The achromatic telescope is a refracting telescope that uses an achromatic lens to correct for chromatic aberration. When an image passes through a lens, the light is refracted at different angles for different wavelengths; this produces focal lengths. So, for example, at the focal plane an image may be focused at the red end of the spectrum, but blurred at the blue end; this effect is noticeable the further an object lies from the central axis of the telescope. The image of a star can appear blue on one orange on the other. Early refracting telescopes with non-achromatic objectives were constructed with long focal lengths to mask the chromatic aberration. An Achromatic telescope uses an achromatic lens to correct for this. An achromatic lens is a compound lenses made with two types of glass with different dispersion. One element, a concave lens made out of Flint glass, has high dispersion, while the other, a convex element made of Crown glass, has a lower dispersion; the crown lens is placed at the front due to the higher susceptibility of flint glass to atmospheric attack.
The lens elements are mounted next to each other and shaped so that the chromatic aberration of one is counterbalanced by the chromatic aberration of the other, while the positive power of the crown lens element is not quite equaled by the negative power of the flint lens element. Together they form a weak positive lens that will bring two different wavelengths of light to a common focus. Uses an equiconvex crown with R1=R2, a flint with R3=-R2 and a flat back. Can produce a ghost image between R2 and R3 because they have the same radii. May produce a ghost image between the flat R4 and rear of the telescope tube. R1 is set greater than R2, R2 is set close to, but not equal, R3. R4 is greater than R3. Uses an equiconvex crown with R1=R2, a flint with R3~R2 and R4>>R3. R3 is set shorter than R2 to create a focus mismatch between R2 and R3, thereby reducing ghosting between the crown and flint; the use of oil between the crown and flint eliminates the effect of ghosting where R2=R3. It can increase light transmission and reduce the impact of errors in R2 and R3.
Is a flint-first doublet in need of stronger curvature than, e.g. a Fraunhofer doublet Apochromat History of telescopes List of telescope types
In physics refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium. Refraction of light is the most observed phenomenon, but other waves such as sound waves and water waves experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed. For light, refraction follows Snell's law, which states that, for a given pair of media, the ratio of the sines of the angle of incidence θ1 and angle of refraction θ2 is equal to the ratio of phase velocities in the two media, or equivalently, to the indices of refraction of the two media. Sin θ 1 sin θ 2 = v 1 v 2 = n 2 n 1 Optical prisms and lenses utilize refraction to redirect light, as does the human eye; the refractive index of materials varies with the wavelength of light, thus the angle of the refraction varies correspondingly. This is called dispersion and causes prisms and rainbows to divide white light into its constituent spectral colors.
Consider a wave going from one material to another where its speed is slower as in the figure. If it reaches the interface between the materials at an angle one side of the wave will reach the second material first, therefore slow down earlier. With one side of the wave going slower the whole wave will pivot towards that side; this is why a wave will bend away from the surface or toward the normal when going into a slower material. In the opposite case of a wave reaching a material where the speed is higher, one side of the wave will speed up and the wave will pivot away from that side. Another way of understanding the same thing is to consider the change in wavelength at the interface; when the wave goes from one material to another where the wave has a different speed v, the frequency f of the wave will stay the same, but the distance between wavefronts or wavelength λ=v/f will change. If the speed is decreased, such as in the figure to the right, the wavelength will decrease. With an angle between the wave fronts and the interface and change in distance between the wave fronts the angle must change over the interface to keep the wave fronts intact.
From these considerations the relationship between the angle of incidence θ1, angle of transmission θ2 and the wave speeds v1 and v2 in the two materials can be derived. This is the law of refraction or Snell's law and can be written as sin θ 1 sin θ 2 = v 1 v 2; the phenomenon of refraction can in a more fundamental way be derived from the 2 or 3-dimensional wave equation. The boundary condition at the interface will require the tangential component of the wave vector to be identical on the two sides of the interface. Since the magnitude of the wave vector depend on the wave speed this requires a change in direction of the wave vector; the relevant wave speed in the discussion above is the phase velocity of the wave. This is close to the group velocity which can be seen as the truer speed of a wave, but when they differ it is important to use the phase velocity in all calculations relating to refraction. A wave traveling perpendicular to a boundary, i.e. having its wavefronts parallel to the boundary, will not change direction if the speed of the wave changes.
