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 describes the behaviour of visible and infrared light; because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical electromagnetic description of light. Complete electromagnetic descriptions of light are, however difficult to apply in practice. Practical optics is 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; 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 the fact that light has both particle-like properties. Explanation of these effects requires quantum mechanics; when considering light's particle-like properties, 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 and medicine. Practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, telescopes, microscopes and fibre optics. Optics began with the development of lenses by Mesopotamians; the earliest known lenses, made from polished crystal quartz, date from as early as 700 BC for Assyrian lenses such as the Layard/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, the development of geometrical optics in the Greco-Roman world. The word optics comes from the ancient Greek word ὀπτική, meaning "appearance, look". Greek philosophy on optics broke down into two opposing theories on how vision worked, the "intromission theory" and the "emission theory"; the intro-mission approach saw vision as coming from objects casting off copies of themselves that were captured by the eye. With many propagators including Democritus, Epicurus and their followers, this theory seems to have some contact with modern theories of what vision is, but it remained only speculation lacking any experimental foundation. Plato first articulated the emission theory, the idea that visual perception is accomplished by rays emitted by the eyes, he commented on the parity reversal of mirrors in Timaeus. Some hundred years Euclid 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 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. Ptolemy, in his treatise Optics, held an extramission-intromission theory of vision: the rays from the eye formed a cone, the vertex being within the eye, the base defining the visual field; the rays were sensitive, conveyed information back to the observer's intellect about the distance and orientation of surfaces. He summarised 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 the angle of incidence. 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 who wrote on 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" describing a law of refraction equivalent to Snell's law. He used this law to compute optimum shapes for curved mirrors. In the early 11th century, Alhazen wrote the Book of Optics 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, instead put forward the idea that light reflected in all directions in straight lines from all points of the objects being viewed and entered the eye, although he was unable to explain how the eye captured the rays. Alhazen's work was 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 a wide range of scientific topics, discussed light from four different perspectives: an epistemology of light, a metaphysics or cosmogony of light, an etiology or physics of light, a theology of light, basing it on the works Aristotle and Platonism.
Grosseteste's most famous disciple, Roger Bacon, wrote w
In optics, the exit pupil is a virtual aperture in an optical system. Only rays which pass through this virtual aperture can exit the system; the exit pupil is the image of the aperture stop in the optics. In a telescope or compound microscope, this image is the image of the objective element as produced by the eyepiece; the size and shape of this disc is crucial to the instrument's performance, because the observer's eye can see light only if it passes through this tiny aperture. The term exit pupil is sometimes used to refer to the diameter of the virtual aperture. Older literature on optics sometimes refers to the exit pupil as the Ramsden disc, named after English instrument-maker Jesse Ramsden. To use an optical instrument, the entrance pupil of the viewer's eye must be aligned with and be of similar size to the instrument's exit pupil; this properly avoids vignetting. The location of the exit pupil thus determines the eye relief of an eyepiece. Good eyepiece designs produce an exit pupil of diameter approximating the eye's apparent pupil diameter, located about 20 mm away from the last surface of the eyepiece for the viewer's comfort.
If the disc is larger than the eye's pupil, light will be lost instead of entering the eye. If the disc is too close to the last surface of the eyepiece, the eye will have to be uncomfortably close for viewing. Since the eye's pupil varies in diameter with viewing conditions, the ideal exit pupil diameter depends on the application. An astronomical telescope requires a large pupil because it is designed to be used for looking at dim objects at night, while a microscope will require a much smaller pupil since the object will be brightly illuminated. A set of 7×50 binoculars has an exit pupil just over 7.1 mm, which corresponds to the average pupil size of a youthful dark-adapted human eye in circumstances with no extraneous light. The emergent light at the eyepiece fills the eye's pupil, meaning no loss of brightness at night due to using such binoculars. In daylight, when the eye's pupil is only 4 mm in diameter, over half the light will be blocked by the iris and will not reach the retina. However, the loss of light in the daytime is not significant since there is so much light to start with.
