Geometrical OpticsThis weekFrom the website:Slide 4Geometrical ProcessWhere’s the image, where’s the object … who cares??? We do!What kind of optics:NoteSignsSigns – We mean (-) or (+)Slide 11Slide 12Paraxial Rays : Small Angle ApproximationSlide 14Slide 15Curved MirrorsConcave MirrorSign ConventionConcave Mirror/Paraxial ApproximationFor this structureSlide 21What about here? R, s, s’ (convex mirror)Concept: Focal Length of a MirrorGoing BackwardsMore Better – A ParabolaImage FormationThe geometry……A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 15 cm from the mirror.A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 10 cm from the mirror.A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 2.5 cm from the mirror.Geometrical OpticsChapter 241This weekThis week we begin the study of optics. I have no idea how far we will get into these chapters.Lenses & MirrorsInterferenceDiffractionProbably not enough material to justify a 7:00AM class. We can use office hours for that purpose.There will be a quiz on Friday.Watch for a new Mastering Physics (I know you just can’t wait!)Last quiz is in the bin.2From the website:Remaining Clicker EvilFix this evil or you will have a ZERO clicker score!! Practice Problem Set (Monday Session) ****** TAKE NOTE OF THE FOLLOWING ******The end of the semester is approaching. The common Final Examination will be on Saturday, Dec 12, 2009 from 9AM-12PMin room PSY 108There will be one more exam this semester but itprobably will be on December 2 (Wednesday).This exam will cover the remaining material covered. It willalso be covered in the final exam.Don't forget to check the evil clicker file! 3Geometrical OpticsYup … more angle stuff!4Geometrical ProcessLens orMirrorObjectImageOh where, oh where, has my bug’s image gone .. oh where or where can it be???5Where’s the image, where’s the object … who cares??? We do!What kind of an image is it?RealVirtualWhere is the object, where is the image?Behind the lensIn front of the lensWhere is the light coming from? Where is it going?What is the size of the image? (magnification)What is the orientation of the image?Same as the object,Inverted (upside down)ReverseQuestions about the image:6What kind of optics:MirrorPlanarConcaveConvexLensconvergingdivergingWhere is the light?Have you seen the light yet?7NoteThe object is usually the source of light.The image is where the light converges to replicate the object.The image can be on either side of the “optical element”The image can be real or virtualThe image can form an object for a second optical element.Yes .. it can be confusing. We will attack this a point at a time.8Signs9Signs – We mean (-) or (+)The distance from the object to the lens/mirror is called the object distance. It is positive if it is on the same side of the optical element as the incoming light. Otherwise it is negativeIt is designated by sThe distance from the image to the lens/mirror is called the image distance.It is positive if it is on the same side as the outgoing lightIt is designated by s’. Otherwise it is negative.Without this sign convention, these problems would be much more difficult. So pay attention to them!!101112Paraxial Rays : Small Angle Approximationsintansintheta sin tan0.01 0.01 0.010.02 0.02 0.020.03 0.03 0.030.04 0.04 0.040.05 0.05 0.050.06 0.06 0.060.07 0.07 0.070.08 0.08 0.080.09 0.09 0.090.10 0.10 0.100.11 0.11 0.110.12 0.12 0.120.13 0.13 0.130.14 0.14 0.140.15 0.15 0.150.16 0.16 0.160.17 0.17 0.170.18 0.18 0.180.19 0.19 0.190.20 0.20 0.200.21 0.21 0.210.22 0.22 0.220.23 0.23 0.230.24 0.24 0.240.25 0.25 0.260.26 0.26 0.270.27 0.27 0.280.28 0.28 0.290.29 0.29 0.300.30 0.30 0.3113'1'ssyym1415Curved MirrorsFor Student Misery Only!16Concave Mirrorcon-CAVE17Sign ConventionWhen the Center of Curvatureis on the same side of theoutgoing ray, R is positive.Otherwise, if the center of curvature is not on the same sideas the outgoing ray, R is negative.18Concave Mirror/Paraxial Approximation22'' shshshshThe normal to thesurface passes through CThereforeRhConsequentlyRssRhshsh2'112'MIRROREQUATION19For this structureA. The Radius R is positive and s’ is negativeB. The Radius R is negative and s’ is negativeC. R is positive and s’ is positiveD. R is negative and s’ is positiveAnswer20When the Center of Curvatureis on the same side of theoutgoing ray, R is positive.the image distance is positive if it is on the same side as the outgoin g light21What about here? R, s, s’ (convex mirror)22Concept: Focal Length of a Mirror23fsssRss1'112Rs'f0)(1/s 2'11Going Backwards24'0'1)2(1/s 22'11ssRRsRssMore Better – A Parabola25surveillanceImage Formation260'00sRs‘‘y’<0(from the diagram) so image is inverted.The geometry……27ss'-mand ''syso Triangles,Similar diagram)in image inverted fromsign (- 'syyymA concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 15 cm from the mirror.2810 cm 5 cmNormal to mirrorand bounces backalong incomingpath.mmyssmsfRss 45.'5.7'12'11A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 10 cm from the mirror.2910 cm 5 cmmmyssmcmsfRss 80.1'10'12'11A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 2.5 cm from the mirror.3010 cm 5 cmeyemmyssmcmsfRss
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