2 . In such situations, Snell's Law describes the resulting deflection of the light ray: n 1 sin θ 1 = n 2 sin θ 2 {\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}} where θ 1 and θ 2 are
1144-501: A child at the time, leading to speculation that, for Johannes' claim to be true, the compound microscope would have to have been invented by Johannes' grandfather, Hans Martens. Another claim is that Janssen's competitor, Hans Lippershey (who applied for the first telescope patent in 1608) also invented the compound microscope. Other historians point to the Dutch innovator Cornelis Drebbel with his 1621 compound microscope. Galileo Galilei
1287-399: A converging lens has positive focal length, while a diverging lens has negative focal length. Smaller focal length indicates that the lens has a stronger converging or diverging effect. The focal length of a simple lens in air is given by the lensmaker's equation . Ray tracing can be used to show how images are formed by a lens. For a thin lens in air, the location of the image is given by
1430-486: A high-powered macro lens and generally do not use transillumination . The camera is attached directly to a computer's USB port to show the images directly on the monitor. They offer modest magnifications (up to about 200×) without the need to use eyepieces and at a very low cost. High-power illumination is usually provided by an LED source or sources adjacent to the camera lens. Digital microscopy with very low light levels to avoid damage to vulnerable biological samples
1573-508: A lens close to the object being viewed to collect light (called the objective lens), which focuses a real image of the object inside the microscope (image 1). That image is then magnified by a second lens or group of lenses (called the eyepiece ) that gives the viewer an enlarged inverted virtual image of the object (image 2). The use of a compound objective/eyepiece combination allows for much higher magnification. Common compound microscopes often feature exchangeable objective lenses, allowing
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#17328447127961716-536: A lens in air, f is then given by 1 f ≈ ( n − 1 ) [ 1 R 1 − 1 R 2 ] . {\displaystyle \ {\frac {1}{\ f\ }}\approx \left(n-1\right)\left[\ {\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}\ \right]~.} The spherical thin lens equation in paraxial approximation
1859-425: A magnification of 40 to 100×. Adjustment knobs move the stage up and down with separate adjustment for coarse and fine focusing. The same controls enable the microscope to adjust to specimens of different thickness. In older designs of microscopes, the focus adjustment wheels move the microscope tube up or down relative to the stand and had a fixed stage. The whole of the optical assembly is traditionally attached to
2002-559: A magnifying glass, or a burning glass. Others have suggested that certain Egyptian hieroglyphs depict "simple glass meniscal lenses". The oldest certain reference to the use of lenses is from Aristophanes ' play The Clouds (424 BCE) mentioning a burning-glass. Pliny the Elder (1st century) confirms that burning-glasses were known in the Roman period. Pliny also has the earliest known reference to
2145-537: A matched cover slip between the objective lens and the sample. The refractive index of the index-matching material is higher than air allowing the objective lens to have a larger numerical aperture (greater than 1) so that the light is transmitted from the specimen to the outer face of the objective lens with minimal refraction. Numerical apertures as high as 1.6 can be achieved. The larger numerical aperture allows collection of more light making detailed observation of smaller details possible. An oil immersion lens usually has
2288-438: A microscope is taken as the ability to distinguish between two closely spaced Airy disks (or, in other words the ability of the microscope to reveal adjacent structural detail as distinct and separate). It is these impacts of diffraction that limit the ability to resolve fine details. The extent and magnitude of the diffraction patterns are affected by both the wavelength of light (λ), the refractive materials used to manufacture
2431-565: A photon-counting camera. The earliest microscopes were single lens magnifying glasses with limited magnification, which date at least as far back as the widespread use of lenses in eyeglasses in the 13th century. Compound microscopes first appeared in Europe around 1620 including one demonstrated by Cornelis Drebbel in London (around 1621) and one exhibited in Rome in 1624. The actual inventor of
2574-610: A result, can achieve much greater magnifications. There are two basic types of optical microscopes: simple microscopes and compound microscopes. A simple microscope uses the optical power of a single lens or group of lenses for magnification. A compound microscope uses a system of lenses (one set enlarging the image produced by another) to achieve a much higher magnification of an object. The vast majority of modern research microscopes are compound microscopes, while some cheaper commercial digital microscopes are simple single-lens microscopes. Compound microscopes can be further divided into
2717-478: A rigid arm, which in turn is attached to a robust U-shaped foot to provide the necessary rigidity. The arm angle may be adjustable to allow the viewing angle to be adjusted. The frame provides a mounting point for various microscope controls. Normally this will include controls for focusing, typically a large knurled wheel to adjust coarse focus, together with a smaller knurled wheel to control fine focus. Other features may be lamp controls and/or controls for adjusting
2860-603: A sample; there are many techniques which can be used to extract other kinds of data. Most of these require additional equipment in addition to a basic compound microscope. Optical microscopy is used extensively in microelectronics, nanophysics, biotechnology, pharmaceutic research, mineralogy and microbiology. Optical microscopy is used for medical diagnosis , the field being termed histopathology when dealing with tissues, or in smear tests on free cells or tissue fragments. In industrial use, binocular microscopes are common. Aside from applications needing true depth perception ,
3003-457: A simple 2-lens ocular system in the late 17th century that was achromatically corrected, and therefore a huge step forward in microscope development. The Huygens ocular is still being produced to this day, but suffers from a small field size, and other minor disadvantages. Antonie van Leeuwenhoek (1632–1724) is credited with bringing the microscope to the attention of biologists, even though simple magnifying lenses were already being produced in
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#17328447127963146-477: A single scalar quantity to represent the electric field of the light wave, rather than using a vector model with orthogonal electric and magnetic vectors. The Huygens–Fresnel equation is one such model. This was derived empirically by Fresnel in 1815, based on Huygens' hypothesis that each point on a wavefront generates a secondary spherical wavefront, which Fresnel combined with the principle of superposition of waves. The Kirchhoff diffraction equation , which
3289-522: A single point on the image, while chromatic aberration occurs because the index of refraction of the lens varies with the wavelength of the light. In physical optics, light is considered to propagate as waves. This model predicts phenomena such as interference and diffraction, which are not explained by geometric optics. The speed of light waves in air is approximately 3.0×10 m/s (exactly 299,792,458 m/s in vacuum ). The wavelength of visible light waves varies between 400 and 700 nm, but
