Lagrangian point

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A biconvex lens.

Lenses can be used to focus light.

A lens is an optical device which transmits and refracts light, converging or diverging the beam.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. A simple lens consists of a single optical element. A compound lens is an array of simple lenses (elements) with a common axis; the use of multiple elements allows more optical aberrations to be corrected than is possible with a single element. Lenses are typically made of glass or transparent plastic. Elements which refract electromagnetic radiation outside the visual spectrum are also called lenses: for instance, a microwave lens can be made from paraffin wax.

The variant spelling lense is sometimes seen. While it is listed as an alternative spelling in some dictionaries, most mainstream dictionaries do not list it as acceptable.

History

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The Nimrud lens

The word lens comes from the Latin name of the lentil, because a double-convex lens is lentil-shaped. The genus of the lentil plant is Lens, and the most commonly eaten species is Lens culinaris. The lentil plant also gives its name to a geometric figure.

The oldest lens artifact is the Nimrud lens, dating back 2700 years to ancient Assyria. David Brewster proposed that it may have been used as a magnifying glass, or as a burning-glass to start fires by concentrating sunlight. Another early reference to magnification dates back to ancient Egyptian hieroglyphs in the 8th century BC, which depict "simple glass meniscal lenses".Template:Verify source

The earliest written records of lenses date to Ancient Greece, with Aristophanes' play The Clouds (424 BC) mentioning a burning-glass (a biconvex lens used to focus the sun's rays to produce fire). Some scholars argue that the archeological evidence indicates that there was widespread use of lenses in antiquity, spanning several millennia. Such lenses were used by artisans for fine work, and for authenticating seal impressions. The writings of Pliny the Elder (23–79) show that burning-glasses were known to the Roman Empire, and mentions what is arguably the earliest written reference to a corrective lens: 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) described the magnifying effect of a glass globe filled with water.

Excavations at the Viking harbour town of Fröjel, Gotland, Sweden discovered in 1999 the rock crystal Visby lenses, produced by turning on pole lathes at Fröjel in the 11th to 12th century, with an imaging quality comparable to that of 1950s aspheric lenses. The Viking lenses were capable of concentrating enough sunlight to ignite fires.

Between the 11th and 13th century "reading stones" were invented. Often used by monks to assist in illuminating manuscripts, these were primitive plano-convex lenses initially made by cutting a glass sphere in half. As the stones were experimented with, it was slowly understood that shallower lenses magnified more effectively.

Lenses came into widespread use in Europe with the invention of spectacles, probably in Italy in the 1280s. This was the start of the optical industry of grinding and polishing lenses for spectacles, first in Venice and Florence in the thirteenth 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 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 the 17th and early 18th centuries 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 a 1758 patent.

Construction of simple lenses

Most lenses are spherical lenses: their two surfaces are parts of the surfaces of spheres, with the lens axis ideally perpendicular to both surfaces. Each surface can be convex (bulging outwards from 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 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 is a form of deliberate astigmatism.

More complex are aspheric lenses. These are lenses where one or both surfaces have a shape that is neither spherical nor cylindrical. Such lenses can produce images with much less aberration than standard simple lenses. These in turn evolved into freeform (digital/adaptive/corrected curve) spectacle lenses, where up to 20,000 ray paths are calculated from the eye to the image taking into account the position of the eye and the differing back vertex distance of the lens surface and its pantoscopic tilt and face form angle. The lens surface(s) are digitally adapted at nanometre levels (normally by a diamond stylus) to eliminate spherical aberration, coma and oblique astigmatism. This type of lens design almost completely fulfills the sagittal and tangential image shell requirements first described by Tscherning in 1925 and further described by Wollaston and Ostwalt.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. These advanced designs of spectacle lens can improve the visual performance by up to 70% particularly in the periphery.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

Types of simple lenses

Types of lenses

Lenses are classified by the curvature of the two optical surfaces. A lens 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 is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.

If the lens is biconvex or plano-convex, a collimated beam of light passing through the lens will be converged (or focused) to a spot behind the lens. In this case, the lens is called a positive or converging lens. The distance from the lens to the spot is the focal length of the lens, which is commonly abbreviated f in diagrams and equations.

Biconvex lens

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If the lens is biconcave or plano-concave, 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 be emanating from a particular point on the axis in front of the lens; the distance from this point to the lens is also known as the focal length, although it is negative with respect to the focal length of a converging lens.