By contrast, 8×32 binoculars sold with emphasis on their compactness, have an exit pupil of only 4 mm. That is sufficient to fill a typical daytime eye pupil, making these binoculars better suited to daytime than night-time use; the maximum pupil size of a human eye is 5–9 mm for individuals below 25 years old, decreases with age as shown as an approximate guide in the table below. The optimum eye relief distance varies with application. For example, a rifle scope needs a long eye relief to prevent recoil from causing it to strike the observer; the exit pupil can be visualized by focusing the instrument on a bright, nondescript field, holding a white card up to the eyepiece. This projects a disc of light onto the card. By moving the card closer to or further away from the eyepiece, the disc of light will be minimized when the card is at the exit pupil, the bright disc shows the diameter of the pupil. A clear vial of milky fluid can be used to visualize the light rays, which appear as an hourglass shape converging and diverging as they exit the eyepiece, with the smallest cross-section representing the exit pupil.
For a telescope, the diameter of the exit pupil can be calculated by dividing the focal length of the eyepiece by the focal ratio of the telescope. In all but the cheapest telescopes, the eyepieces are interchangeable, for this reason, the magnification is not written on the scope, as it will change with different eyepieces. Instead, the f-number f=L/D of the telescope is written on the scope, as well as the objective diameter D and focal length L; the individual eyepieces have their focal lengths written on them as well. In the case of binoculars however, the two eyepieces are permanently attached, the magnification and objective diameter is written on the binoculars in the form, e.g. 7×50. In that case, the exit pupil can be calculated as the diameter of the objective lens divided by the magnification; the two formulas are of course equivalent and it is a matter of which information one starts with as to which formula to use. The distance of the exit pupil from the sensor plane determines the range of angles of incidence that light will make with the sensor.
Digital image sensors have a limited range of angles over which they will efficiently accept light those that use microlenses to increase their sensitivity. The closer the exit pupil to the focal plane, the higher the angles of incidence at the extreme edges of the field; this can lead to pixel vignetting. For this reason, many small digital cameras are image-space telecentric. Transmittance Diaphragm Pupil magnification Greivenkamp, John E.. Field Guide to Geometrical Optics. SPIE Field Guides vol. FG01. SPIE. ISBN 0-8194-5294-7. Hecht, Eugene. Optics. Addison Wesley. ISBN 0-201-11609-X. A short definition of relative brightness
SPIE is an international not-for-profit professional society for optics and photonics technology, founded in 1955. It organizes technical conferences, trade exhibitions, continuing education programs for researchers and developers in the light-based fields of physics, including: optics and imaging engineering. SPIE is most known for Photonics West, held in San Francisco; the society publishes peer-reviewed scientific journals, conference proceedings, tutorial texts, field guides, reference volumes in print and online. In 2018, the society provided more than $4 million in support of optics education and outreach programs around the world. On July 1, 1955 SPIE was founded as the Society of Photographic Instrumentation Engineers in California to specialize in the application of photographic instrumentation. In 1964 the society changed its name to the Society of Photo-Optical Instrumentation Engineers. In 1977 SPIE moved its headquarters to Bellingham, in 1981 the Society began doing business as SPIE—The International Society for Optical Engineering to reflect a changing membership.
In 2007, the society ended its DBA and is now referred to as "SPIE." SPIE Conferences and Exhibitions connect the optics industry. The society is affiliated with events each year; the society's first publication, SPIE Newsletter, was launched in 1957. In 1959, the society published its first book; the newsletter morphed into the society’s first journal, now known as Optical Engineering, SPIE’s flagship monthly journal. Throughout the years, SPIE has created many publications including journals, newspapers and books. SPIE publishes: Ten scientific online journals SPIE Technical Paper Proceedings At least 25 original technical books per year via SPIE Press All SPIE journals are peer-reviewed. Journal of Applied Remote Sensing is an quarterly published journal on remote sensing. Journal of Astronomical Telescopes and Systems is published quarterly and covers development and application of telescopes, instrumentation and systems for ground- and space-based astronomy. Journal of Biomedical Optics is published monthly with the latest on optical technology in health care and research.
Journal of Electronic Imaging, co-published bi-monthly with the Society for Imaging Science and Technology, publishes papers on electronic imaging science and technology. Journal of Medical Imaging is published quarterly and covers fundamental and translational research and applications focused on photonics in medical imaging, which continue to yield physical and biomedical advancements in early detection and therapy of disease as well as in the understanding of normal. Journal of Micro/Nanolithography, MEMS, MOEMS is published quarterly and contains papers on technologies for the needs of the electronics, micro-opto-electro-mechanical systems, photonics industries. Journal of Nanophotonics is an online-only, quarterly published journal on fabrication and application of nanostructures that generate or manipulate light from the infrared to the ultraviolet regimes. Journal of Photonics for Energy is an e-journal published quarterly that covers fundamental and applied research applications of photonics for renewable energy harvesting, storage, monitoring and efficient usage.