3432-437: A spectrum. The discovery of this phenomenon when passing light through a prism is famously attributed to Isaac Newton. Some media have an index of refraction which varies gradually with position and, therefore, light rays in the medium are curved. This effect is responsible for mirages seen on hot days: a change in index of refraction air with height causes light rays to bend, creating the appearance of specular reflections in
3575-829: A spherical lens in air or vacuum for paraxial rays can be calculated from the lensmaker's equation : 1 f = ( n − 1 ) [ 1 R 1 − 1 R 2 + ( n − 1 ) d n R 1 R 2 ] , {\displaystyle {\frac {1}{\ f\ }}=\left(n-1\right)\left[\ {\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}+{\frac {\ \left(n-1\right)\ d~}{\ n\ R_{1}\ R_{2}\ }}\ \right]\ ,} where The focal length f {\textstyle \ f\ }
3718-465: A thickness of one-fourth the wavelength of incident light. The reflected wave from the top of the film and the reflected wave from the film/material interface are then exactly 180° out of phase, causing destructive interference. The waves are only exactly out of phase for one wavelength, which would typically be chosen to be near the centre of the visible spectrum, around 550 nm. More complex designs using multiple layers can achieve low reflectivity over
3861-511: A turret, allowing them to be rotated into place and providing an ability to zoom-in. The maximum magnification power of optical microscopes is typically limited to around 1000x because of the limited resolving power of visible light. While larger magnifications are possible no additional details of the object are resolved. Alternatives to optical microscopy which do not use visible light include scanning electron microscopy and transmission electron microscopy and scanning probe microscopy and as
4004-495: A variety of other types of microscopes, which differ in their optical configurations, cost, and intended purposes. A simple microscope uses a lens or set of lenses to enlarge an object through angular magnification alone, giving the viewer an erect enlarged virtual image . The use of a single convex lens or groups of lenses are found in simple magnification devices such as the magnifying glass , loupes , and eyepieces for telescopes and microscopes. A compound microscope uses
4147-476: A variety of technologies and everyday objects, including mirrors , lenses , telescopes , microscopes , lasers , and fibre optics . Optics began with the development of lenses by the ancient Egyptians and Mesopotamians . The earliest known lenses, made from polished crystal , often quartz , date from as early as 2000 BC from Crete (Archaeological Museum of Heraclion, Greece). Lenses from Rhodes date around 700 BC, as do Assyrian lenses such as
4290-525: A wide range of scientific topics, and discussed light from four different perspectives: an epistemology of light, a metaphysics or cosmogony of light, an etiology or physics of light, and a theology of light, basing it on the works of Aristotle and Platonism. Grosseteste's most famous disciple, Roger Bacon , wrote works citing a wide range of recently translated optical and philosophical works, including those of Alhazen, Aristotle, Avicenna , Averroes , Euclid, al-Kindi, Ptolemy, Tideus, and Constantine
4433-403: Is biconvex (or double convex , or just convex ) if both surfaces are convex . If both surfaces have the same radius of curvature, the lens is equiconvex . A lens with two concave surfaces is biconcave (or just concave ). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side
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4576-407: Is convex-concave or meniscus . Convex-concave lenses are most commonly used in corrective lenses , since the shape minimizes some aberrations. For a biconvex or plano-convex lens in a lower-index medium, a collimated beam of light passing through the lens converges to a spot (a focus ) behind the lens. In this case, the lens is called a positive or converging lens. For a thin lens in air,
4719-445: Is h ), and v {\textstyle v} is the on-axis image distance from the line. Due to paraxial approximation where the line of h is close to the vertex of the spherical surface meeting the optical axis on the left, u {\textstyle u} and v {\textstyle v} are also considered distances with respect to the vertex. Moving v {\textstyle v} toward
4862-493: Is a microscope equipped with a digital camera allowing observation of a sample via a computer . Microscopes can also be partly or wholly computer-controlled with various levels of automation. Digital microscopy allows greater analysis of a microscope image, for example, measurements of distances and areas and quantitation of a fluorescent or histological stain. Low-powered digital microscopes, USB microscopes , are also commercially available. These are essentially webcams with
5005-427: Is a simple paraxial physical optics model for the propagation of coherent radiation such as laser beams. This technique partially accounts for diffraction, allowing accurate calculations of the rate at which a laser beam expands with distance, and the minimum size to which the beam can be focused. Gaussian beam propagation thus bridges the gap between geometric and physical optics. In the absence of nonlinear effects,
5148-422: Is also what causes the colourful rainbow patterns seen in oil slicks. Optical microscope The optical microscope , also referred to as a light microscope , is a type of microscope that commonly uses visible light and a system of lenses to generate magnified images of small objects. Optical microscopes are the oldest design of microscope and were possibly invented in their present compound form in
5291-430: Is available using sensitive photon-counting digital cameras. It has been demonstrated that a light source providing pairs of entangled photons may minimize the risk of damage to the most light-sensitive samples. In this application of ghost imaging to photon-sparse microscopy, the sample is illuminated with infrared photons, each spatially correlated with an entangled partner in the visible band for efficient imaging by
5434-415: Is best to begin with prepared slides that are centered and focus easily regardless of the focus level used. Many sources of light can be used. At its simplest, daylight is directed via a mirror . Most microscopes, however, have their own adjustable and controllable light source – often a halogen lamp , although illumination using LEDs and lasers are becoming a more common provision. Köhler illumination
5577-529: Is called the focal plane . For paraxial rays , if the distances from an object to a spherical thin lens (a lens of negligible thickness) and from the lens to the image are S 1 and S 2 respectively, the distances are related by the (Gaussian) thin lens formula : Optics Most optical phenomena can be accounted for by using the classical electromagnetic description of light, however complete electromagnetic descriptions of light are often difficult to apply in practice. Practical optics
5720-416: Is completely round. When used in novelty photography it is often called a "lensball". A ball-shaped lens has the advantage of being omnidirectional, but for most optical glass types, its focal point lies close to the ball's surface. Because of the ball's curvature extremes compared to the lens size, optical aberration is much worse than thin lenses, with the notable exception of chromatic aberration . For
