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Oregon enforces federal rules for contractors engaged on housing or youngster-occupied facilities built earlier than 1978. When a business is staying put by the renovation, the final contractor should make special accommodations as least invasive as doable. Sad reality is: There's a real disconnect when trying to find reliable house renovation contractors and repairmen. We're a good inside designer & builder, with in depth experience & initiatives to our portfolio.
The recourse for contractors like this nonetheless doesn't fully stop them from doing this to different people. An interior designer is someone who coordinates and manages your renovation undertaking. It's distinctive in providing consulting for the preparation of renovation tasks and in its wide selection of design and decoration providers. As part of the application course of for all types of house owners, chances are you'll be required to interact an expert engineer to endorse the project plan.
Inside designers tend to arrange a Whatsapp group chat for the homeowners earlier than the commencement of a project. At present there aren't any incentives or tangible benefits for non-obligatory trades, resembling common contractors, to register with these provincial associations. From our base in Skokie, we are uniquely situated to being Chicago's greatest common contractors.
The engagement of the renovation contractors listed in the DRC is strictly on a non-public basis between the flat house owners and the contractors. It could be nice in case you can present the corporate identify and the names of the contractors for all his piers to know. Whereas primarily referred to as a trusted supply for renovation quotes, is also a platform for folks to find contractors in different fields, from plumbers to pest exterminators and even customized cake bakers.
Most contractors will count on a small down fee (say, 10 p.c of the whole job) to cowl the initial materials prices and to indicate that you are serious. Reworking tasks that touch the property line, like fences, are an exception. Reno-Help was founded to assist homeowners join with qualified contractors. This may very well be a very good choice if you're selling your property and want to improve its value shortly – hire a renovation contractor to redesign and renovate a number of rooms of your house with out the effort of dealing with various professionals or the time-consuming effort of doing it yourself.


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Glenn Starkman is a Professor of Physics and Astronomy and Director of the Center for Education and Research in Cosmology and Astrophysics(CERCA) and of the Institute for the Science or Origins (ISO) at Case Western Reserve University.
An alumnus of the University of Toronto, Canada (his native city), with a PhD from Stanford University, his research career took him to the institute for Advanced Study, Princeton, and the Canadian Institute for Theoretical Astrophysics before bringing him to Case Western Reserve.
His research extends from searching for habitable planets around other stars to understanding the shape of the universe, from looking for miniature black holes in particle accelerators to extending and testing Einstein's General Theory of Relativity.
In 2003 he was awarded a prestigious Guggenheim Fellowship. Glenn is dedicated to advancing the role of research universities in education at all levels. He was among the founding board members of the Reinvention Center, a national center focusing on undergraduate education at research universities.

subset: commoncrawl


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WGA Garners More Attention, All of it Bad
While Microsoft continues to both defend and roll out its spyware-like Windows Genuine Advantage (WGA) service around the world, the company is facing two WGA-related threats. Security researchers have identified a software worm that disguises itself as
July 5, 2006
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While Microsoft continues to both defend and roll out its spyware-like Windows Genuine Advantage (WGA) service around the world, the company is facing two WGA-related threats. First, security researchers have identified a software worm that disguises itself as WGA. Second, a new class-action lawsuit was filed against Microsoft late last week, alleging that WGA is spyware and that Microsoft is misleading consumers about the technology.
WGA is a downloadable software service that Microsoft makes available via Windows Update and Automatic Updates. The service is divided into two components: WGA Validation, which checks to ensure that your PC isn't running a pirated version of Windows XP, and WGA Notifications, which is the piece that has raised privacy and security concerns. WGA Notifications was designed to display annoying pop-up alerts to users who are running pirated versions of Windows. But the software was also secretly phoning home to Microsoft servers every time an XP system rebooted. And Microsoft had made WGA a critical security update on Windows Update and Automatic Updates, despite the fact that it was until recently in beta. That means millions of users inadvertently downloaded unfinished Microsoft code to their PCs without understanding what they were doing and how the software behaved.