Neurophotonics, published quarterly, is at the interface of optics and neuroscience covering advances in optical technology applicable to study of the brain and their impact on the basic and clinical neuroscience applications. Optical Engineering is the flagship monthly journal of the society, with papers on research and development in all areas of optics and imaging science and engineering. SPIE Press, the only independent, not-for-profit book publisher specializing in optics and photonics technologies, produces print monographs, tutorial texts, field guides, as well as electronic books and apps for mobile devices, its origins date back to 1989 with the publication of The New Physical Optics Notebook. The SPIE Digital Library publishes online technical papers from SPIE Journals and Conference Proceedings from 1962 to the present, as well as eBooks published by SPIE Press. There are more than 480,000 articles, with more than 18,000 new research papers added annually. SPIE Professional is a quarterly magazine that covers optics industry insights, technology overviews, career trends, provides informational articles for optics and photonics professionals.
The SPIE Newsroom includes technical articles. SPIE started a new open access program in January 2013 to promote knowledge transfer and awareness of technology and industry developments in optics and photonics. All new articles published in SPIE journals for which authors pay voluntary page charges are accessible to anyone; the society issues several awards: Gold Medal of the Society Award Britton Chance Biomedical Optics Award Biophotonics Technology Innovator Award A. E. Conrady Award Harold E. Edgerton Award Dennis Gabor Award George W. Goddard Award Rudolf Kingslake Medal and Prize G. G. Stokes Award Chandra S. Vikram Award in Optical Metrology Frits Zernike Award for Microlithography Early Career Achievement Award SPIE Educator Award SPIE Technology Achievement Award (since
A telecentric lens is a compound lens that has its entrance or exit pupil at infinity. This means that the chief rays are parallel to the optical axis in front of or behind the system, respectively; the simplest way to make a lens telecentric is to put the aperture stop at one of the lens's focal points. An entrance pupil at infinity makes the lens object-space telecentric; such lenses are used in machine vision systems because image magnification is independent of the object's distance or position in the field of view. An exit pupil at infinity makes the lens image-space telecentric; such lenses are used with image sensors. For example, a three-CCD color beamsplitter prism assembly works best with a telecentric lens, many digital image sensors have a minimum of color crosstalk and shading problems when used with telecentric lenses. If both pupils are at infinity, the lens is double telecentric. Non-telecentric lenses exhibit varying magnification for objects at different distances from the lens.
Most lenses are entocentric—objects further away have lower magnification. For pericentric lenses, objects further away have higher magnification; the variation of magnification with distance causes several problems for machine vision and other applications: The apparent size of objects changes with distance from the camera. Some features or objects may be hidden by objects; the apparent shape of objects varies with distance from the center of the field of view. Objects appearing close to the edges are viewed from an angle, while objects near the centre of the FOV are viewed frontally. Telecentric lenses, on the other hand, provide an orthographic projection, providing the same magnification at all distances. An object, too close or too far from the lens may still be out of focus, but the resulting blurry image will have the same size as the focused image would; because their images have constant magnification and geometry, telecentric lenses are used for metrology applications, when a machine vision system must determine the precise size of objects independently from their position within the FOV and when their distance is affected by some degree of unknown variations.
These lenses are commonly used in optical lithography for forming patterns in semiconductor chips. Object-space telecentric lenses have an entrance pupil infinitely far behind the lens. Telecentric lenses tend to be larger and more expensive than normal lenses of similar focal length and f-number; this is due to the extra components needed to achieve telecentricity, because the object or image lens elements of an object or image-space telecentric lens must be at least as large as the largest object to be photographed or image to be formed. As of 2006, these lenses can range in cost from hundreds to thousands of US dollars or euros, depending on quality; because of their intended applications, telecentric lenses have higher resolution and transmit more light than normal photographic lenses. In order to optimize the telecentric effect, these lenses are used in conjunction with telecentric illuminators, which produce a parallel light flow from LED sources. An image-space telecentric lens produces images of the same size regardless of the distance between the lens and the film or image sensor.