5863-486: Is considered to travel in straight lines, while in physical optics, light is considered as an electromagnetic wave. Geometrical optics can be viewed as an approximation of physical optics that applies when the wavelength of the light used is much smaller than the size of the optical elements in the system being modelled. Geometrical optics , or ray optics , describes the propagation of light in terms of "rays" which travel in straight lines, and whose paths are governed by
Lens - Misplaced Pages Continue
6006-793: Is derived here with respect to the right figure. The 1st spherical lens surface (which meets the optical axis at V 1 {\textstyle \ V_{1}\ } as its vertex) images an on-axis object point O to the virtual image I , which can be described by the following equation, n 1 u + n 2 v ′ = n 2 − n 1 R 1 . {\displaystyle \ {\frac {\ n_{1}\ }{\ u\ }}+{\frac {\ n_{2}\ }{\ v'\ }}={\frac {\ n_{2}-n_{1}\ }{\ R_{1}\ }}~.} For
6149-484: Is derived using Maxwell's equations, puts the Huygens-Fresnel equation on a firmer physical foundation. Examples of the application of Huygens–Fresnel principle can be found in the articles on diffraction and Fraunhofer diffraction . More rigorous models, involving the modelling of both electric and magnetic fields of the light wave, are required when dealing with materials whose electric and magnetic properties affect
6292-460: Is further along in the direction of the ray travel (right, in the accompanying diagrams), while negative R means that rays reaching the surface have already passed the center of curvature. Consequently, for external lens surfaces as diagrammed above, R 1 > 0 and R 2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R 1 < 0 and R 2 > 0 indicate concave surfaces. The reciprocal of
6435-407: Is negative with respect to the focal length of a converging lens. The behavior reverses when a lens is placed in a medium with higher refractive index than the material of the lens. In this case a biconvex or plano-convex lens diverges light, and a biconcave or plano-concave one converges it. Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of
6578-492: Is not practical. A mechanical stage, typical of medium and higher priced microscopes, allows tiny movements of the slide via control knobs that reposition the sample/slide as desired. If a microscope did not originally have a mechanical stage it may be possible to add one. All stages move up and down for focus. With a mechanical stage slides move on two horizontal axes for positioning the specimen to examine specimen details. Focusing starts at lower magnification in order to center
6721-463: Is often provided on more expensive instruments. The condenser is a lens designed to focus light from the illumination source onto the sample. The condenser may also include other features, such as a diaphragm and/or filters, to manage the quality and intensity of the illumination. For illumination techniques like dark field , phase contrast and differential interference contrast microscopy additional optical components must be precisely aligned in
6864-433: Is positive for converging lenses, and negative for diverging lenses. The reciprocal of the focal length, 1 f , {\textstyle \ {\tfrac {1}{\ f\ }}\ ,} is the optical power of the lens. If the focal length is in metres, this gives the optical power in dioptres (reciprocal metres). Lenses have the same focal length when light travels from
7007-512: Is sometimes cited as a compound microscope inventor. After 1610, he found that he could close focus his telescope to view small objects, such as flies, close up and/or could look through the wrong end in reverse to magnify small objects. The only drawback was that his 2 foot long telescope had to be extended out to 6 feet to view objects that close. After seeing the compound microscope built by Drebbel exhibited in Rome in 1624, Galileo built his own improved version. In 1625, Giovanni Faber coined
7150-400: Is the radius of the spherical surface, n 2 is the refractive index of the material of the surface, n 1 is the refractive index of medium (the medium other than the spherical surface material), u {\textstyle u} is the on-axis (on the optical axis) object distance from the line perpendicular to the axis toward the refraction point on the surface (which height
7293-409: Is to the lens, the further the image is from the lens. With diverging lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at a spot one focal length in front of the lens. This is the lens's front focal point. Rays from an object at a finite distance are associated with a virtual image that is closer to the lens than the focal point, and on
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#17328447127967436-406: Is usually done using simplified models. The most common of these, geometric optics , treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically,
7579-1134: Is with respect to the principal planes of the lens, and the locations of the principal planes h 1 {\textstyle \ h_{1}\ } and h 2 {\textstyle \ h_{2}\ } with respect to the respective lens vertices are given by the following formulas, where it is a positive value if it is right to the respective vertex. h 1 = − ( n − 1 ) f d n R 2 {\displaystyle \ h_{1}=-\ {\frac {\ \left(n-1\right)f\ d~}{\ n\ R_{2}\ }}\ } h 2 = − ( n − 1 ) f d n R 1 {\displaystyle \ h_{2}=-\ {\frac {\ \left(n-1\right)f\ d~}{\ n\ R_{1}\ }}\ } The focal length f {\displaystyle \ f\ }
7722-476: The Book of Optics ( Kitab al-manazir ) in which he explored reflection and refraction and proposed a new system for explaining vision and light based on observation and experiment. He rejected the "emission theory" of Ptolemaic optics with its rays being emitted by the eye, and instead put forward the idea that light reflected in all directions in straight lines from all points of the objects being viewed and then entered
7865-607: The Nimrud lens . The ancient Romans and Greeks filled glass spheres with water to make lenses. These practical developments were followed by the development of theories of light and vision by ancient Greek and Indian philosophers, and the development of geometrical optics in the Greco-Roman world . The word optics comes from the ancient Greek word ὀπτική , optikē ' appearance, look ' . Greek philosophy on optics broke down into two opposing theories on how vision worked,
8008-449: The emission theory , the idea that visual perception is accomplished by rays emitted by the eyes. He also commented on the parity reversal of mirrors in Timaeus . Some hundred years later, Euclid (4th–3rd century BC) wrote a treatise entitled Optics where he linked vision to geometry , creating geometrical optics . He based his work on Plato's emission theory wherein he described
8151-468: The intromission theory and the emission theory . The intromission approach saw vision as coming from objects casting off copies of themselves (called eidola) that were captured by the eye. With many propagators including Democritus , Epicurus , Aristotle and their followers, this theory seems to have some contact with modern theories of what vision really is, but it remained only speculation lacking any experimental foundation. Plato first articulated
8294-448: The superposition principle , which is a wave-like property not predicted by Newton's corpuscle theory. This work led to a theory of diffraction for light and opened an entire area of study in physical optics. Wave optics was successfully unified with electromagnetic theory by James Clerk Maxwell in the 1860s. The next development in optical theory came in 1899 when Max Planck correctly modelled blackbody radiation by assuming that