Since owning up to the software's clandestine behavior, Microsoft changed WGA Notifications so that it doesn't phone home on every system reboot. But the company also took WGA out of beta and began rolling out the service, automatically, to Windows users worldwide. Last week, a class-action lawsuit was filed in the state of Washington, alleging that Microsoft was violating California and Washington consumer-protection laws. Unfortunately for Microsoft, that was only the start of its WGA-related problems.
This week, security researchers at Sophos identified a worm called Cuebot-K that disguises itself as WGA and is spreading via AOL's Instant Messenger network. The worm identifies itself as "wgavn" and "Windows Genuine Advantage Validation Notification," and is installed to run each time the system boots. If the user tries to disable the worm, he or she is warned that doing so could result in system instability. Behind the scenes, Cuebot-K disables the Windows firewall and opens a back door from which hackers could remotely control the PC, steal personal information, or launch Distributed Denial-of-Service (DDOS) attacks.
But wait, there's more. A group of companies and individuals has filed a second class-action lawsuit against Microsoft for delivering spyware to consumers in the guise of WGA and deceiving consumers about its intentions. The suit complains that WGA secretly communicates with Microsoft's servers and "gathers data that can easily identify individual PCs," contrary to Microsoft's assertions.
Microsoft says the suit is without merit. "This distorts the real objectives of the [WGA] program and obscures the real issue, which is the harm to consumers posed by software piracy," a Microsoft spokesperson said. "As with all of our programs, we've gotten constructive customer feedback, the program has evolved, and we've made improvements. Microsoft continues its efforts to foster better communications with its customers."
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Long s
In most works printed before about 1800 two forms of the lower-case s were used. One was the s that is still in use today; the other was the long s, a character which looks like f without the right-hand part of its crossbar. The italic form of long s usually lacks the 'crossbar' altogether. (The image above is a detail of the showing of Pica No. 2 in William Caslon, Specimen of Printing Types, London, 1766.)
The present form of the minuscule s (called 'short s' here for convenience) resembles the capital letter S in Roman inscriptions. The long s originates in the straggling form given to this letter in Roman cursive script.
In the late Roman cursive of the fourth century the letter had already acquired the shape that it kept when it was was adopted in more formal hands, such as the 'half uncial' of the sixth century and other minuscule hands of the middle ages, including the Carolingian script. (The example above, a letter written on papyrus in about 400, reads ...sam uilissima...) The inscriptional S was used in uncial scripts, and in capital letters for headings and initials. Some minuscule scripts used both the long and the short s: the script of the Lindisfarne Gospels, written in Northumbria in the 'insular' form of half uncial in about 698, is an example. (Is there any rule that governs this early use of two forms of s?) The Carolingian script of the ninth century used only long s, but in late Carolingian or early gothic scripts from the twelfth century onwards, the convention was adopted of using long s at the beginning and in the middle of words, and short s at the end.
The first types were based on gothic hands, and the early printers followed the established use of initial and medial long s and final short s. However the first writers of the humanistic script, which was based on the Carolingian hand, had followed its convention of using only long s thoughout. Some printers who began to use types influenced by the humanistic script (Sweynheym and Pannartz, Subiaco, 1465, for example, and Ulric Gering, Paris, 1470) did the same, but they soon reverted to the 'gothic' use of initial and medial long and final short s, and this became the almost universal rule in printing until the end of the eighteenth century. Because long s was kerned and overlapped adjacent characters, the short s was sometimes used as an expedient in front of the tall letters with which the long s would have collided. Special ligatured types were eventually made for many of the combinations, such as (for printing English) sb, sh, si, sk, sl, ss, st, ssi, ssl.
