Geometrical OpticsGetting There Fast – Are you studying for the final yet??This weekNext WeekAbout the final examinationBring ALL Lab Units from Magnetism Through Optics to class on Friday. One of them will be collected for grading.Slide 7Geometrical ProcessWhere’s the image, where’s the object … who cares??? We do!What kind of optics:NoteSigns – We mean (-) or (+)Consider looking in a plane mirror in your bathroom. Your image distance isSlide 14Slide 15Paraxial Rays : Small Angle ApproximationSlide 17Slide 18Curved MirrorsConcave MirrorSign ConventionConcave Mirror/Paraxial ApproximationFor this structureSlide 24This image isWhat about here? R, s, s’ (convex mirror)Concept: Focal Length of a MirrorGoing BackwardsFor a convex mirror, the RadiusSlide 30Image Formation – Ray DiagramContinue the current UnitExamples to reviewA 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.The Concave MirrorMore Convex MirrorGraphical Methods are very useful to check your work.Geometrical Optics14.21Getting There Fast – Are you studying for the final yet??2Sunday Monday TuesdayWednesdayThursday Friday Saturday1 23 4 Complete Induction5 6AC7 8ACQuiz?910 11COMPLETEAC EXPT12 13 OPTICSEM WavesPOLARIZATION14 15 OPTICSQuiz1617 18EXAM #3(No Optics)19 20 OPTICS21 22 OPTICS2324 25 (LAST LASS)OPTICS26 27 28 29 30 FINALHPA 1199:00 AMThis weekThis week we will cover some topics in geometrical optics. This will include mirrors and lenses. This is about all that we will be able to accomplish. Only what we cover in class will be covered on the final examination.There will be NO QUIZ this week.The final exam will be on Saturday, April 30th in room HPA 119. (Two Index Cards allowed)Entire semesters work.Joint exam with other Studio Class.Watch for new WebAssign and probably one after that.3Next WeekMonday Post Test (will be used for borderline cases)Complete topics and possibly some problemsWednesday-FridayIf there is coordinated interest, I might be able to come to campus and go over some problems. Need to find some common day/time to do this.Saturday Final Examination (2 index cards allowed).4About the final examinationOnly topics discussed In class, On class PowerPoint lectures Contained in the lab sheets, Included in WebAssigns or  Assigned for reading will be covered on the final exam.That’s a lot of stuff!5Bring ALL Lab Units from Magnetism Through Optics to class on Friday. One of them will be collected for grading.6STUDIO UNIT ???Geometrical OpticsYup … more angle stuff!7Geometrical ProcessLens orMirrorObjectImage8Where’s the image, where’s the object … who cares??? We do!What kind of an image is it?RealVirtualWhere is the object, where is the image?Behind the mirrorIn front of the mirrorWhere 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:9What kind of optics:MirrorPlanarConcaveConvexLensconvergingdivergingWhere is the light?Have you seen the light yet?10mirrorsNoteThe 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 virtualThe image can form an object for a second optical element.Yes .. it can be confusing. We will attack this a point at a time. You have done some of this in the units so this is a review of sorts.11Signs – 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 negativeIt is designated by sThe 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 lightIt is designated by s’. Otherwise it is negative.Without this sign convention, these problems would be much more difficult. So pay attention to them!!12Consider looking in a plane mirror in your bathroom. Your image distance isA. PositiveB. NegativeC. This convention doesn’t apply to my bathroom mirror.131415Paraxial Rays : Small Angle Approximationsintansintheta 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 0.3116'1'ssyym1718Curved MirrorsFor Student Misery Only!19Concave Mirrorcon-CAVE20Sign 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.21Concave Mirror/Paraxial Approximation2angle) (external 2'' shshshshThe normal to thesurface passes through CThereforeRhConsequentlyRssRhshsh2'112'MIRROREQUATION22For 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 positiveAnswer23When 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 light24This image isA. real, reversedB. virtual, not reversedC. real, not reversedD. virtual, reversed25What about here? R, s, s’ (convex mirror)26Concept: Focal Length of a Mirror27fsssRss1'112Rs'f0)(1/s 2'11Going Backwards28'0'1)2(1/s 22'11ssRRsRssFor a convex mirror, the RadiusA. Is positiveB. Is negativeC. The sign