8437-463: The surface normal , a line perpendicular to the surface at the point where the ray hits. The incident and reflected rays and the normal lie in a single plane, and the angle between the reflected ray and the surface normal is the same as that between the incident ray and the normal. This is known as the Law of Reflection . For flat mirrors , the law of reflection implies that images of objects are upright and
8580-472: The 11th and 13th century " reading stones " were invented. These were primitive plano-convex lenses initially made by cutting a glass sphere in half. The medieval (11th or 12th century) rock crystal Visby lenses may or may not have been intended for use as burning glasses. Spectacles were invented as an improvement of the "reading stones" of the high medieval period in Northern Italy in the second half of
8723-528: The 13th century. This was the start of the optical industry of grinding and polishing lenses for spectacles, first in Venice and Florence in the late 13th century, and later in the spectacle-making centres in both the Netherlands and Germany . Spectacle makers created improved types of lenses for the correction of vision based more on empirical knowledge gained from observing the effects of the lenses (probably without
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#17328447127968866-420: The 16th century. Van Leeuwenhoek's home-made microscopes were simple microscopes, with a single very small, yet strong lens. They were awkward in use, but enabled van Leeuwenhoek to see detailed images. It took about 150 years of optical development before the compound microscope was able to provide the same quality image as van Leeuwenhoek's simple microscopes, due to difficulties in configuring multiple lenses. In
9009-588: The 17th and early 18th centuries by those trying to correct chromatic errors seen in lenses. Opticians tried to construct lenses of varying forms of curvature, wrongly assuming errors arose from defects in the spherical figure of their surfaces. Optical theory on refraction and experimentation was showing no single-element lens could bring all colours to a focus. This led to the invention of the compound achromatic lens by Chester Moore Hall in England in 1733, an invention also claimed by fellow Englishman John Dollond in
9152-408: The 17th century. Basic optical microscopes can be very simple, although many complex designs aim to improve resolution and sample contrast . The object is placed on a stage and may be directly viewed through one or two eyepieces on the microscope. In high-power microscopes, both eyepieces typically show the same image, but with a stereo microscope , slightly different images are used to create
9295-418: The 1850s, John Leonard Riddell , Professor of Chemistry at Tulane University , invented the first practical binocular microscope while carrying out one of the earliest and most extensive American microscopic investigations of cholera . While basic microscope technology and optics have been available for over 400 years it is much more recently that techniques in sample illumination were developed to generate
9438-505: The African . Bacon was able to use parts of glass spheres as magnifying glasses to demonstrate that light reflects from objects rather than being released from them. The first wearable eyeglasses were invented in Italy around 1286. This was the start of the optical industry of grinding and polishing lenses for these "spectacles", first in Venice and Florence in the thirteenth century, and later in
9581-974: The Gaussian thin lens equation is 1 u + 1 v = 1 f . {\displaystyle \ {\frac {1}{\ u\ }}+{\frac {1}{\ v\ }}={\frac {1}{\ f\ }}~.} For the thin lens in air or vacuum where n 1 = 1 {\textstyle \ n_{1}=1\ } can be assumed, f {\textstyle \ f\ } becomes 1 f = ( n − 1 ) ( 1 R 1 − 1 R 2 ) {\displaystyle \ {\frac {1}{\ f\ }}=\left(n-1\right)\left({\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}\right)\ } where
9724-548: The Huygens–Fresnel principle states that every point of a wavefront is associated with the production of a new disturbance, it is possible for a wavefront to interfere with itself constructively or destructively at different locations producing bright and dark fringes in regular and predictable patterns. Interferometry is the science of measuring these patterns, usually as a means of making precise determinations of distances or angular resolutions . The Michelson interferometer
9867-478: The Latin name of the lentil (a seed of a lentil plant), because a double-convex lens is lentil-shaped. The lentil also gives its name to a geometric figure . Some scholars argue that the archeological evidence indicates that there was widespread use of lenses in antiquity, spanning several millennia. The so-called Nimrud lens is a rock crystal artifact dated to the 7th century BCE which may or may not have been used as
10010-466: The Latin translation of an incomplete and very poor Arabic translation. The book was, however, received by medieval scholars in the Islamic world, and commented upon by Ibn Sahl (10th century), who was in turn improved upon by Alhazen ( Book of Optics , 11th century). The Arabic translation of Ptolemy's Optics became available in Latin translation in the 12th century ( Eugenius of Palermo 1154). Between
10153-484: The amplitude of the wave, which for light is associated with a brightening of the waveform in that location. Alternatively, if the two waves of the same wavelength and frequency are out of phase, then the wave crests will align with wave troughs and vice versa. This results in destructive interference and a decrease in the amplitude of the wave, which for light is associated with a dimming of the waveform at that location. See below for an illustration of this effect. Since
10296-542: The angle of incidence. Plutarch (1st–2nd century AD) described multiple reflections on spherical mirrors and discussed the creation of magnified and reduced images, both real and imaginary, including the case of chirality of the images. During the Middle Ages , Greek ideas about optics were resurrected and extended by writers in the Muslim world . One of the earliest of these was Al-Kindi ( c. 801 –873) who wrote on
10439-435: The angles between the normal (to the interface) and the incident and refracted waves, respectively. The index of refraction of a medium is related to the speed, v , of light in that medium by n = c / v , {\displaystyle n=c/v,} where c is the speed of light in vacuum . Snell's Law can be used to predict the deflection of light rays as they pass through linear media as long as
10582-404: The back to the front as when light goes from the front to the back. Other properties of the lens, such as the aberrations are not the same in both directions. The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but in this article a positive R indicates a surface's center of curvature
10725-419: The compound microscope is unknown although many claims have been made over the years. These include a claim 35 years after they appeared by Dutch spectacle-maker Johannes Zachariassen that his father, Zacharias Janssen , invented the compound microscope and/or the telescope as early as 1590. Johannes' testimony, which some claim is dubious, pushes the invention date so far back that Zacharias would have been