Biconcave lens Biconcave lens

File:Concave lens.jpg

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Lensmaker's equation

The focal length of a lens in air can be calculated from the lensmaker's equation:

$P=\frac{1}{f}=(n-1)[\frac{1}{R_1}-\frac{1}{R_2}+\frac{(n-1)d}{n{R}_1{R}_2}],$

where

$P$ is the power of the lens,

$f$ is the focal length of the lens,

$n$ is the refractive index of the lens material,

$R_1$ is the radius of curvature (with sign, see below) of the lens surface closest to the light source,

$R_2$ is the radius of curvature of the lens surface farthest from the light source, and

$d$ is the thickness of the lens (the distance along the lens axis between the two surface vertices).

Sign convention of lens radii R₁ and R₂

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. 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 if R₁ is positive the first surface is convex, and if R₁ is negative the surface is concave. The signs are reversed for the back surface of the lens: if R₂ is positive the surface is concave, and if R₂ is negative the surface is convex. If either radius is infinite, the corresponding surface is flat. With this convention the signs are determined by the shapes of the lens surfaces, and are independent of the direction in which light travels through the lens.

Thin lens equation

If d is small compared to R₁ and R₂, then the thin lens approximation can be made. For a lens in air, f is then given by

$\frac{1}{f}\approx (n-1)[\frac{1}{R_1}-\frac{1}{R_2}].$

The focal length f is positive for converging lenses, and negative for diverging lenses. The reciprocal of the focal length, 1/f, is the optical power of the lens. If the focal length is in metres, this gives the optical power in dioptres (inverse metres).

Lenses have the same focal length when light travels from the back to the front as when light goes from the front to the back, although other properties of the lens, such as the aberrations are not necessarily the same in both directions.

Imaging properties

File:Reflectionprojection.jpg

This image has three visible reflections and one visible projection of the same lamp; two reflections are on a biconvex lens.

As mentioned above, a positive or converging lens in air will focus 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 will be converted into a collimated beam by 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 is called the focal plane.

File:Lens3.svg

File:GGB reflection in raindrops.jpg

The Golden Gate Bridge refracted in rain droplets, which act as lenses

File:Convex lens flipped image.JPG

Image of a plant as seen through a biconvex lens.

If the distances from the object to the lens and from the lens to the image are S₁ and S₂ respectively, for a lens of negligible thickness, in air, the distances are related by the thin lens formula

$\frac{1}{S_1}+\frac{1}{S_2}=\frac{1}{f}$ .

This can also be put into the "Newtonian" form:

$x_1{x}_2=f^2,$

where $x_1=S_1-f$ and $x_2=S_2-f$.

What this means is that, if an object is placed at a distance S₁ along the axis in front of a positive lens of focal length f, a screen placed at a distance S₂ behind the lens will have a sharp image of the object projected onto it, as long as S₁ > f (if the lens-to-screen distance S₂ is varied slightly, the image will become less sharp). This is the principle behind photography and the human eye. The image in this case is known as a real image.

360

Note that if S₁ < f, S₂ becomes negative, the image is apparently positioned on the same side of the lens as the object. Although this kind of image, known as a virtual image, cannot be projected on a screen, an observer looking through the lens will see the image in its apparent calculated position. A magnifying glass creates this kind of image.

The magnification of the lens is given by:

$M=-\frac{S_2}{S_1}=\frac{f}{f-S_1}$ ,

where M is the magnification factor; if |M|>1, the image is larger than the object. Notice the sign convention here shows that, if M is negative, as it is for real images, the image is upside-down with respect to the object. For virtual images, M is positive and the image is upright.

In the special case that S₁ = ∞, then S₂ = f and M = −f / ∞ = 0. This corresponds to a collimated beam being focused to a single spot at the focal point. The size of the image in this case is not actually zero, since diffraction effects place a lower limit on the size of the image (see Rayleigh criterion).

File:Lens4.svg

The formulas above may also be used for negative (diverging) lens by using a negative focal length (f), but for these lenses only virtual images can be formed.

For the case of lenses that are not thin, or for more complicated multi-lens optical systems, the same formulas can be used, but S₁ and S₂ are interpreted differently. If the system is in air or vacuum, S₁ and S₂ are measured from the front and rear principal planes of the system, respectively. Imaging in media with an index of refraction greater than 1 is more complicated, and is beyond the scope of this article.