Refraction of light can be seen in many places in our everyday life. It makes objects under a water surface appear closer than they are, it is what optical lenses are based on, allowing for instruments such as glasses, binoculars and the human eye. Refraction is responsible for some natural optical phenomena including rainbows and mirages. For light, the refractive index n of a material is more used than the wave phase speed v in the material, they are, directly related through the speed of light in vacuum c as n = c v. In optics, the law of refraction is written as n 1 sin θ 1 = n 2 sin θ 2. Refraction occurs when light goes through a water surface since water has a refractive index of 1.33 and air has a refractive index of about 1. Looking at a straight object, such as a pencil in the figure here, placed at a slant in the water, the object appears to bend at the water's surface; this is due to the bending of light rays. Once the rays reach the eye, the eye traces them back as straight lines.
The lines of sight intersect at a higher position than. This causes the pencil to appear higher and the water to appear shallower than it is; the depth that the water appears to be when viewed from above is known as the apparent depth. This is an important consideration for spearfishing from the surface because it will make the target fish appear to be in a different place, the fisher must aim lower to catch the fish. Conversely
In geometrical optics, a focus called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle; this non-ideal focusing may be caused by aberrations of the imaging optics. In the absence of significant aberrations, the smallest possible blur circle is the Airy disc, caused by diffraction from the optical system's aperture. Aberrations tend to get worse as the aperture diameter increases, while the Airy circle is smallest for large apertures. An image, or image point or region, is in focus if light from object points is converged as much as possible in the image, out of focus if light is not well converged; the border between these is sometimes defined using a "circle of confusion" criterion. A principal focus or focal point is a special focus: For a lens, or a spherical or parabolic mirror, it is a point onto which collimated light parallel to the axis is focused.
Since light can pass through a lens in either direction, a lens has two focal points – one on each side. The distance in air from the lens or mirror's principal plane to the focus is called the focal length. Elliptical mirrors have two focal points: light that passes through one of these before striking the mirror is reflected such that it passes through the other; the focus of a hyperbolic mirror is either of two points which have the property that light from one is reflected as if it came from the other. Diverging lenses and convex mirrors do not focus a collimated beam to a point. Instead, the focus is the point from which the light appears to be emanating, after it travels through the lens or reflects from the mirror. A convex parabolic mirror will reflect a beam of collimated light to make it appear as if it were radiating from the focal point, or conversely, reflect rays directed toward the focus as a collimated beam. A convex elliptical mirror will reflect light directed towards one focus as if it were radiating from the other focus, both of which are behind the mirror.
A convex hyperbolic mirror will reflect rays emanating from the focal point in front of the mirror as if they were emanating from the focal point behind the mirror. Conversely, it can focus rays directed at the focal point, behind the mirror towards the focal point, in front of the mirror as in a Cassegrain telescope. Autofocus Cardinal point Defocus aberration Depth of field Depth of focus Far point Focus Fixed focus Bokeh Focus stacking Focal Plane Manual focus
The focal length of an optical system is a measure of how the system converges or diverges light. For an optical system in air, it is the distance over which collimated rays are brought to a focus. A system with a shorter focal length has greater optical power than one with a long focal length. In most photography and all telescopy, where the subject is infinitely far away, longer focal length leads to higher magnification and a narrower angle of view. On the other hand, in applications such as microscopy in which magnification is achieved by bringing the object close to the lens, a shorter focal length leads to higher magnification because the subject can be brought closer to the center of projection. For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci of the lens. For a converging lens, the focal length is positive, is the distance at which a beam of collimated light will be focused to a single spot. For a diverging lens, the focal length is negative, is the distance to the point from which a collimated beam appears to be diverging after passing through the lens.