10868-406: The condenser. The stage is a platform below the objective lens which supports the specimen being viewed. In the center of the stage is a hole through which light passes to illuminate the specimen. The stage usually has arms to hold slides (rectangular glass plates with typical dimensions of 25×75 mm, on which the specimen is mounted). At magnifications higher than 100× moving a slide by hand
11011-403: The development of fluorescent probes for specific structures within a cell. In contrast to normal transilluminated light microscopy, in fluorescence microscopy the sample is illuminated through the objective lens with a narrow set of wavelengths of light. This light interacts with fluorophores in the sample which then emit light of a longer wavelength . It is this emitted light which makes up
11154-420: The development of lighthouses in terms of cost, design, and implementation. Fresnel lens were developed that considered these constraints by featuring less material through their concentric annular sectioning. They were first fully implemented into a lighthouse in 1823. Most lenses are spherical lenses : their two surfaces are parts of the surfaces of spheres. Each surface can be convex (bulging outwards from
11297-449: The distance (as if on the surface of a pool of water). Optical materials with varying indexes of refraction are called gradient-index (GRIN) materials. Such materials are used to make gradient-index optics . For light rays travelling from a material with a high index of refraction to a material with a low index of refraction, Snell's law predicts that there is no θ 2 when θ 1 is large. In this case, no transmission occurs; all
11440-403: The distance from the lens to the spot is the focal length of the lens, which is commonly represented by f in diagrams and equations. An extended hemispherical lens is a special type of plano-convex lens, in which the lens's curved surface is a full hemisphere and the lens is much thicker than the radius of curvature. Another extreme case of a thick convex lens is a ball lens , whose shape
11583-424: The effect of the lens' thickness. For a single refraction for a circular boundary, the relation between object and its image in the paraxial approximation is given by n 1 u + n 2 v = n 2 − n 1 R {\displaystyle {\frac {n_{1}}{u}}+{\frac {n_{2}}{v}}={\frac {n_{2}-n_{1}}{R}}} where R
11726-426: The exchange of energy between light and matter only occurred in discrete amounts he called quanta . In 1905, Albert Einstein published the theory of the photoelectric effect that firmly established the quantization of light itself. In 1913, Niels Bohr showed that atoms could only emit discrete amounts of energy, thus explaining the discrete lines seen in emission and absorption spectra . The understanding of
11869-525: The eye, although he was unable to correctly explain how the eye captured the rays. Alhazen's work was largely ignored in the Arabic world but it was anonymously translated into Latin around 1200 A.D. and further summarised and expanded on by the Polish monk Witelo making it a standard text on optics in Europe for the next 400 years. In the 13th century in medieval Europe, English bishop Robert Grosseteste wrote on
12012-535: The feud between the two lasted until Hooke's death. In 1704, Newton published Opticks and, at the time, partly because of his success in other areas of physics, he was generally considered to be the victor in the debate over the nature of light. Newtonian optics was generally accepted until the early 19th century when Thomas Young and Augustin-Jean Fresnel conducted experiments on the interference of light that firmly established light's wave nature. Young's famous double slit experiment showed that light followed
12155-474: The focus to be smeared out in space. In particular, spherical mirrors exhibit spherical aberration . Curved mirrors can form images with a magnification greater than or less than one, and the magnification can be negative, indicating that the image is inverted. An upright image formed by reflection in a mirror is always virtual, while an inverted image is real and can be projected onto a screen. Refraction occurs when light travels through an area of space that has
12298-411: The gloss of surfaces such as mirrors, which reflect light in a simple, predictable way. This allows for the production of reflected images that can be associated with an actual ( real ) or extrapolated ( virtual ) location in space. Diffuse reflection describes non-glossy materials, such as paper or rock. The reflections from these surfaces can only be described statistically, with the exact distribution of
12441-439: The high quality images seen today. In August 1893, August Köhler developed Köhler illumination . This method of sample illumination gives rise to extremely even lighting and overcomes many limitations of older techniques of sample illumination. Before development of Köhler illumination the image of the light source, for example a lightbulb filament, was always visible in the image of the sample. The Nobel Prize in physics
12584-496: The image. Since the mid-20th century chemical fluorescent stains, such as DAPI which binds to DNA , have been used to label specific structures within the cell. More recent developments include immunofluorescence , which uses fluorescently labelled antibodies to recognise specific proteins within a sample, and fluorescent proteins like GFP which a live cell can express making it fluorescent. All modern optical microscopes designed for viewing samples by transmitted light share
12727-1499: The imaging by second lens surface, by taking the above sign convention, u ′ = − v ′ + d {\textstyle \ u'=-v'+d\ } and n 2 − v ′ + d + n 1 v = n 1 − n 2 R 2 . {\displaystyle \ {\frac {n_{2}}{\ -v'+d\ }}+{\frac {\ n_{1}\ }{\ v\ }}={\frac {\ n_{1}-n_{2}\ }{\ R_{2}\ }}~.} Adding these two equations yields n 1 u + n 1 v = ( n 2 − n 1 ) ( 1 R 1 − 1 R 2 ) + n 2 d ( v ′ − d ) v ′ . {\displaystyle \ {\frac {\ n_{1}\ }{u}}+{\frac {\ n_{1}\ }{v}}=\left(n_{2}-n_{1}\right)\left({\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}\right)+{\frac {\ n_{2}\ d\ }{\ \left(\ v'-d\ \right)\ v'\ }}~.} For
12870-416: The incident rays came. This is called retroreflection . Mirrors with curved surfaces can be modelled by ray tracing and using the law of reflection at each point on the surface. For mirrors with parabolic surfaces , parallel rays incident on the mirror produce reflected rays that converge at a common focus . Other curved surfaces may also focus light, but with aberrations due to the diverging shape causing
13013-418: The indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. In most materials, the index of refraction varies with the frequency of the light, known as dispersion . Taking this into account, Snell's Law can be used to predict how a prism will disperse light into
13156-436: The interaction between light and matter that followed from these developments not only formed the basis of quantum optics but also was crucial for the development of quantum mechanics as a whole. The ultimate culmination, the theory of quantum electrodynamics , explains all optics and electromagnetic processes in general as the result of the exchange of real and virtual photons. Quantum optics gained practical importance with
13299-426: The interaction of light with the material. For instance, the behaviour of a light wave interacting with a metal surface is quite different from what happens when it interacts with a dielectric material. A vector model must also be used to model polarised light. Numerical modeling techniques such as the finite element method , the boundary element method and the transmission-line matrix method can be used to model