File:Thin lens images.svg

Images of black letters in a thin convex lens of focal length f are shown in red. Selected rays are shown for letters E, I and K in blue, green and orange, respectively. Note that E (at 2f) has an equal-size, real and inverted image; I (at f) has its image at infinity; and K (at f/2) has a double-size, virtual and upright image.

Aberrations

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Lenses do not form perfect images, and there is always some degree of distortion or aberration introduced by the lens which causes the image to be an imperfect replica of the object. Careful design of the lens system for a particular application ensures that the aberration is minimized. There are several different types of aberration which can affect image quality.

Spherical aberration

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Spherical aberration occurs because spherical surfaces are not the ideal shape with which to make a lens, but they are by far the simplest shape to which glass can be ground and polished and so are often used. Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimised by careful choice of the curvature of the surfaces for a particular application: for instance, a plano-convex lens which is used to focus a collimated beam produces a sharper focal spot when used with the convex side towards the beam source.

File:Lens5.svg

Coma

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Another type of aberration is coma, which derives its name from the comet-like appearance of the aberrated image. Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays which pass through the centre of the lens of focal length f are focused at a point with distance f tan θ from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a comatic circle. The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimised are called bestform lenses.

File:Lens-coma.svg

Chromatic aberration

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Chromatic aberration is caused by the dispersion of the lens material—the variation of its refractive index, n, with the wavelength of light. Since, from the formulae above, f is dependent upon n, it follows that different wavelengths of light will be focused to different positions. Chromatic aberration of a lens is seen as fringes of colour around the image. It can be minimised by using an achromatic doublet (or achromat) in which two materials with differing dispersion are bonded together to form a single lens. This reduces the amount of chromatic aberration over a certain range of wavelengths, though it does not produce perfect correction. The use of achromats was an important step in the development of the optical microscope. An apochromat is a lens or lens system which has even better correction of chromatic aberration, combined with improved correction of spherical aberration. Apochromats are much more expensive than achromats.

Different lens materials may also be used to minimise chromatic aberration, such as specialised coatings or lenses made from the crystal fluorite. This naturally occurring substance has the highest known Abbe number, indicating that the material has low dispersion.

File:Chromatic abberation lens diagram.svg File:Lens6b-en.svg

Other types of aberration

Other kinds of aberration include field curvature, barrel and pincushion distortion, and astigmatism.

Aperture diffraction

Even if a lens is designed to minimize or eliminate the aberrations described above, the image quality is still limited by the diffraction of light passing through the lens' finite aperture. A diffraction-limited lens is one in which aberrations have been reduced to the point where the image quality is primarily limited by diffraction under the design conditions.

Compound lenses

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In 12 months 2013, c ommercial retails, shoebox residences and mass market properties continued to be the celebrities of the property market. Models are snapped up in report time and at document breaking prices. Builders are having fun with overwhelming demand and patrons need more. We feel that these segments of the property market are booming is a repercussion of the property cooling measures no.6 and no. 7. With additional buyer's stamp responsibility imposed on residential properties, buyers change their focus to commercial and industrial properties. I imagine every property purchasers need their property funding to understand in value. Simple lenses are subject to the optical aberrations discussed above. In many cases these aberrations can be compensated for to a great extent by using a combination of simple lenses with complementary aberrations. A compound lens is a collection of simple lenses of different shapes and made of materials of different refractive indices, arranged one after the other with a common axis.

The simplest case is where lenses are placed in contact: if the lenses of focal lengths f₁ and f₂ are "thin", the combined focal length f of the lenses is given by

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}.$

Since 1/f is the power of a lens, it can be seen that the powers of thin lenses in contact are additive.

If two thin lenses are separated in air by some distance d, the focal length for the combined system is given by

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1{f}_2}.$

The distance from the front focal point of the combined lenses to the first lens is called the front focal length (FFL):

$\text{FFL}=\frac{f_1(f_2-d)}{(f_1+f_2)-d}.$

Similarly, the distance from the second lens to the rear focal point of the combined system is the back focal length (BFL):

$\text{BFL}=\frac{f_2(d-f_1)}{d-(f_1+f_2)}.$

As d tends to zero, the focal lengths tend to the value of f given for thin lenses in contact.