Like the printers, writers of the formal humanistic script in the later fifteenth century generally reverted to initial and medial long s and final short s. But writers of the cursive form of the script and the hands that developed from it (chancery cursive and the later 'Italian' hands) often made no use at all of long s, and the relaxed and inconsistent usage of calligraphers is strikingly different from the rigid practice observed by printers. Examples of initial and medial short s can be found towards the end of the fifteenth century in the work of Bartolomeo Sanvito, and perhaps a significant figure in this context (as in many others) is the reforming sixteenth-century calligrapher and teacher Giovan Francesco Cresci in Rome who, unlike earlier writers of the cancellaresca corsiva, including his arch-rival Giovanni Battista Palatino, made little use of long s in his own manuscripts and writing books. His new style, adopted by his pupils and followers, changed the look of Western handwriting, and the use of long s became less common. Lodovico Curione was one of the pupils listed by Cresci. His Lanotomia, shown here, was engraved on copper and published in Rome in 1588.
However, from the fifteenth to the late eighteenth centuries there are very few exceptions in texts printed from type to the rule that the initial and medial s was long and the final s was short. One of the exceptions is seen in the series of works printed at Vicenza in the 1520s for the Italian linguistic reformer Gian Giorgio Trissino, in which short and long s are used to distinguish the voiced and unvoiced consonant. The same distinction between short and long s, an idea perhaps derived from Trissino, was made by Edward Capell in his Prolusions, or select pieces of antient poetry, printed in London by Dryden Leach and published in 1760, and in his edition of Shakespeare (1768, etc.).
Pierre Moreau, Paris, who printed in the 1640s with types based on a current version of the Italian cursive hand, followed the practice of contemporary calligraphers and used only short s. The long s was not used in Joseph Ames, Typographical Antiquities (London, 1749), nor in the Virgil of 1758 printed by Robert and Andrew Foulis of Glasgow and a few of their other titles.
The first consistent move away from long s among printers from type appears to take place in Spain. An example identified by Paul Nash, and still the earliest example recorded in Spain, is in Compendio de los diez libros de arquitectura de Vitruvio (Madrid: Gabriel Ramirez, 1761). Not long after there is one printed by Joaquín Ibarra: Tomás Lopez, Descripción de la Provincia de Madrid (Madrid, 1763). The first known type specimen of Antonio Espinosa, Madrid, Muestras de la letra nueva de los grados de Atanasia y Lectura, dated 13 August 1764, shows texts and alphabets of roman and italic that wholly omit the long s, and it appears only intermittently in his later specimens. Other early examples include Andres Xímenez, Descripción del ... Escorial (Madrid: Antonio Marín, 1764), and some other works printed by Ibarra, including his Sallust (Madrid, 1772), using types by Espinosa (and also a Small Pica by Caslon). D. B. Updike, Printing types, 2nd ed. (1937), figs. 233–44, shows examples of the omission of long s in the setting of some books of the 1770s. For the specimen of Espinosa, 1764, see Albert Corbeto, Especímenes tipográficas españoles (Madrid, 2010), p. 78, plate 16. Settings with the use of just one or two lines with long s appear in Espinosa's specimen book of 1780. Clearly its use and disuse in setting books in Spain, together with the roles of Ibarra and Espinosa and the links between them, are matters that are still in need of attention.
Giambattista Bodoni followed the current convention and used long s in his first books printed at Parma and in his early undated single-leaf type specimens. However there are intermittent instances of the omission of long s in some works that he printed during the 1770s. In one, to which my attention has been drawn by James Clough, long s is used in the early sheets but not in the later ones: Atti della solenne coronazione fatta in Campidoglio della insigne poetessa Maria Maddalena Morelli Fernandez... (Parma: Stamperia Reale, 1779), Brooks 135. Is this perhaps the piece of printing in which Bodoni began to abandon long s? Another work printed in the same year omits long s altogether, Panegirico in lode di San Vincenzio Ferreri, Brooks 146, and thereafter this appears to have been Bodoni's established practice. Perhaps the spectacular example of the usage in Spain by Ibarra in his Sallust had provided the model. The long s is omitted throughout the first Manuale tipografico of 1788, with just two exceptions: it appears, as Paul Nash has pointed out, on leaves 68 and 78, once in an st ligature and once within a word, in types for the body of Canoncino. Since these are both examples of the reuse of settings of types that had first appeared as earlier single-leaf specimens using long s, it is likely that they are cases of its accidental survival.