13442-477: The invention of the compound optical microscope around 1595, and the refracting telescope in 1608, both of which appeared in the spectacle making centres in the Netherlands. In the early 17th century, Johannes Kepler expanded on geometric optics in his writings, covering lenses, reflection by flat and curved mirrors, the principles of pinhole cameras , inverse-square law governing the intensity of light, and
13585-491: The inventions of the maser in 1953 and of the laser in 1960. Following the work of Paul Dirac in quantum field theory , George Sudarshan , Roy J. Glauber , and Leonard Mandel applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics of light. Classical optics is divided into two main branches: geometrical (or ray) optics and physical (or wave) optics. In geometrical optics, light
13728-421: The knowledge of the rudimentary optical theory of the day). The practical development and experimentation with lenses led to the invention of the compound optical microscope around 1595, and the refracting telescope in 1608, both of which appeared in the spectacle-making centres in the Netherlands . With the invention of the telescope and microscope there was a great deal of experimentation with lens shapes in
13871-576: The latter ranges from 0.14 to 0.7, corresponding to focal lengths of about 40 to 2 mm, respectively. Objective lenses with higher magnifications normally have a higher numerical aperture and a shorter depth of field in the resulting image. Some high performance objective lenses may require matched eyepieces to deliver the best optical performance. Some microscopes make use of oil-immersion objectives or water-immersion objectives for greater resolution at high magnification. These are used with index-matching material such as immersion oil or water and
14014-504: The laws of reflection and refraction at interfaces between different media. These laws were discovered empirically as far back as 984 AD and have been used in the design of optical components and instruments from then until the present day. They can be summarised as follows: When a ray of light hits the boundary between two transparent materials, it is divided into a reflected and a refracted ray. The laws of reflection and refraction can be derived from Fermat's principle which states that
14157-417: The lens), concave (depressed into the lens), or planar (flat). The line joining the centres of the spheres making up the lens surfaces is called the axis of the lens. Typically the lens axis passes through the physical centre of the lens, because of the way they are manufactured. Lenses may be cut or ground after manufacturing to give them a different shape or size. The lens axis may then not pass through
14300-399: The lens. These two cases are examples of image formation in lenses. In the former case, an object at an infinite distance (as represented by a collimated beam of waves) is focused to an image at the focal point of the lens. In the latter, an object at the focal length distance from the lens is imaged at infinity. The plane perpendicular to the lens axis situated at a distance f from the lens
14443-449: The light is modelled as a collection of particles called " photons ". Quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy , various engineering fields, photography , and medicine (particularly ophthalmology and optometry , in which it is called physiological optics). Practical applications of optics are found in
14586-422: The light is reflected. This phenomenon is called total internal reflection and allows for fibre optics technology. As light travels down an optical fibre, it undergoes total internal reflection allowing for essentially no light to be lost over the length of the cable. A device that produces converging or diverging light rays due to refraction is known as a lens . Lenses are characterized by their focal length :
14729-486: The light path to generate an improved contrast image from a sample. Major techniques for generating increased contrast from the sample include cross-polarized light , dark field , phase contrast and differential interference contrast illumination. A recent technique ( Sarfus ) combines cross-polarized light and specific contrast-enhanced slides for the visualization of nanometric samples. Modern microscopes allow more than just observation of transmitted light image of
14872-486: The light path. The actual power or magnification of a compound optical microscope is the product of the powers of the eyepiece and the objective lens. For example a 10x eyepiece magnification and a 100x objective lens magnification gives a total magnification of 1,000×. Modified environments such as the use of oil or ultraviolet light can increase the resolution and allow for resolved details at magnifications larger than 1,000x. Many techniques are available which modify
15015-443: The mathematical rules of perspective and described the effects of refraction qualitatively, although he questioned that a beam of light from the eye could instantaneously light up the stars every time someone blinked. Euclid stated the principle of shortest trajectory of light, and considered multiple reflections on flat and spherical mirrors. Ptolemy , in his treatise Optics , held an extramission-intromission theory of vision:
15158-489: The merits of Aristotelian and Euclidean ideas of optics, favouring the emission theory since it could better quantify optical phenomena. In 984, the Persian mathematician Ibn Sahl wrote the treatise "On burning mirrors and lenses", correctly describing a law of refraction equivalent to Snell's law. He used this law to compute optimum shapes for lenses and curved mirrors . In the early 11th century, Alhazen (Ibn al-Haytham) wrote
15301-583: The name microscope for the compound microscope Galileo submitted to the Accademia dei Lincei in 1624 (Galileo had called it the " occhiolino " or " little eye "). Faber coined the name from the Greek words μικρόν (micron) meaning "small", and σκοπεῖν (skopein) meaning "to look at", a name meant to be analogous with "telescope", another word coined by the Linceans. Christiaan Huygens , another Dutchman, developed
15444-405: The object and image distances are positive if the object and image are on opposite sides of the lens. Incoming parallel rays are focused by a converging lens onto a spot one focal length from the lens, on the far side of the lens. This is called the rear focal point of the lens. Rays from an object at a finite distance are focused further from the lens than the focal distance; the closer the object
15587-440: The objective lens and the numerical aperture (NA) of the objective lens. There is therefore a finite limit beyond which it is impossible to resolve separate points in the objective field, known as the diffraction limit . Assuming that optical aberrations in the whole optical set-up are negligible, the resolution d , can be stated as: Usually a wavelength of 550 nm is assumed, which corresponds to green light. With air as
15730-464: The optical configuration of the objective lens and eyepiece are matched to give the best possible optical performance. This occurs most commonly with apochromatic objectives. Objective turret, revolver, or revolving nose piece is the part that holds the set of objective lenses. It allows the user to switch between objective lenses. At the lower end of a typical compound optical microscope, there are one or more objective lenses that collect light from