This allows the lens to be focused to different distances without changing the size of the image. Image-space telecentric lenses have an exit pupil infinitely far in front of the lens. At the film or image sensor, all of the chief rays from these lenses hit "straight on", or at zero angle of incidence; this property minimizes any angle-of-incidence dependence of the sensor, or of any beam-splitter prism assembly behind the lens, such as a color separation prism in a three-CCD camera. Many lenses that have been specially optimized for digital SLR cameras are nearly telecentric on the image side, to avoid the vignetting and color crosstalk that occur in color filter array-based digital image sensors with oblique incident rays; the Four Thirds System uses this approach. Since the ray cones approaching the detector surface have the same angle of incidence and angular subtense everywhere in the image plane, the image is evenly illuminated; this feature is used in photography and is useful for radiometric and color measurement applications, where one would need the irradiance to be the same regardless of the field position.
Lenses that are double-telecentric have magnification, more constant than those that are only object-side telecentric, because the principal ray intercept position on the detector does not change. This property allows precise measurement of objects regardless of position. Orthographic projection Technical description of telecentric effect from Edmund Optics, a manufacturer of telecentric lenses Telecentric lenses tutorial from Opto Engineering, a manufacturer of telecentric lenses Another good explanatory page by Donald Simanek A course on Gaussian optics of telecentric systems from Schneider Kreuznach Optical measurement techniques with telecentric lenses
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
OCLC Online Computer Library Center, Incorporated d/b/a OCLC is an American nonprofit cooperative organization "dedicated to the public purposes of furthering access to the world's information and reducing information costs". It was founded in 1967 as the Ohio College Library Center. OCLC and its member libraries cooperatively produce and maintain WorldCat, the largest online public access catalog in the world. OCLC is funded by the fees that libraries have to pay for its services. OCLC maintains the Dewey Decimal Classification system. OCLC began in 1967, as the Ohio College Library Center, through a collaboration of university presidents, vice presidents, library directors who wanted to create a cooperative computerized network for libraries in the state of Ohio; the group first met on July 5, 1967 on the campus of the Ohio State University to sign the articles of incorporation for the nonprofit organization, hired Frederick G. Kilgour, a former Yale University medical school librarian, to design the shared cataloging system.
Kilgour wished to merge the latest information storage and retrieval system of the time, the computer, with the oldest, the library. The plan was to merge the catalogs of Ohio libraries electronically through a computer network and database to streamline operations, control costs, increase efficiency in library management, bringing libraries together to cooperatively keep track of the world's information in order to best serve researchers and scholars; the first library to do online cataloging through OCLC was the Alden Library at Ohio University on August 26, 1971. This was the first online cataloging by any library worldwide. Membership in OCLC is based on use of services and contribution of data. Between 1967 and 1977, OCLC membership was limited to institutions in Ohio, but in 1978, a new governance structure was established that allowed institutions from other states to join. In 2002, the governance structure was again modified to accommodate participation from outside the United States.
As OCLC expanded services in the United States outside Ohio, it relied on establishing strategic partnerships with "networks", organizations that provided training and marketing services. By 2008, there were 15 independent United States regional service providers. OCLC networks played a key role in OCLC governance, with networks electing delegates to serve on the OCLC Members Council. During 2008, OCLC commissioned two studies to look at distribution channels. In early 2009, OCLC negotiated new contracts with the former networks and opened a centralized support center. OCLC provides bibliographic and full-text information to anyone. OCLC and its member libraries cooperatively produce and maintain WorldCat—the OCLC Online Union Catalog, the largest online public access catalog in the world. WorldCat has holding records from private libraries worldwide; the Open WorldCat program, launched in late 2003, exposed a subset of WorldCat records to Web users via popular Internet search and bookselling sites.
In October 2005, the OCLC technical staff began a wiki project, WikiD, allowing readers to add commentary and structured-field information associated with any WorldCat record. WikiD was phased out; the Online Computer Library Center acquired the trademark and copyrights associated with the Dewey Decimal Classification System when it bought Forest Press in 1988. A browser for books with their Dewey Decimal Classifications was available until July 2013; until August 2009, when it was sold to Backstage Library Works, OCLC owned a preservation microfilm and digitization operation called the OCLC Preservation Service Center, with its principal office in Bethlehem, Pennsylvania. The reference management service QuestionPoint provides libraries with tools to communicate with users; this around-the-clock reference service is provided by a cooperative of participating global libraries. Starting in 1971, OCLC produced catalog cards for members alongside its shared online catalog. OCLC commercially sells software, such as CONTENTdm for managing digital collections.