The general discarding of the long s by printers was given what may have been its decisive encouragement by François-Ambroise Didot, Paris, who in about 1781 initiated the cutting of the style of type that later became known in English as 'modern face'. Long s was not included in his new types, and the example was quickly followed by printers under his influence. One of these was John Bell, printer and typefounder in London, to whom the movement for its disuse used to be attributed, mistakenly. Bell did not use long s in his newspaper The World, first published on 1 January 1787, nor in the text of the specimen of the new types cut for his British Letter-Foundry by Richard Austin (1788), although the synopsis of the fount shows that long s and its combinations were made for it. Bell was familiar with contemporary French books, which he imported into England, and he had made use of a small size of one of the types cut by Firmin, son of François-Ambroise Didot.
In the 'Prolegomena' to his Shakspeare (1788) Bell explained that his objects in omitting long s were to give the lines 'the effect of being more open' (an aim of many printers of the late 18th century, when texts were commonly leaded) and to avoid the confusion of long s with f.
When typefounders in Britain introduced 'modern-cut' types during the decade from 1795 to 1805, long s was often not supplied in the fount, and as these new types were bought by printers its general use quickly declined. It was revived for a time for the sake of its antiquarian flavour by printers like Charles Whittingham and Louis Perrin when old face types were again used for printing towards the middle of the nineteenth century, but the long s never returned in everyday printing with roman types.
Long s and its combinations are still used when German is set correctly in gothic types like Schwabacher and Fraktur. The character ß, a ligature which is known as Eszett (or some such spelling) since it is essentially based on sz, is still used when the German language is set in roman type, except in Switzerland, where it has disappeared. Some attempt is made to give its history, some models for its design and the rules for its use in the post that follows. Recent changes to German orthography have modified the rules and reduced the occasions for its use.
Several other scripts, notably Arabic and Hebrew, have differing initial, medial and final forms for many letters. Greek retains two forms of sigma, one for initial and medial and one for final use, but the existence of the two forms seems completely unconnected with the duplication of s in the Latin script.
This text was written years ago for giving out in classes and it was printed in 1995. I am adding a revised version of it to this blog because it still seems to give rather more historical information about the use of long s by printers and professional calligraphers than can easily be found. One or two of the references that are added above relating to the discarding of the long s are from a study by Paul Nash, 'The abandoning of the long s in Britain in 1800', Journal of the Printing Historical Society, new series 3 (2001), pp. 3–19. Two online references are The Long and the Short of the Letter S, and The Rules for Long s. These 'rules' are given in a series of detailed tables. Their compiler might have learned something from the brief notes above on the printer's need to use the short s, regardless of its position in a word, in order to avoid the collision of the overhanging kerned part of long s with ascending types that followed
Long into the 19th century it was still common practice in English handwriting to use long and short s for double s, notably in 'Miss' in the address on letters. William Bulmer's grand folio Shakspeare [sic], 1792, and Milton, 1794, were a British rejoinder to the austere magnificence of the books printed by Pierre Didot with the types of Firmin. They display a certain conservatism. The forms of the types are almost closer to those of Baskerville, cut forty years earlier, than to those of the Didots. The warmly-tinted Whatman wove paper avoids the icy whiteness of the French papers. And although the long s was generally omitted in the text, it was retained – as in handwriting – for the combination ss. Note 'glassy' in this detail from the Milton:
My thanks for help to Albert Corbeto for references to Espinosa, and to James Clough for titles by Bodoni. Last edited 15 February 2011


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We've written about the meaning of poor as used in the Bible.
"[T]he case can overwhelmingly be made that references in Scripture to the poor or to poverty should be taken to mean economic poverty, unless the passage can clearly be argued to have a different meaning."
Today, we addresses some key biblical perspectives on poverty.