15873-401: The optical explanations of astronomical phenomena such as lunar and solar eclipses and astronomical parallax . He was also able to correctly deduce the role of the retina as the actual organ that recorded images, finally being able to scientifically quantify the effects of different types of lenses that spectacle makers had been observing over the previous 300 years. After the invention of
16016-676: The path taken between two points by a ray of light is the path that can be traversed in the least time. Geometric optics is often simplified by making the paraxial approximation , or "small angle approximation". The mathematical behaviour then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of Gaussian optics and paraxial ray tracing , which are used to find basic properties of optical systems, such as approximate image and object positions and magnifications . Reflections can be divided into two types: specular reflection and diffuse reflection . Specular reflection describes
16159-406: The physical centre of the lens. Toric or sphero-cylindrical lenses have surfaces with two different radii of curvature in two orthogonal planes. They have a different focal power in different meridians. This forms an astigmatic lens. An example is eyeglass lenses that are used to correct astigmatism in someone's eye. Lenses are classified by the curvature of the two optical surfaces. A lens
16302-511: The propagation of light in systems which cannot be solved analytically. Such models are computationally demanding and are normally only used to solve small-scale problems that require accuracy beyond that which can be achieved with analytical solutions. All of the results from geometrical optics can be recovered using the techniques of Fourier optics which apply many of the same mathematical and analytical techniques used in acoustic engineering and signal processing . Gaussian beam propagation
16445-414: The radius of curvature is called the curvature . A flat surface has zero curvature, and its radius of curvature is infinite . This convention seems to be mainly used for this article, although there is another convention such as Cartesian sign convention requiring different lens equation forms. If d is small compared to R 1 and R 2 then the thin lens approximation can be made. For
16588-416: The ray-based model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that light waves were in fact electromagnetic radiation. Some phenomena depend on light having both wave-like and particle-like properties . Explanation of these effects requires quantum mechanics . When considering light's particle-like properties,
16731-416: The rays (or flux) from the eye formed a cone, the vertex being within the eye, and the base defining the visual field. The rays were sensitive, and conveyed information back to the observer's intellect about the distance and orientation of surfaces. He summarized much of Euclid and went on to describe a way to measure the angle of refraction , though he failed to notice the empirical relationship between it and
16874-423: The reflected light depending on the microscopic structure of the material. Many diffuse reflectors are described or can be approximated by Lambert's cosine law , which describes surfaces that have equal luminance when viewed from any angle. Glossy surfaces can give both specular and diffuse reflection. In specular reflection, the direction of the reflected ray is determined by the angle the incident ray makes with
17017-574: The required shape. A lens can focus light to form an image , unlike a prism , which refracts light without focusing. Devices that similarly focus or disperse waves and radiation other than visible light are also called "lenses", such as microwave lenses, electron lenses , acoustic lenses , or explosive lenses . Lenses are used in various imaging devices such as telescopes , binoculars , and cameras . They are also used as visual aids in glasses to correct defects of vision such as myopia and hypermetropia . The word lens comes from lēns ,
17160-774: The right infinity leads to the first or object focal length f 0 {\textstyle f_{0}} for the spherical surface. Similarly, u {\textstyle u} toward the left infinity leads to the second or image focal length f i {\displaystyle f_{i}} . f 0 = n 1 n 2 − n 1 R , f i = n 2 n 2 − n 1 R {\displaystyle {\begin{aligned}f_{0}&={\frac {n_{1}}{n_{2}-n_{1}}}R,\\f_{i}&={\frac {n_{2}}{n_{2}-n_{1}}}R\end{aligned}}} Applying this equation on
17303-626: The same basic components of the light path. In addition, the vast majority of microscopes have the same 'structural' components (numbered below according to the image on the right): The eyepiece , or ocular lens, is a cylinder containing two or more lenses; its function is to bring the image into focus for the eye. The eyepiece is inserted into the top end of the body tube. Eyepieces are interchangeable and many different eyepieces can be inserted with different degrees of magnification. Typical magnification values for eyepieces include 5×, 10× (the most common), 15× and 20×. In some high performance microscopes,
17446-415: The same distance behind the mirror as the objects are in front of the mirror. The image size is the same as the object size. The law also implies that mirror images are parity inverted, which we perceive as a left-right inversion. Images formed from reflection in two (or any even number of) mirrors are not parity inverted. Corner reflectors produce reflected rays that travel back in the direction from which
17589-407: The same side of the lens as the object. The closer the object is to the lens, the closer the virtual image is to the lens. As with mirrors, upright images produced by a single lens are virtual, while inverted images are real. Lenses suffer from aberrations that distort images. Monochromatic aberrations occur because the geometry of the lens does not perfectly direct rays from each object point to
17732-579: The sample. The objective is usually in a cylinder housing containing a glass single or multi-element compound lens. Typically there will be around three objective lenses screwed into a circular nose piece which may be rotated to select the required objective lens. These arrangements are designed to be parfocal , which means that when one changes from one lens to another on a microscope, the sample stays in focus . Microscope objectives are characterized by two parameters, namely, magnification and numerical aperture . The former typically ranges from 5× to 100× while
17875-410: The sign) would have zero optical power (as its focal length becomes infinity as shown in the lensmaker's equation ), meaning that it would neither converge nor diverge light. All real lenses have a nonzero thickness, however, which makes a real lens with identical curved surfaces slightly positive. To obtain exactly zero optical power, a meniscus lens must have slightly unequal curvatures to account for
18018-405: The simple equation 1 S 1 + 1 S 2 = 1 f , {\displaystyle {\frac {1}{S_{1}}}+{\frac {1}{S_{2}}}={\frac {1}{f}},} where S 1 is the distance from the object to the lens, θ 2 is the distance from the lens to the image, and f is the focal length of the lens. In the sign convention used here,
18161-409: The specimen by the user on the stage. Moving to a higher magnification requires the stage to be moved higher vertically for re-focus at the higher magnification and may also require slight horizontal specimen position adjustment. Horizontal specimen position adjustments are the reason for having a mechanical stage. Due to the difficulty in preparing specimens and mounting them on slides, for children it
