PHYS 219 Spring semester Lecture 20: Reflection of Electromagnetic Radiation: Mirrors and Images Formed by Mirrors

Transcription

1 PHYS 219 Sprng semester 2014 Lecture 20: eflecton of Electromagnetc adaton: Mrrors and Images Formed by Mrrors on efenberger Brck Nanotechnology Center Purdue Unversty Lecture 20 1 evew: Snapshot of an Electromagnetc Wave c = f For next TWO lectures, we wll treat an EM wave as a lght ray that s perpendcular to the EM wavefronts. wavefronts ray 2 1

2 Interacton of EM radaton wth matter a) I b) A T EM radaton (lght) travels slower n a materal: n=c/v c= speed of lght n vacuum (ar) v=speed of lght n a materal I(W/m 2 ) = + T + A (conservaton of energy) Three regmes: f I, mrrors f AI, flters and abrbers f TI, lenses materal n glass 1.5 water 1.33 damond eflecton The Physcs of Mrrors Source of lght Lght ray specular reflecton many rays 4 2

3 What the Pengun sees h o Θ r Θ h s o object dstance s mage dstance The pengun sees a vrtual mage. How are s o, s and h o, h related? 5 For plane mrrors, the mage dstance equals the object dstance planar mrror s o s eal object, Vrtual mage 6 3

4 Mrrors made from curved surfaces are more nterestng r Concave mrror Convex mrror 7 Defnton of Terms: Two specal ponts: C and F One specal length: f=/2 Center of curvature Prncpal Axs Concave mrror focal length Focal Pont f Convex mrror f=/2 f=-/2 8 4

5 Where s the Image? ay Tracng for Concave Sphercal Mrror three predctable rays: 1. parallel to Prncpal Axs 2. thru F Three predctable lght rays; two mportant ponts 3. thru C Students often have dffculty understandng how the entre mage of an object can be deduced once a sngle pont on the mage has been determned. h o specular reflecton r h s specular reflecton One clck See Appendx for dervaton = + f s s o h m= =- h o s s o magnfcaton 9 un Smulatons

6 Sgn Conventons are Important (dfferent textbooks may use dfferent conventons) Curved Mrrors Quantty Symbol* Postve Sgn means Negatve Sgn means Focal Length f Concave mrror Convex mrror Image Dstance s In front of mrror (real) Behnd mrror (vrtual) Object Dstance s o In front of mrror (real) Behnd mrror (vrtual) Magnfcaton m Image uprght Image nverted Image Heght h Image uprght Image nverted *each symbol can be assgned ether a + or - value Be able to dstngush between eal and Vrtual Images A negatve or postve sgn n front of a numercal value s used to represent nformaton about drecton. 11 Concave Mrror: A Systematc Summary Fve (5) possble locatons of an OBJECT: Case 1: the object s located beyond the center of curvature (C) Case 2: the object s located at the center of curvature (C) Case 3: the object s located between the center of curvature (C) and the focal pont (F) Case 4: the object s located at the focal pont (F) Case 5: the object s located n front of the focal pont (F)

7 Schematc: Object-Image Locatons Case 1 Case 2 Case 3 Case 4 Case 5 13 Understandng Object-Image Locatons for a Concave Mrror Dfferent object locatons are drawn n red and labeled wth a number; the correspondng mage locatons are drawn n blue and labeled wth the dentcal number. real objects mages C 3 4 mages 2 1 F Concave mrror real vrtual

8 Understandng Object-Image Locatons for a Convex Mrror Dfferent object locatons are drawn n red and labeled wth a number; the correspondng mage locatons are drawn n blue and labeled wth the dentcal number. objects mages F C Convex mrror real objects vrtual mages 15 Applcaton: Mrrors n European Cathedrals Concave mrror Image of artwork on dome 16 8

9 Gazng Globe Example I A gazng globe has a dameter of 12 nches. If a brd that s sx nches tall stands 36 nches n front of the globe, what wll the brd see? Convex mrror dameter = 12 n f=- =-3n = + f s = - = - =- - =- s f s = n (vrtual mage,behnd mrror) h s m= =- =- =+0.23 uprghtmage ho 12 h 0.23 = h = 0.23 h o = 0.23(6) = 1.38 n h 17 o specular reflecton Not to scale Example II Butters stands 1 m n front of a concave mrror that has a radus of curvature of 1 m. Where s the mage formed? radus of curvature = 1 m object concave mrror C F radus = 1.0 m f=+ =+0.5 m 2 h s m= =- =- =-1.0 nvertedmage = + ho 1.00 f s h = h = -ho = - = - =+1.0 ho s f s o s = +1.0 m (real mage,n front of mrror) 18 mage 9

10 APPENDIX: Dervaton of the Curved Mrror Equaton from Eucld: the sum of opposte nteror angles equals the exteror angle Q P α γ += 19 How are s o, s and f related for concave mrror? the sum of f s Q from Eucld: opposte nteror angles equals the exteror angle 2 2 (1) QA QA s QA from (1) s defne f / 2 Pont object α C Θ Θ γ β F s specular reflecton A dstances measured from A s o, s, and f are by defnton postve can be extended to convex mrrors (requres negatve sgns see prevous slde) becomes less accurate as pont object s 20 moved off central axs 10