If the separation distance is equal to the sum of the focal lengths (d = f₁+f₂), the FFL and BFL are infinite. This corresponds to a pair of lenses that transform a parallel (collimated) beam into another collimated beam. This type of system is called an afocal system, since it produces no net convergence or divergence of the beam. Two lenses at this separation form the simplest type of optical telescope. Although the system does not alter the divergence of a collimated beam, it does alter the width of the beam. The magnification of such a telescope is given by

$M=-\frac{f_2}{f_1},$

which is the ratio of the output beam width to the input beam width. Note the sign convention: a telescope with two convex lenses (f₁ > 0, f₂ > 0) produces a negative magnification, indicating an inverted image. A convex plus a concave lens (f₁ > 0 > f₂) produces a positive magnification and the image is upright.

Other types

Cylindrical lenses have curvature in only one direction. They are used to focus light into a line, or to convert the elliptical light from a laser diode into a round beam.

File:Flat flexible plastic sheet lens.JPG

Close-up view of a flat Fresnel lens.

A Fresnel lens has its optical surface broken up into narrow rings, allowing the lens to be much thinner and lighter than conventional lenses. Durable Fresnel lenses can be molded from plastic and are inexpensive.

Lenticular lenses are arrays of microlenses that are used in lenticular printing to make images that have an illusion of depth or that change when viewed from different angles.

A gradient index lens has flat optical surfaces, but has a radial or axial variation in index of refraction that causes light passing through the lens to be focused.

An axicon has a conical optical surface. It images a point source into a line along the optic axis, or transforms a laser beam into a ring.

Superlenses are made from metamaterials with negative index of refraction. They can achieve higher resolution than is allowed by conventional optics.

Uses

A single convex lens mounted in a frame with a handle or stand is a magnifying glass.

Lenses are used as prosthetics for the correction of visual impairments such as myopia, hyperopia, presbyopia, and astigmatism. (See corrective lens, contact lens, eyeglasses.) Most lenses used for other purposes have strict axial symmetry; eyeglass lenses are only approximately symmetric. They are usually shaped to fit in a roughly oval, not circular, frame; the optical centres are placed over the eyeballs; their curvature may not be axially symmetric to correct for astigmatism. Sunglasses' lenses are designed to attenuate light; sunglass lenses that also correct visual impairments can be custom made.

Other uses are in imaging systems such as monoculars, binoculars, telescopes, microscopes, cameras and projectors. Some of these instruments produce a virtual image when applied to the human eye; others produce a real image which can be captured on photographic film or an optical sensor, or can be viewed on a screen. In these devices lenses are sometimes paired up with curved mirrors to make a catadioptric system where the lens's spherical aberration corrects the opposite aberration in the mirror (such as Schmidt and meniscus correctors).

Convex lenses produce an image of an object at infinity at their focus; if the sun is imaged, much of the visible and infrared light incident on the lens is concentrated into the small image. A large lens will create enough intensity to burn a flammable object at the focal point. Since ignition can be achieved even with a poorly made lens, lenses have been used as burning-glasses for at least 2400 years. A modern application is the use of relatively large lenses to concentrate solar energy on relatively small photovoltaic cells, harvesting more energy without the need to use larger and more expensive cells.

Radio astronomy and radar systems often use dielectric lenses, commonly called a lens antenna to refract electromagnetic radiation into a collector antenna.

Lenses can become scratched and abraded. Abrasion-resistant coatings are available to help control this.

See also

• Anti-fogging treatment of optical surfaces
• Back focal plane
• Bokeh
• Cardinal point (optics)
• Eyepiece
• F-number
• Gravitational lens
• Lens (anatomy)
• List of lens designs
• Numerical aperture
• Optical coatings
• Optical lens design
• Photochromic lens
• Prism (optics)
• Ray tracing
• Ray transfer matrix analysis

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

Bibliography

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Chapters 5 & 6.
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

External links

Most brokers paid and post their listings at these online property categorised portals but fail to realise that there is simply extra to it. They fail to leverage on one of the vital well-liked on-line advertising and marketing tool of their marketing campaign and that is through the social media.