18304-464: The spectacle making centres in both the Netherlands and Germany. Spectacle makers created improved types of lenses for the correction of vision based more on empirical knowledge gained from observing the effects of the lenses rather than using the rudimentary optical theory of the day (theory which for the most part could not even adequately explain how spectacles worked). This practical development, mastery, and experimentation with lenses led directly to
18447-408: The subscript of 2 in n 2 {\textstyle \ n_{2}\ } is dropped. As mentioned above, a positive or converging lens in air focuses a collimated beam travelling along the lens axis to a spot (known as the focal point ) at a distance f from the lens. Conversely, a point source of light placed at the focal point is converted into a collimated beam by
18590-444: The superposition principle can be used to predict the shape of interacting waveforms through the simple addition of the disturbances. This interaction of waves to produce a resulting pattern is generally termed "interference" and can result in a variety of outcomes. If two waves of the same wavelength and frequency are in phase , both the wave crests and wave troughs align. This results in constructive interference and an increase in
18733-467: The telescope, Kepler set out the theoretical basis on how they worked and described an improved version, known as the Keplerian telescope , using two convex lenses to produce higher magnification. Optical theory progressed in the mid-17th century with treatises written by philosopher René Descartes , which explained a variety of optical phenomena including reflection and refraction by assuming that light
18876-440: The term "light" is also often applied to infrared (0.7–300 μm) and ultraviolet radiation (10–400 nm). The wave model can be used to make predictions about how an optical system will behave without requiring an explanation of what is "waving" in what medium. Until the middle of the 19th century, most physicists believed in an "ethereal" medium in which the light disturbance propagated. The existence of electromagnetic waves
19019-859: The thin lens approximation where d → 0 , {\displaystyle \ d\rightarrow 0\ ,} the 2nd term of the RHS (Right Hand Side) is gone, so n 1 u + n 1 v = ( n 2 − n 1 ) ( 1 R 1 − 1 R 2 ) . {\displaystyle \ {\frac {\ n_{1}\ }{u}}+{\frac {\ n_{1}\ }{v}}=\left(n_{2}-n_{1}\right)\left({\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}\right)~.} The focal length f {\displaystyle \ f\ } of
19162-1110: The thin lens is found by limiting u → − ∞ , {\displaystyle \ u\rightarrow -\infty \ ,} n 1 f = ( n 2 − n 1 ) ( 1 R 1 − 1 R 2 ) → 1 f = ( n 2 n 1 − 1 ) ( 1 R 1 − 1 R 2 ) . {\displaystyle \ {\frac {\ n_{1}\ }{\ f\ }}=\left(n_{2}-n_{1}\right)\left({\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}\right)\rightarrow {\frac {1}{\ f\ }}=\left({\frac {\ n_{2}\ }{\ n_{1}\ }}-1\right)\left({\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}\right)~.} So,
19305-1258: The two spherical surfaces of a lens and approximating the lens thickness to zero (so a thin lens) leads to the lensmaker's formula . Applying Snell's law on the spherical surface, n 1 sin i = n 2 sin r . {\displaystyle n_{1}\sin i=n_{2}\sin r\,.} Also in the diagram, tan ( i − θ ) = h u tan ( θ − r ) = h v sin θ = h R {\displaystyle {\begin{aligned}\tan(i-\theta )&={\frac {h}{u}}\\\tan(\theta -r)&={\frac {h}{v}}\\\sin \theta &={\frac {h}{R}}\end{aligned}}} , and using small angle approximation (paraxial approximation) and eliminating i , r , and θ , n 2 v + n 1 u = n 2 − n 1 R . {\displaystyle {\frac {n_{2}}{v}}+{\frac {n_{1}}{u}}={\frac {n_{2}-n_{1}}{R}}\,.} The (effective) focal length f {\displaystyle f} of
19448-418: The two surfaces. A negative meniscus lens has a steeper concave surface (with a shorter radius than the convex surface) and is thinner at the centre than at the periphery. Conversely, a positive meniscus lens has a steeper convex surface (with a shorter radius than the concave surface) and is thicker at the centre than at the periphery. An ideal thin lens with two surfaces of equal curvature (also equal in
19591-461: The use of a corrective lens when he mentions that Nero was said to watch the gladiatorial games using an emerald (presumably concave to correct for nearsightedness , though the reference is vague). Both Pliny and Seneca the Younger (3 BC–65 AD) described the magnifying effect of a glass globe filled with water. Ptolemy (2nd century) wrote a book on Optics , which however survives only in
19734-462: The use of dual eyepieces reduces eye strain associated with long workdays at a microscopy station. In certain applications, long-working-distance or long-focus microscopes are beneficial. An item may need to be examined behind a window , or industrial subjects may be a hazard to the objective. Such optics resemble telescopes with close-focus capabilities. Measuring microscopes are used for precision measurement. There are two basic types. One has
19877-431: The user to quickly adjust the magnification. A compound microscope also enables more advanced illumination setups, such as phase contrast . There are many variants of the compound optical microscope design for specialized purposes. Some of these are physical design differences allowing specialization for certain purposes: Other microscope variants are designed for different illumination techniques: A digital microscope
20020-400: Was a famous instrument which used interference effects to accurately measure the speed of light. The appearance of thin films and coatings is directly affected by interference effects. Antireflective coatings use destructive interference to reduce the reflectivity of the surfaces they coat, and can be used to minimise glare and unwanted reflections. The simplest case is a single layer with
20163-554: Was awarded to Dutch physicist Frits Zernike in 1953 for his development of phase contrast illumination which allows imaging of transparent samples. By using interference rather than absorption of light, extremely transparent samples, such as live mammalian cells, can be imaged without having to use staining techniques. Just two years later, in 1955, Georges Nomarski published the theory for differential interference contrast microscopy, another interference -based imaging technique. Modern biological microscopy depends heavily on
20306-540: Was emitted by objects which produced it. This differed substantively from the ancient Greek emission theory. In the late 1660s and early 1670s, Isaac Newton expanded Descartes's ideas into a corpuscle theory of light , famously determining that white light was a mix of colours that can be separated into its component parts with a prism . In 1690, Christiaan Huygens proposed a wave theory for light based on suggestions that had been made by Robert Hooke in 1664. Hooke himself publicly criticised Newton's theories of light and
20449-467: Was predicted in 1865 by Maxwell's equations . These waves propagate at the speed of light and have varying electric and magnetic fields which are orthogonal to one another, and also to the direction of propagation of the waves. Light waves are now generally treated as electromagnetic waves except when quantum mechanical effects have to be considered. Many simplified approximations are available for analysing and designing optical systems. Most of these use
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