[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-656859-105":59,"doc-detail-656859-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","reflection-and-mirrors-o2-images-virtual-and-real-ray-tracing-formulas-and-sign-convention","Reflection and Mirrors - O2 - Images: virtual and real - Ray tracing - Formulas and sign convention","","Reflection and Mirrors section O2 introduces key optics concepts centered on mirror reflection. It explains the formation of real and virtual images, emphasizing how ray convergence produces a real image that can be projected on a screen, while virtual images arise when reflected rays appear to originate from a point behind the mirror. The material then outlines ray tracing using critical rays, establishes formulas and sign conventions for quantitative results, and applies them to convex, concave, and plane mirrors.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/reflection-and-mirrors-o2-images-virtual-and-real-ray-tracing-formulas-and-sign-convention/656859/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/reflection-and-mirrors-o2-images-virtual-and-real-ray-tracing-formulas-and-sign-convention/656859.png","ImageObject",300,407,{"name":92,"@type":93},"Nguyễn Văn Học","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-10-25",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How does a real image formed by a concave mirror differ from a virtual image?","Question",{"text":112,"@type":113},"A real image forms where reflected rays actually converge, so it can appear sharply on a screen. A virtual image results when reflected rays only appear to come from a point; there is no convergence that would allow a screen image.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Why is the distinction between real and virtual images important for compound optical systems?",{"text":117,"@type":113},"In compound systems, the image from one element effectively acts as the object for the next. Even when the image is not physically located (as with virtual images), it still serves as the correct reference for subsequent ray behavior.",{"name":119,"@type":110,"acceptedAnswer":120},"What is ray tracing in the context of mirrors, and why are sign conventions needed?",{"text":121,"@type":113},"Ray tracing uses a small set of critical rays to describe how light behaves when reflecting from mirrors. To obtain quantitative answers consistently, the method also relies on defined sign conventions that are used across later compound-system studies.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},656859,1793029777,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144},1374402739827,"https://ap-avatar.wpscdn.com/avatar/14000c97e7351f1a627?x-image-process=image/resize,m_fixed,w_180,h_180&k=1787885694763230660","O2  \nReflection and Mirrors  \nO2. 1 Introduction to Single Mirrors  \nIn this section we will be introduced to a number of new ideas. We will start with mirrors because the interaction of light with mirrors, based on reflection, is easier to deal with than the interaction of light with lenses, which is based on refraction. However, we must make a special effort to understand the ideas of real and virtual images in addition to understanding the title subject of mirrors. If we finish this section with only a recipe for dealing with mirrors and not an understanding of the two types of images, we will be unprepared for future work.  \nO2.2 IMAGES-VIRTUAL AND REAL. We will introduce the ideas of real and virtual images here and revisit these ideas repeatedly. The two types of images tends to be a confusing subject, but if we use the precise definitions instead of thinking about what we “see”, the subject will be routine.  \nO2.3 RAY TRACING. We will introduce the idea of using a few critical rays to graphically understand the behavior of light and mirrors.  \nO2.4 FORMULAS AND SIGN CONVENTION. It is not sufficient to stop with the graphical solution. We will also want a quantitative answer. In order to do this consistently we will need to define certain sign conventions which we will use here and in later studies of compound systems.  \nO2.5 CONVEX MIRRORS - VIRTUAL IMAGE. We will apply the graphical techniques and formulas to examine the behavior of light reflecting off a surface curved like the back of a spoon.  \nO2.6 CONCAVE MIRRORS-VIRTUAL AND REAL IMAGES. We will apply the graphical techniques and formulas to examine the behavior of light reflecting off a surface curved like the front of a spoon.  \nO2.7 PLANE MIRRORS-VIRTUAL IMAGES. We will finish the simple systems by examining the limiting case between convex and concave shapes.  \n©Paul A. DeYoung April 21, 2003  \n10  \nO2.2 Images-virtual and real.  \nWhen you look in a mirror, you see what appears to be you standing behind the mirror looking back at yourself. What makes this image appear? Let’s start by  \nlooking at how an image forms, starting with a concave mirror (one in which the reflecting surface is“caved” in) . The arrowhead in Figure O2.1 emits light rays in all directions. Some of the light rays strike the mirror surface and reflect back toward the arrow. The angle at which a light ray reflects is the same as the angle of incidence. As you can see, the reflected rays all pass through one point as they travel away from the mirror. If a piece of paper or screen were placed at this point, an image of the arrow head would appear. In fact, this is called a real  \nThis real image appears sharp and in focus on a screen, although it may be enlarged or reduced compared to the object. Even if the screen is removed, the location where all of the light rays are converging is still called the location of the real image. The light rays really are converging at that spot.  \nTechnically, the object in Figure O2.1 (the arrow) is called a REAL OBJECT. This is not because the arrow is physically located at this point, but because it is a point in space from which the light rays emanate. Light rays really leave the location of the arrow head and travel outward through space.  \nWhy is this distinction important? In compound systems, where there are several lenses and/or mirrors, an image from one component effectively becomes the object for another. Thus, even though the arrow is not physically located at point S’, it appears as if an arrow is located there as far as the second optical component is concerned. The image from the first mirror becomes the object for the second component.  \nIn summary, the rays converge as they approach the location of the real image. The rays diverge as they leave a real object and travel to the next optical element.  \nWe should note that the images formed by mirrors or lenses are not always real. For example, if the arrow was placed in front of a convex mirror","cbCaikd8OGDrQg68","https://ap.wps.com/l/cbCaikd8OGDrQg68","pdf",85894,"English","# O2 Reflection and Mirrors\n## O2.1 Introduction to Single Mirrors\n## O2.2 Images - virtual and real\n## O2.3 Ray tracing\n## O2.4 Formulas and sign convention\n## O2.5 Convex mirrors - virtual image\n## O2.6 Concave mirrors - virtual and real images\n## O2.7 Plane mirrors - virtual images","[{\"question\":\"How does a real image formed by a concave mirror differ from a virtual image?\",\"answer\":\"A real image forms where reflected rays actually converge, so it can appear sharply on a screen. A virtual image results when reflected rays only appear to come from a point; there is no convergence that would allow a screen image.\"},{\"question\":\"Why is the distinction between real and virtual images important for compound optical systems?\",\"answer\":\"In compound systems, the image from one element effectively acts as the object for the next. Even when the image is not physically located (as with virtual images), it still serves as the correct reference for subsequent ray behavior.\"},{\"question\":\"What is ray tracing in the context of mirrors, and why are sign conventions needed?\",\"answer\":\"Ray tracing uses a small set of critical rays to describe how light behaves when reflecting from mirrors. To obtain quantitative answers consistently, the method also relies on defined sign conventions that are used across later compound-system studies.\"}]","Reflection and Mirrors - O2 - Images: virtual and real - Ray tracing - Formulas and sign convention | PDF",1792971245,25]