Several conclusions about poverty are clear from Scripture:
- God does not desire or intend that anyone live in economic poverty (Deuteronomy 15:4).
- God created laws and social practices for His people to minimize the impact of economic disparity by wealth redistribution (Leviticus 25), by the tithe system to ensure food security for the vulnerable (Deuteronomy 26:12), by practices of generosity (Leviticus 23:22), by no-interest loans (Exodus 22:25), and by impartial legal representation as well as other practices.
- God is angered when these laws and practices are not followed and the vulnerable suffer for it. Conversely, God is pleased, hears our prayers, and brings blessing (Isaiah 58) to those who follow these commands and practice generosity toward the poor and who seek justice on their behalf.
These three conclusions offer a foundation for the Christian response to poverty. God's intent, commands and feelings inform Christian action.
Furthermore, His omnipotence should allow us to believe that the end of economic poverty is possible because "with God all things are possible" (Matthew 19:26).
Many people and organizations view poverty in economic terms. In 1990 the World Bank set a widely used definition of "extreme poverty" as a per-capita income of less than $1 per day. The World Bank revised that standard to $1.25 per day in 2009.
In reflection on what the Bible has to say about poverty and the poor, there is an important event recorded in Scripture in which Jesus is at a party in the home of Simon the Leper. The party was thrown in honor of Jesus in the town of Bethany just a few days before Jesus' death.
During this party Jesus says to Judas Iscariot and perhaps to the others at the party a phrase that strongly influences common theologies of poverty. Jesus says, "The poor you will always have with you" (Matthew 26:11).
The misinterpretation of this statement has justified a fatalistic belief that, by divine decree, the world will always have poor people.
Yet even an amateur study of this statement shows that it is extremely unlikely that Jesus was decreeing economic poverty as an unchangeable human condition.
Jesus was affirming Mary for her act of worship and alerting His disciples to the limited opportunities remaining to worship Him in person (in His physical presence). He was three days from His death.
In contrast, they would have many future opportunities to help the poor.
Correcting this unfortunate misinterpretation may open Christian imagination to the possibility of ending economic poverty.
Do you agree or disagree?


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Jira Chart Macro
Add the Jira Charts macro to a page to build visual graphs and charts from information in Jira.
This is great for:
- team meetings and retrospectives
- project status updates
- sharing updates with people in your organization who don't use Jira regularly.
The macro can display issues from any connected Jira Server, Data Center, or Cloud application, including Jira Software and Jira Service Management.
On this page:
Screenshot: Meeting notes page with a Jira Chart macro showing a breakdown of all issues for a software version, by priority.
Connect Confluence and Jira
Before you can use this macro, your Confluence and Jira applications must be connected via Application Links. People viewing the page will see charts for publicly accessible issues. If your Jira application has restricted viewing (that is, people need permission to view issues) then they'll need to authenticate before seeing the charts. This macro is compatible with Jira 5.x and later.
See Use Jira applications and Confluence together for more information.
Add this macro to your page
To add the Jira Chart macro to a page:
- From the editor toolbar, choose Insert > Other Macros.
- Choose Jira Chart from the Development category.
- Choose the type of report you want to create (for example Pie, Created vs Resolved)
Select your Jira server.
If you have multiple Jira servers linked to Confluence the drop down will default to the primary application link.- Search for issues - you can enter the query in JQL or paste a Jira URL directly into the search field.
- Choose Preview to generate the chart.
- Choose Display Options to further control how your chart appears.
- Choose Insert.
You can then publish your page to see the macro in action.
To find out more about searching for issues see Displaying issues using JIRA Query Language (JQL).
Screenshot: Configuring the Jira Chart Macro in the macro browser.
Pie chart
Pie charts can be used to report on issue status, priority, assignee and more.
To further control how this chart appears on your page. Choose Display options:
- Chart by - select the field you want to segment the pie chart by such as:
- Status
- Fix version
- Assignee name
- Priority
- Component
- Issue type
- Width - define the total width of the chart area. You can enter values in pixels, percent or leave blank to auto fit.