It offers the bibliographic discovery system WorldCat Discovery, which allows for library patrons to use a single search interface to access an institution's catalog, database subscriptions and more. OCLC has been conducting research for the library community for more than 30 years. In accordance with its mission, OCLC makes its research outcomes known through various publications; these publications, including journal articles, reports and presentations, are available through the organization's website. OCLC Publications – Research articles from various journals including Code4Lib Journal, OCLC Research, Reference & User Services Quarterly, College & Research Libraries News, Art Libraries Journal, National Education Association Newsletter; the most recent publications are displayed first, all archived resources, starting in 1970, are available. Membership Reports – A number of significant reports on topics ranging from virtual reference in libraries to perceptions about library funding. Newsletters – Current and archived newsletters for the library and archive community.
Presentations – Presentations from both guest speakers and OCLC research from conferences and other events. The presentations are organized into five categories: Conference presentations, Dewey presentations, Distinguished Seminar Series, Guest presentations, Research staff
Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a calculated number called "magnification"; when this number is less than one, it refers to a reduction in size, sometimes called minification or de-magnification. Magnification is related to scaling up visuals or images to be able to see more detail, increasing resolution, using microscope, printing techniques, or digital processing. In all cases, the magnification of the image does not change the perspective of the image; some optical instruments provide visual aid by magnifying distant subjects. A magnifying glass, which uses a positive lens to make things look bigger by allowing the user to hold them closer to their eye. A telescope, which uses its large objective lens or primary mirror to create an image of a distant object and allows the user to examine the image with a smaller eyepiece lens, thus making the object look larger. A microscope, which makes a small object appear as a much larger image at a comfortable distance for viewing.
A microscope is similar in layout to a telescope except that the object being viewed is close to the objective, much smaller than the eyepiece. A slide projector, which projects a large image of a small slide on a screen. A photographic enlarger is similar. Optical magnification is the ratio between the apparent size of an object and its true size, thus it is a dimensionless number. Optical magnification is sometimes referred to as "power", although this can lead to confusion with optical power. For real images, such as images projected on a screen, size means a linear dimension. For optical instruments with an eyepiece, the linear dimension of the image seen in the eyepiece cannot be given, thus size means the angle subtended by the object at the focal point. Speaking, one should take the tangent of that angle. Thus, angular magnification is given by: where ε 0 is the angle subtended by the object at the front focal point of the objective and ε is the angle subtended by the image at the rear focal point of the eyepiece.
For example, the mean angular size of the Moon's disk as viewed from Earth's surface is about 0.52°. Thus, through binoculars with 10× magnification, the Moon appears to subtend an angle of about 5.2°. By convention, for magnifying glasses and optical microscopes, where the size of the object is a linear dimension and the apparent size is an angle, the magnification is the ratio between the apparent size as seen in the eyepiece and the angular size of the object when placed at the conventional closest distance of distinct vision: 25 cm from the eye; the linear magnification of a thin lens is where f is the focal length and d o is the distance from the lens to the object. Note that for real images, M is negative and the image is inverted. For virtual images, M is positive and the image is upright. With d i d_ being the distance from the lens to the image, h i h_ the height of the image and h o h_ the height of the object, the magnification can be written as: Note again that a negative magnification implies an inverted image.
The image recorded by a photographic film or image sensor is always a real image and is inverted. When measuring the height of an inverted image using the cartesian sign convention the value for hi will be negative, as a result M will be negative. However, the traditional sign convention used in photography is "real is positive, virtual is negative". Therefore, in photography: Object height and distance are always positive; when the focal length is positive the image's height and magnification are real and positive. Only if the focal length is negative, the image's height and magnification are virtual and negative. Therefore, the photographic magnification formulae are traditionally presented as: The angular magnification of an optical telescope is given by in which f o f_ is the focal length of the objective lens in a refractor or of the primary mirror in a reflector, f e f_ is the focal length of the eyepiece; the maximum angular magnification of a magnifying glass depends on how the glass and the object are held, relative to the eye.
If the lens is held at a distance from the object such that its front focal point is on the object being viewed, the relaxed eye can view the image with angular magnification Here, f f is the focal length of the lens in centimeters. The constant 25 cm is an estimate of the "near point" distance of the eye—the closest distance at which the healthy naked eye can focus. In this case the angular magnification is independent from the distance kept between the eye and the magnifying glass. If instead the lens is held close to the eye and the object is placed closer to the lens than its focal point so that the observer focuses on the near point, a larger angular magnification can be obtained, approaching A different interpretation of the working of the latter case is that the magnifying glass changes the diopter of the eye so that the object can be placed closer to the eye resulting in a larger angular magnification; the angular ma