When a lens is used to form an image of some object, the distance from the object to the lens u, the distance from the lens to the image v, the focal length f are related by 1 f = 1 u + 1 v. The focal length of a thin lens can be measured by using it to form an image of a distant light source on a screen; the lens is moved. In this case 1/u is negligible, the focal length is given by f ≈ v. For a thick lens, or an imaging system consisting of several lenses or mirrors, the focal length is called the effective focal length, to distinguish it from other used parameters: Front focal length or front focal distance is the distance from the front focal point of the system to the vertex of the first optical surface. Back focal length or back focal distance is the distance from the vertex of the last optical surface of the system to the rear focal point. For an optical system in air, the effective focal length gives the distance from the front and rear principal planes to the corresponding focal points.
If the surrounding medium is not air the distance is multiplied by the refractive index of the medium. Some authors call these distances the front/rear focal lengths, distinguishing them from the front/rear focal distances, defined above. In general, the focal length or EFL is the value that describes the ability of the optical system to focus light, is the value used to calculate the magnification of the system; the other parameters are used in determining where an image will be formed for a given object position. For the case of a lens of thickness d in air, surfaces with radii of curvature R1 and R2, the effective focal length f is given by the Lensmaker's equation: 1 f =, where n is the refractive index of the lens medium; the quantity 1/f is known as the optical power of the lens. The corresponding front focal distance is: FFD = f, the back focal distance: BFD = f. In the sign convention used here, the value of R1 will be positive if the first lens surface is convex, negative if it is concave.
The value of R2 is negative if the second surface is convex, positive if concave. Note that sign conventions vary between different authors, which results in different forms of these equations depending on the convention used. For a spherically curved mirror in air, the magnitude of the focal length is equal to the radius of curvature of the mirror divided by two; the focal length is positive for a concave mi
In optics, aberration is a property of optical systems such as lenses that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics. In an imaging system, it occurs when light from one point of an object does not converge into a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements. An image-forming optical system with aberration will produce an image, not sharp. Makers of optical instruments need to correct optical systems to compensate for aberration. Aberration can be analyzed with the techniques of geometrical optics; the articles on reflection and caustics discuss the general features of reflected and refracted rays.
With an ideal lens, light from any given point on an object would pass through the lens and come together at a single point in the image plane. Real lenses do not focus light to a single point, however when they are made; these deviations from the idealized lens performance are called aberrations of the lens. Aberrations fall into two classes: chromatic. Monochromatic aberrations are caused by the geometry of the lens or mirror and occur both when light is reflected and when it is refracted, they appear when using monochromatic light, hence the name. Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength; because of dispersion, different wavelengths of light come to focus at different points. Chromatic aberration does not appear; the most common monochromatic aberrations are: Defocus Spherical aberration Coma Astigmatism Field curvature Image distortionAlthough defocus is technically the lowest-order of the optical aberrations, it is not considered as a lens aberration, since it can be corrected by moving the lens to bring the image plane to the optical focus of the lens.
In addition to these aberrations and tilt are effects which shift the position of the focal point. Piston and tilt are not true optical aberrations, since when an otherwise perfect wavefront is altered by piston and tilt, it will still form a perfect, aberration-free image, only shifted to a different position. Chromatic aberration occurs. Types of chromatic aberration are: Axial chromatic aberration Lateral chromatic aberration A perfect optical system would follow the theorem: Rays of light proceeding from any object point unite in an image point; the introduction of simple auxiliary terms, due to Gauss, named the focal lengths and focal planes, permits the determination of the image of any object for any system. The Gaussian theory, however, is only true so long as the angles made by all rays with the optical axis are infinitely small, i.e. with infinitesimal objects and lenses. The investigations of James Clerk Maxwell and Ernst Abbe showed that the properties of these reproductions, i.e. the relative position and magnitude of the images, are not special properties of optical systems, but necessary consequences of the supposition of the reproduction of all points of a space in image points, are independent of the manner in which the reproduction is effected.
