[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-656981-105":59,"doc-detail-656981-en":135},{"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":128,"head_meta":130,"extra_data":132,"updated_unix":134},105,"en","physics-25-chapter-25-mirrors","Physics 25 - Chapter 25 Mirrors","","Physics 25 Chapter 25 focuses on mirror image formation, starting with plane mirrors and the law of reflection. It explains how the eye-mind extrapolates reflected rays to locate the apparent image behind a plane mirror and distinguishes virtual images from real ones. The chapter then develops concave mirror ray behavior using special rays (paraxial and focal-point rays), defines focal length and magnification, and presents the mirror equations and sign conventions. Worked examples illustrate real vs virtual images and how magnification and distances are determined.",{"@graph":69,"@context":127},[70,84,106],{"@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/physics-25-chapter-25-mirrors/656981/",{"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/physics-25-chapter-25-mirrors/656981.png","ImageObject",300,407,{"name":92,"@type":93},"Patrick","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-10-25",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119,123],{"name":110,"@type":111,"acceptedAnswer":112},"How does a plane mirror form an image and what makes the image virtual?","Question",{"text":113,"@type":114},"Reflected rays obey the law of reflection, and the eye-mind extrapolates them backward to an intersection point behind the mirror. Because the rays do not truly originate from that location, the image is virtual and appears to be behind the mirror.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What are paraxial rays and the focal-point ray for a concave mirror?",{"text":118,"@type":114},"Paraxial rays are incident rays parallel to the axis; they reflect through a common point on the axis called the focal point F. A focal-point ray starts at the focal point, reaches the mirror, and reflects paraxially as a parallel beam.",{"name":120,"@type":111,"acceptedAnswer":121},"What equations and sign conventions are used for concave mirrors?",{"text":122,"@type":114},"The chapter uses 1/x + 1/y = 1/f and M = -y/x, with additional relations like M = f/(f - x) and HI = MHo. Object distance x is positive, focal length f is positive, and the image distance y is negative for images behind the mirror (virtual).",{"name":124,"@type":111,"acceptedAnswer":125},"How do you determine whether a concave mirror image is real or inverted?",{"text":126,"@type":114},"The text provides a YIRE approach: image is real when it is inverted, on the eye-side, or when light rays truly emanate from the image location. Magnification M is positive for upright images and negative for inverted ones, and M > 1 indicates a taller image while M \u003C 1 indicates a shorter image.","https://schema.org",{"og:url":83,"og:type":129,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":131,"canonical":83},"index,follow",{"doc_id":133,"site_id":62},656981,1793106919,{"code":4,"msg":5,"data":136},{"doc_id":133,"user_id":137,"nickname":92,"user_avatar":138,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":139,"file_id":140,"file_url":141,"file_type":142,"file_size":143,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":56,"language":144,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":145,"faqs":146,"seo_title":147,"seo_description":67,"update_tm":148,"read_time":149},549758146520,"https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470","Physics 25 Chapter 25 Mirrors  \nDr. Joseph F. Alward  \n| Example:\u003Cbr>The sides of two mirrors, M 1 and M2, perpendicular to the plane are aligned as shown in the figure. A ray of light is incident on M 1 from the left and is reflected onto M2.\u003Cbr>What is the angle θ?\u003Cbr>Answer: 70o | |\n| --- | --- |\n\nImage Formation with Plane Mirrors  \nA light source is illuminating the chess-piece castle in Figure 1 below. Rays 1 and 2 emanating from the top of the object reflect off the mirror according to the reflection law and are directed toward the eye. Figure 2 illustrates the adherence to the reflection law for each of the two rays: the angle of incidence equals the angle of reflection.  \nThe eye-mind system extrapolates Rays 1 and 2 back to their intersection point in back of the mirror; the intersection point is the location of the top of the image. Other image points (not shown) corresponding to the bottom, middle, and other points of the castle would be determined in a similar manner.  \nFigure 1  \nThe figures below illustrate the Law of Reflection applied to Rays 1 and 2:  \n\n| | |\n| --- | --- |\n\nFigure 2  \nNote that the castle image is in back of the mirror, so light rays that reach the eye only appear tobe coming from the image. Images from which light rays are not really coming, are said to be“virtual.”  \nConcave Mirrors  \nCreation of concave mirror image diagrams requires a knowledge of the behavior of two special rays, the first one of which is described below.  \nSpecial Ray \\#1: Paraxial Rays  \nIncident rays that are parallel to the axis are called “paraxial rays.” These rays are reflected through a common point on the axis at a point called “the focal point,” F, also called “the focus.”  \nThe distance of the focal point from the mirror is called,“the focal length.”Concave mirror focal lengths are positive.  \nParaxial ray sunlight is focused on the cooking pot at the focus.  \nSpecial Ray \\#2: Focal Point Ray  \n\n| Focal point rays emanate from the focal point on their way to the mirror, where they are reflected paraxially.\u003Cbr>| A light source placed at the focal point of a concave mirror produces a parallel beam of light. Photo below shows a searchlight in operation in Great Britain in World War II.\u003Cbr>|\n| --- | --- |\n\nImage Formation with Concave Mirrors  \nA light source (not shown) illuminates the castle chess-piece resting on the “axis” below. Rays 1 and 2 of light reflected off the top of the castle travel in the directions indicated.  \nRay 1 is a paraxial ray: it reflects through the focal point.  \nRay 2 is a focal point ray: after passing through the focal point it reflects paraxially.  \nThe eye-mind system uses Rays 1 and 2 to extrapolate backward to their intersection point at the bottom of the chess-piece; to the uninformed mind, that is the apparent location and orientation of the chess-piece. Other chesspiece points are determined by a similar extrapolation procedure. The image in this case is inverted, and is below the axis.  \nWe earlier noted that images that appear to come from behind the mirror are not real, but “virtual.” Light does not really emanate from such images. In this case, light really does travel from the image to the eye. Such images are called “real.”  \nAny image that is on the eye-side, not in back of the mirror, is real.  \nConcave Mirror Equations  \nExample above: All positive: f = Focal length x = Object distance y = Image distance  \n\n| HI = Image Height Negative if inverted. | Ho = Object Height\u003Cbr>Always positive | M = Magnification\u003Cbr>= HI/Ho Negative if inverted. |\n| --- | --- | --- |\n\nMirror Equations:  \n(1) 1/x + 1/y = 1/f  \n(2) M = -y/x  \n(3) M = f / (f– x)  \n(4) HI = MHo  \nEqn. (1) is sometimes called “the reciprocals equation.”  \nFacts and Examples: Concave Mirrors  \n\n| Objects: are always on the eye-side (in front) a distance x away from the mirror. “Object distances” x, are always positive. |\n| --- |\n| Images: Images on the “eye-side”(in front) of the mirror of the mirror are a distan","cbCaiiEu3vr6Ajff","https://ap.wps.com/l/cbCaiiEu3vr6Ajff","pdf",402939,"English","# Image Formation with Plane Mirrors\n## Concave Mirrors\n## Concave Mirror Equations\n## Facts and Examples: Concave Mirrors","[{\"question\":\"How does a plane mirror form an image and what makes the image virtual?\",\"answer\":\"Reflected rays obey the law of reflection, and the eye-mind extrapolates them backward to an intersection point behind the mirror. Because the rays do not truly originate from that location, the image is virtual and appears to be behind the mirror.\"},{\"question\":\"What are paraxial rays and the focal-point ray for a concave mirror?\",\"answer\":\"Paraxial rays are incident rays parallel to the axis; they reflect through a common point on the axis called the focal point F. A focal-point ray starts at the focal point, reaches the mirror, and reflects paraxially as a parallel beam.\"},{\"question\":\"What equations and sign conventions are used for concave mirrors?\",\"answer\":\"The chapter uses 1/x + 1/y = 1/f and M = -y/x, with additional relations like M = f/(f - x) and HI = MHo. Object distance x is positive, focal length f is positive, and the image distance y is negative for images behind the mirror (virtual).\"},{\"question\":\"How do you determine whether a concave mirror image is real or inverted?\",\"answer\":\"The text provides a YIRE approach: image is real when it is inverted, on the eye-side, or when light rays truly emanate from the image location. Magnification M is positive for upright images and negative for inverted ones, and M \\u003e 1 indicates a taller image while M \\u003c 1 indicates a shorter image.\"}]","Physics 25 - Chapter 25 Mirrors | PDF",1792971994,48]