Image formation – University of Wisconsin–Madison

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1Image formationA. KarlePhysics 202Nov. 27, 2007Chapter 36•Mirrors•Images•Ray diagrams•Lenses As usual, these notes are only a complement to the notes on the whiteboard.Types of Images•A real image is formed when light rays passthrough and diverge from the image point–Real images can be displayed on screens•A virtual image is formed when light rays donot pass through the image point but onlyappear to diverge from that point–Virtual images cannot be displayed on screens 2Images Formed by Flat Mirrors•Simplest possible mirror•Light rays leave thesource and arereflected from the mirror•Point I is called theimage of the object atpoint O•The image is virtualImages Formed by Flat MirrorsDefinitions:•The object distance–Denoted by p•The image distance–Denoted by q•The lateral magnification–Denoted by M=h’/hFlat mirror: •-|p|=|q|•M = 1•The image is virtual•The image is upright 3Application – Day and Night Settingson Auto Mirrors•With the daytime setting, the bright beam of reflected light isdirected into the driver’s eyes•With the nighttime setting, the dim beam of reflected light isdirected into the driver’s eyes, while the bright beam goeselsewhereSpherical mirrors:Concave MirrorNotation•Radius of curvature: R•Center of curvature: C•A line drawn from C to V:principal axis of the mirror 4Spherical Aberration•Rays that are far from theprincipal axis converge to otherpoints on the principal axis•This produces a blurred image•The effect is called sphericalaberrationImage Formed by a Concave MirrorGeometrical analysisshows:1. magnification:2. mirror equation:Special case: p ! ! ; q!R/2 5Focal Length•Object very far away: p ! !incoming rays are essentiallyparallel–image point = focal point =F–distance from mirror to focalpoint = focal length = f–f = R/2Image Formed by a Convex Mirror•In general, the image formed by a convex mirror isupright, virtual, and smaller than the object 6Sign Conventions•These sign conventionsapply to both concaveand convex mirrors•The equations used forthe concave mirror alsoapply to the convexmirrorSign Conventions, Summary Table 7Ray Diagram for a Concave Mirror, p > R•The center of curvature is between the object and the concavemirror surface•The image–real–inverted–smaller than the object (reduced)3 rays need to be drawn!Ray Diagram for a Concave Mirror, p < f•The object is between the mirror surface and the focal point•The image is–virtual–upright–is larger than the object (enlarged) 8Ray Diagram for a Convex Mirror•The object is in front of a convex mirror•The image is–virtual–upright–smaller than the object (reduced)Notes on Images•With a concave mirror, the image may be either realor virtual•With a convex mirror, the image is always virtual andupright•An image is real when the rays are passing through,virtual when this is not the case.