- Show border - add a border around the chart area.
- Show chart information - include a text summary under the chart with the total issues count and chart by value.
Created vs Resolved chart
Created vs Resolved charts can be used to show the difference between the number of issues created versus the number of issues resolved over time.
To further control how this chart appears on your page choose Display options:
- Period - choose a time frame to report by (week, month, quarter etc).
- Days previously - the total number of days to report on (counting back from today).
- Cumulative totals - choose to progressively add totals or report individual values for each period.
- Show unresolved trend - add a subplot showing unresolved issues over time.
- Show versions - indicate version release dates as a vertical line on the chart.
- Width - define the total width of the chart area. Enter values in pixels, percent or leave blank to auto fit.
- Show border - add a border around the chart area
- Show chart information - include a text summary under the chart with the total issues count and chart by value.
Two Dimensional Chart
Two Dimensional Charts can be used to show issue statistics in a matrix. You can configure the X and Y axes to display these issue fields:
- Status
- Priority
- Assignee
- Fix version
- Component
- Issue type.
For example you could use the chart to show issue types by status (as shown above).
To configure the chart axes choose Display options:
- X Axis - the issue field to display on the X axis (columns).
- Y Axis - the issue field to display on the Y axis (rows).
- Rows to display - the maximum number to display in the chart.
Disable the Jira Chart macro
The functionality is provided by a system app (plugin) called 'Jira Macros'. This is also used for the Jira Issues macro. To make the macro unavailable on your site, you can disable the app. See Disabling and enabling apps.
HTTPS: The Jira Chart macro can access a Jira site running under SSL provided the Confluence server is configured to accept the Jira SSL certificate. See Connecting to LDAP or Jira applications or Other Services via SSL.
Authentication: If the query includes issues that require authentication (issues that are not visible to anonymous users in Jira), users will be prompted to authenticate to view charts on the Confluence page.
In order to search for issues in the macro browser you will need to authenticate.
Other ways to add this macro
Add this macro as you type
Add this macro using wiki markup
You can't use wiki markup to add this macro.


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Yes, her correct rank is General. Someone here is… possibly a little behind the times. Say, ten years or so behind?
In other news… I set up a Twitter account a while back, mostly because my friends kept insisting I needed one, and with no real desire to enter a whole new world of social media I never did much with it. But it seems my days of flying under the radar are done! I hardly know how it happened, but a couple people found me and started "following" me, and then more arrived, so I guess now I might as well submit to the inevitable and jump into the pool. So if you're a Twittering sort, you can find me @t_tallan. You'll have to forgive me while I bumble around a bit, getting the hang of it, learn the etiquette, that kind of thing. Wheee!
Lastly… some time ago I talked about getting a facelift for the ol' website. Well, I dragged my feet for a long time about it, but cool things are starting to happen at last! I don't know when you'll start to see some of the magic go live, but probably in the next couple of weeks. So if you hit the site one day and it all looks different and awesome, don't panic, it's still Galaxion.


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One major principle discussed in both Unit 13 and Unit 14 of The Physics Classroom Tutorial is the line of sight principle:
In order to view an object, you must sight along a line at that object; and when you do light will come from that object to your eye along the line of sight.
This very principle is combined with rules of reflection and refraction in order to explain how an image is formed and what the characteristics of such images will be.
Plane Mirror Image Formation
In the plane mirror Lesson of Unit 13, it was mentioned that an image is formed by a plane mirror as light emanates from an object in a variety of directions. Some of this light reaches the mirror and reflects off the mirror according to the law of reflection. Each one of these rays of light can be extended backwards behind the mirror where they will all intersect at a point (the image point). Any person who is positioned along the line of one of these reflected rays can sight along the line and view the image – a representation of the object. Thus, an image location is a location in space where all the reflected light appears to come from. Since light from the object appears to diverge from this location, a person who sights along a line at this location will perceive a replica or likeness of the actual object. In the case of plane mirrors, the image is said to be a virtual image. Virtual images are images that are formed in locations where light does not actually reach. Light does not actually pass through the location on the other side of the plane mirror; it only appears to an observer as though the light were coming from this position.