These authors showed, that no optical system can justify these suppositions, since they are contradictory to the fundamental laws of reflection and refraction. The Gaussian theory only supplies a convenient method of approximating to reality. At present, all that can be attempted is to reproduce a single plane in another plane; the classical theory of optics and related systems has been analyzed by numerous authors. Let S be any optical system, rays proceeding from an axis point O under an angle u1 will unite in the axis point O'1. If there is refraction at a collective spherical surface, or through a thin positive lens, O'2 will lie in front of O'1 so long as the angle u2 is greater than u1; the caustic, in the first case, resembles the sign >. If the angle u1 is small, O'1 is the Gaussian image. If the pencil with the angle u2 is that of the maximum aberration of all the pencils transmitted in a plane perpendicular to the axis at O'1 there is a circular disk of confusion of radius O'1R, in a parallel plane at O'2 another one of radius O'2R2.
The largest opening of the pencils, which take part in the reproduction of O, i.e. the angle u, is gener
The Barlow lens, named after Peter Barlow, is a diverging lens which, used in series with other optics in an optical system, increases the effective focal length of an optical system as perceived by all components that are after it in the system. The practical result is. A real barlow lens is not a single glass element, because that would generate chromatic aberration, spherical aberration if the lens is not aspheric. More common configurations use three or more elements for achromatic correction or apochromatic correction and higher image quality. In its astronomical use, a Barlow lens may be placed before an eyepiece to decrease the eyepiece's focal length by the amount of the Barlow's divergence. Since the magnification provided by a telescope and eyepiece is equal to the telescope's focal length divided by the eyepiece's focal length, this has the effect of increasing the magnification of the image. Astronomical Barlow lenses are rated for the amount of magnification they induce. Most Barlow lenses are 2x or 3x, but adjustable Barlows are available.
The power of an adjustable Barlow lens is changed by adding an extension tube between the Barlow and the eyepiece to increase the magnification. The amount of magnification is one more than the distance between the Barlow lens and the eyepiece lens, when the distance is measured in units of the focal length of the Barlow lens. A standard Barlow lens is housed in a tube, one Barlow focal-length long, so that a focusing lens inserted into the end of the tube will be separated from the Barlow lens at the other end by one Barlow focal-length, hence produce a 2x magnification over and above what the eyepiece would have produced alone. If the length of a standard 2x Barlow lens' tube is doubled the lenses are separated by 2 Barlow focal lengths and it becomes a 3x Barlow. If the tube length is tripled the lenses are separated by 3 Barlow focal lengths and it becomes a 4x Barlow, so on. A common misconception is. However, in practice, the quality of the image depends on the quality of the optics and viewing conditions, not on magnification.
Teleconverters are variations on Barlow lenses. A teleconverter increases the effective focal length of the photographic lens it is attached to, making it a telephoto lens. A true telephoto lens uses a configuration similar to a Barlow lens to obtain a shorter tube length for a given focal length. In microscopy the Barlow lens is used to increase working decrease magnification; the lenses are "objective lenses" that are mounted in front of the microscope's last objective element. Barlow lenses for microscopes can be found with magnifications ranging from 0.3× to 2×. Some standard lenses are 2×, which decreases the working distance by half and doubles the magnification, 0.75×, which increases the working distance by 4/3× and decreases the magnification by 0.75×, a 0.5× Barlow doubles the working distance and halves the magnification. Secondary lens Teleconverter
A barrister is a type of lawyer in common law jurisdictions. Barristers specialise in courtroom advocacy and litigation, their tasks include taking cases in superior courts and tribunals, drafting legal pleadings, researching the philosophy and history of law, giving expert legal opinions. Barristers are recognised as legal scholars. Barristers are distinguished from solicitors, who have more direct access to clients, may do transactional-type legal work, it is barristers who are appointed as judges, they are hired by clients directly. In some legal systems, including those of Scotland, South Africa, Pakistan, India and the British Crown dependencies of Jersey and the Isle of Man, the word barrister is regarded as an honorific title. In a few jurisdictions, barristers are forbidden from "conducting" litigation, can only act on the instructions of a solicitor, who performs tasks such as corresponding with parties and the court, drafting court documents. In England and Wales, barristers may seek authorisation from the Bar Standards Board to conduct litigation.