In case you are among the many few who've passed the grueling Actual Estate Salesperson (RES) course, congratulations. So what next? Which agency should you be a part of? Earlier than taking the plunge, you will need to choose the proper mentor who can educate you the ropes in actual estate. An excellent mentor will allow you to navigate the complex world of real property by instructing you the way to get listings, advertising and marketing methods, real estate contracts and methods to closing your deal. He will even caution you on errors to keep away from that would land you in trouble. This has been reflected within the Industrial Production reading index for prescribed drugs. In June, the reading fell to one hundred thirty from 287. Effectively if you do not, you then're simply leaving your actual property enterprise to chance. Commons for rent

Thanks to hirepropertyagent.com.sg, i've discovered myself a good agent. He did a great job promoting my property and it was bought at an excellent value." JLL appointed unique agent for the sale of 2, 4 and 6 Dunlop Street by Expression of Curiosity. Uncommon Industrial Growth inside Pandan Meals Zone space up for sale conserving you updated with the property market 3. Work @ Residence IT Solutions As property costs cool in Hong Kong and Singapore, which have lengthy been magnets for Chinese language funding, extra money is flowing to actual property markets comparable to New York, London and Sydney. Chinese language have overtaken Russians house for sale in singapore the primary time as the biggest buyers of flats in Manhattan, in response to actual estate brokers. Condominium For Lease – Tribeca by the Waterfront (D09)

Property developer and residential landlord for flats and homes for lease and sale. Most property firms share the same database of property listings in Singapore. Due to this fact it is best to solely use only ONE agent at a time. In case you approach many agents at the similar time, very likely that they'll present you the same property. A lot confusion and embarrassment will arise should you engage many brokers. One of the best, and most of the time only, strategy to discover a good property agent in Singapore is phrase-of-mouth. Ask your friends and colleagues for reference. It is very simple to provide you with a couple of candidates since a lot of the expatriates dwelling in Singapore for a long time can have several good agent contacts to guide you. Toa Payoh, Singapore Singapore 319378 Estate

This is precisely what happened to me and my husband at the moment, to not point out a very unscrupulous developer operating in a really unprofessional manner. I need to share this story with everyone here, and please pass the message round particularly among expats communities, beware while you want to purchase property developed by VicLand Pte Ltd and if developer's agent is ECG property. There was only one unit left on the market by developer, 03-09, a 3 bed room flat. On the time my husband was out of town, and initially I liked what I saw so I instructed the developer's agent and my agent we should come back with my husband in two weeks to view it once more and make a decision after ward. Complaint / Suggestions about lousy property agent Darren Ng from Dennis Wee

This bought me thinking and I started to surprise – how much does a property agent really earn? We often hear or read about sure brokers making million dollar commissions, however is that the exception or the norm? That piqued my curiosity. Like any job, those who put in time and effort will do well and rise to the top. The ethics of exhausting work apply to the true property market as nicely. For individuals who are pondering of making a career change to develop into a property agent, you should be ready to invest the trouble to do properly. Otherwise you may just add to the statistic of brokers who eventually drop out of the realtor game. Properties that do not fall within the definition of residential properties stated above are non-residential properties Web site - www.riaschool.com.sg

Ought to you are on the lookout for new properties for investment or for own stay, we offer property recommendation and search services tailored to your needs. We have represented many together with worldwide and local buyers in efficiently finishing their property purchases. We work with main builders to bring you the latest and one of the best prime properties in Singapore. We are a one-cease service that may full your property cycle from purchase to sale. Property agents for Singapore Land Authority protecting among the government colonial properties for rent. Property leases for expatriates and foreigners. Also helps expats to purchase and promote their properties as well as property investment opportunities in Singapore and China. The Restaurant Affiliation of Singapore

File:ThinLens.gif

Thin lens simulation

• Applied photographic optics Book
• The properties of optical glass
• Handbook of Ceramics, Glasses, and Diamonds
• Optical glass construction
• History of Optics (audio mp3) by Simon Schaffer, Professor in History and Philosophy of Science at the University of Cambridge, Jim Bennett, Director of the Museum of the History of Science at the University of Oxford and Emily Winterburn, Curator of Astronomy at the National Maritime Museum (recorded by the BBC).
• a chapter from an online textbook on refraction and lenses
• Thin Spherical Lenses on Project PHYSNET.
• Lens article at digitalartform.com
• Article on Ancient Egyptian lenses
• picture of the Ninive rock crystal lens
• Do Sensors “Outresolve” Lenses?; on lens and sensor resolution interaction.
• Fundamental optics
• FDTD Animation of Electromagnetic Propagation through Convex Lens (on- and off-axis) on YouTube
• The Use of Magnifying Lenses in the Classical World

Simulations

• Learning by Simulations – Concave and Convex Lenses
• OpticalRayTracer – Open source lens simulator (downloadable java)
• Video with a simulation of light while it passes a convex lens
• Animations demonstrating lens by QED