Curved Mirror Image Formation
We have also seen how images are created by the reflection of light off curved mirrors. Suppose that a light bulb is placed in front of a concave mirror; the light bulb will emit light in a variety of directions, some of which will strike the mirror. Each individual ray of light will reflect according to the law of reflection. Upon reflecting, the light will converge at a point. At the point where the light from the object converges, a replica or likeness of the actual object is created; this replica is known as the image. Once the reflected light rays reached the image location, they begin to diverge. The point where all the reflected light rays converge is known as the image point. Not only is it the point where light rays converge, it is also the point where reflected light rays appear to an observer to be coming from. Regardless of the observer's location, the observer will see a ray of light passing through the real image location. To view the image, the observer must line her sight up with the image location in order to see the image via the reflected light ray. The diagram below depicts several rays from the object reflecting from the mirror and converging at the image location. The reflected light rays then begin to diverge, with each one being capable of assisting an individual in viewing the image of the object.
For plane mirrors, virtual images are formed. Light does not actually pass through the virtual image location; it only appears to an observer as though the light was emanating from the virtual image location. The image formed by this concave mirror is a real image. When a real image is formed, it still appears to an observer as though light is diverging from the real image location. Only in the case of a real image, light is actually passing through the image location.
Converging Lens Image Formation
Converging lenses can produce both real and virtual images while diverging lenses can only produce virtual images. The process by which images are formed for lenses is the same as the process by which images are formed for plane and curved mirrors. Images are formed at locations where any observer is sighting as they view the image of the object through the lens. So if the path of several light rays through a lens is traced, each of these light rays will intersect at a point upon refraction through the lens. Each observer must sight in the direction of this point in order to view the image of the object. While different observers will sight along different lines of sight, each line of sight intersects at the image location. The diagram below shows several incident rays emanating from an object – a light bulb. Three of these incident rays correspond to our three strategic and predictable light rays. Each incident ray will refract through the lens and be detected by a different observer (represented by the eyes). The location where the refracted rays are intersecting is the image location.
In this case, the image is a real image since the light rays are actually passing through the image location. To each observer, it appears as though light is coming from this location.
Diverging Lens Image Formation
Diverging lenses create virtual images since the refracted rays do not actually converge to a point. In the case of a diverging lens, the image location is located on the object's side of the lens where the refracted rays would intersect if extended backwards. Every observer would be sighting along a line in the direction of this image location in order to see the image of the object. As the observer sights along this line of sight, a refracted ray would come to the observer's eye. This refracted ray originates at the object, and refracts through the lens. The diagram below shows several incident rays emanating from an object – a light bulb. Three of these incident rays correspond to our three strategic and predictable light rays. Each incident ray will refract through the lens and be detected by a different observer (represented by the eyes). The location where the refracted rays are intersecting is the image location. Since refracted light rays do not actually exist at the image location, the image is said to be a virtual image. It would only appear to an observer as though light were coming from this location to the observer's eye.
Images of Objects That Do Not Occupy a Single Point
The above discussion relates to the formation of an image by a "point object" – in this case, a small light bulb. The same principles apply to objects that occupy more than one point in space. For example, a person occupies a multitude of points in space. As you sight at a person through a lens, light emanates from each individual point on that person in all directions. Some of this light reaches the lens and refracts. All the light that originates from one single point on the object will refract and intersect at one single point on the image. This is true for all points on the object; light from each point intersects to create an image of this point. The result is that a replica or likeness of the object is created as we sight at the object through the lens. This replica or likeness is the image of that object. This is depicted in the diagram below.
Now that we have discussed how an image is formed, we will turn our attention to the use of ray diagrams to predict the location and characteristics of images formed by converging and diverging lenses.


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