This allows a barrister to practise in a'dual capacity', fulfilling the role of both barrister and solicitor. In some countries with common law legal systems, such as New Zealand and some regions of Australia, lawyers are entitled to practise both as barristers and solicitors, but it remains a separate system of qualification to practise as a barrister. A barrister, who can be considered as a jurist, is a lawyer who represents a litigant as advocate before a court of appropriate jurisdiction. A barrister presents the case before a judge or jury. In some jurisdictions, a barrister receives additional training in evidence law and court practice and procedure. In contrast, a solicitor meets with clients, does preparatory and administrative work and provides legal advice. In this role, he or she may draft and review legal documents, interact with the client as necessary, prepare evidence, manage the day-to-day administration of a lawsuit. A solicitor can provide a crucial support role to a barrister when in court, such as managing large volumes of documents in the case or negotiating a settlement outside the courtroom while the trial continues inside.
There are other essential differences. A barrister will have rights of audience in the higher courts, whereas other legal professionals will have more limited access, or will need to acquire additional qualifications to have such access; as in common law countries in which there is a split between the roles of barrister and solicitor, the barrister in civil law jurisdictions is responsible for appearing in trials or pleading cases before the courts. Barristers have particular knowledge of case law and the skills to "build" a case; when a solicitor in general practice is confronted with an unusual point of law, they may seek the "opinion of counsel" on the issue. In most countries, barristers operate as sole practitioners, are prohibited from forming partnerships or from working as a barrister as part of a corporation. However, barristers band together into "chambers" to share clerks and operating expenses; some chambers grow to be large and sophisticated, have a distinctly corporate feel. In some jurisdictions, they may be employed by firms of solicitors, banks, or corporations as in-house legal advisers.
In contrast and attorneys work directly with the clients and are responsible for engaging a barrister with the appropriate expertise for the case. Barristers have little or no direct contact with their'lay clients' without the presence or involvement of the solicitor. All correspondence, invoices, so on, will be addressed to the solicitor, responsible for the barrister's fees. In court, barristers are visibly distinguished from solicitors by their apparel. For example, in Ireland and Wales, a barrister wears a horsehair wig, stiff collar, a gown. Since January 2008, solicitor advocates have been entitled to wear wigs, but wear different gowns. In many countries the traditional divisions between barristers and solicitors are breaking down. Barristers once enjoyed a monopoly on appearances before the higher courts, but in Great Britain this has now been abolished, solicitor advocates can appear for clients at trial. Firms of solicitors are keeping the most advanced advisory and litigation work in-house for economic and client relationship reasons.
The prohibition on barristers taking instructions directly from the public has been abolished. But, in practice, direct instruction is still a rarity in most jurisdictions because barristers with narrow specializations, or who are only trained for advocacy, are not prepared to provide general advice to members of the public. Barristers have had a major role in trial preparation, including drafting pleadings and reviewing evidence. In some areas of law, still the case. In other areas, it is common for the barrister to receive the brief from the instructing solicitor to represent a client at trial only a day or two before the proceeding. Part of the reason for this is cost. A barrister is entitled to a'brief fee' when a brief is delivered, this represents the bulk of her/his fee in relation to any trial, they are usually entitled to a'refresher' for each day of the trial after the first. But if a case is settled before the trial, the barrister is not needed and the brief fee would be wast