Chapter 23Geometrical Optics: Mirrorsand Lenses and otherInstrumentsHITT 1You stand two feet away from aplane mirror. How far is it from youto your image?a. 2.0 ft b. 3.0 ft c. 4.0 ft d. 5.0 ft3/31/09TelescopeThe 100 inch (2.5 m)Hooker reflectingtelescope at MountWilson Observatorynear Los Angeles,California.International Year of Astronomy, Public Lecture, Fri. April 3rd 7.20pm, NPB 1002 "100 HOURS OF ASTRONOMY"Unlocking the Mysteries of the Heavens: From Galileo'sTelescope to the Future Generation of Giant TelescopesProfessors Rafael Guzman and ElizabethLadaThe lecture will be preceeded by a telescope assembly workshop inthe Physics lobby beginning at 6:30pm. Anyone with a telescopewho would like help with assemby should bring it to the lobbybefore the talk. After the talk, a public night will be held at theCampus Teaching Observatory, weather permitting. Those withtheir own telescopes are encouraged to bring them for observingassistance and training during the public observing night beginningat 8:30pm.! http://www.astro.ufl.edu/IYA/home.htmlSpherical Mirrors! A spherical mirror has the shape of asegment of a sphere! A concave spherical mirror has thesilvered surface of the mirror on theinner, or concave, side of the curve! A convex spherical mirror has thesilvered surface of the mirror on theouter, or convex, side of the curveConcave Mirror, Notation! The mirror has aradius of curvatureof R! Its center ofcurvature is thepoint C! Point V is the centerof the sphericalsegment! A line drawn from Cto V is called theprinciple axis of themirrorSpherical Aberration! Rays are generallyassumed to make smallangles with the mirror! When the rays makelarge angles, they mayconverge to pointsother than the imagepoint! This results in a blurredimage! This effect is calledspherical aberrationImage Formed by aConcave Mirror! Geometry can be used todetermine the magnification of theimage! h’ is negative when the image isinverted with respect to the objectImage Formed by aConcave Mirror! Geometry showsthe relationshipbetween theimage and objectdistances! This is called themirror equationFocal Length! If an object is very faraway, then p=! and 1/p= 0! Incoming rays areessentially parallel! In this special case, theimage point is called thefocal point! The distance from themirror to the focal pointis called the focal length! The focal length is ! theradius of curvatureFocal Point and FocalLength, cont! The focal point is dependent solelyon the curvature of the mirror, notby the location of the object! f = R / 2! The mirror equation can beexpressed asFocal Length Shown byParallel RaysConvex Mirrors! A convex mirror is sometimes called adiverging mirror! The rays from any point on the objectdiverge after reflection as though they werecoming from some point behind the mirror! The image is virtual because it lies behindthe mirror at the point where the reflectedrays appear to originate! In general, the image formed by a convexmirror is upright, virtual, and smaller thanthe objectImage Formed by aConvex MirrorSign Conventions forMirrorsRay Diagrams! A ray diagram can be used to determinethe position and size of an image! They are graphical constructions whichtell the overall nature of the image! They can also be used to check theparameters calculated from the mirrorand magnification equationsDrawing A Ray Diagram! To make the ray diagram, you need toknow! The position of the object! The position of the center of curvature! Three rays are drawn! They all start from the same position on theobject! The intersection of any two of the raysat a point locates the image! The third ray serves as a check of theconstructionThe Rays in a RayDiagram! Ray 1 is drawn parallel to the principleaxis and is reflected back through thefocal point, F! Ray 2 is drawn through the focal pointand is reflected parallel to the principleaxis! Ray 3 is drawn through the center ofcurvature and is reflected back on itselfNotes About the Rays! The rays actually go in alldirections from the object! The three rays were chosen fortheir ease of construction! The image point obtained by theray diagram must agree with thevalue of q calculated from themirror equationRay Diagram for ConcaveMirror, p > R! The object is outside the center of curvature ofthe mirror (p> R/2)! The image is real (q >0)! The image is inverted (m>0)! The image is smaller than the object (|m| <1)Ray Diagram for aConcave Mirror, p < f! The object is between the mirror and the focalpoint! The image is virtual! The image is upright! The image is larger than the objectalgebra! q = pf/(p-f)" q > 0 if p>f " the image is real(q>0), inverted (m<0) and smaller (|m|<1) if ..q/p <1 if p>2f = RIf p<f, q <0, m >0, image is virtual,straight and larger, m>1 (f/(f-p) >1)fqp111=+Ray Diagram for a ConvexMirror! The object is in front of a convex mirror! The image is virtual! The image is upright! The image is smaller than the objectNotes on Images! With a concave mirror, the image maybe either real or virtual! When the object is outside the focal point,the image is real! When the object is at the focal point, theimage is infinitely far away! When the object is between the mirror andthe focal point, the image is virtual! With a convex mirror, the image isalways virtual and upright! As the object distance increases, the virtualimage gets smallerImages Formed byRefraction! Rays originate fromthe object point, O,and pass through theimage point, I! When n2 > n1,! Real images areformed on the sideopposite from theobjectSign Conventions forRefracting SurfacesFlat Refracting Surface! The image formed bya flat refractingsurface is on thesame side of thesurface as the object! The image is virtual! The image formsbetween the objectand the surface! The rays bend awayfrom the normal sincen1 > n2Atmospheric Refraction! There are many interesting resultsof refraction in the atmosphere! Sunsets! MiragesAtmospheric Refractionand Sunsets! Light rays from the sun arebent as they pass into theatmosphere! It is a gradual bendbecause the light passesthrough layers of theatmosphere! Each layer has a slightlydifferent index ofrefraction! The Sun is seen to beabove the horizon evenafter it has fallen below itAtmospheric Refractionand Mirages! A mirage can beobserved when theair above the groundis warmer than theair at higherelevations! The rays in path Bare directed towardthe ground and thenbent by refraction! The observer seesboth an upright andan inverted imageThin Lenses! A thin lens consists of a