Slde 1 SPH3UW: OPTICS I Introducton to Mrrors Slde 2 Lght ncdent on an object Absorpton Relecton (bounces)** See t Mrrors Reracton (bends) Lenses Oten some o each Everythng true or wavelengths << object sze Slde 3 Relecton Angle o ncdence = Angle o relecton q = q r (Angles between lght beam and normal) q r q
Slde 4 Object Locaton Lght rays rom sun bounce o object and go n all drectons Some o the rays ht your eyes We know object s locaton by the drecton the lght rays come rom. Color: some lght s absorbed by object beore bouncng o. Slde 5 Relecton rom a Plane Mrror The angle o ncdence equals the angle o relecton. Ths assumes the surace s perectly smooth. Slde 6 Duse Relecton When the surace s rough, the surace at any pont makes some angle wth respect to the horzontal. The angle o ncdence stll equals the angle o relecton.
Slde 7 Plane Mrrors In the let hand pcture wth a rough surace, you can place your eye anywhere and you wll see some relected rays. On the rght hand sde, you eye has to be n the correct poston to see the relected lght. Ths s called specular relecton. Slde 8 Plane Mrrors A plane mrror provdes the opportunty to ool you by makng your eye and bran perceve an mage. Slde 9 Plane Mrrors The mage appears to be the same dstance behnd the mrror as the object s n ront o the mrror.
Slde 1 Plane Mrrors The mage s called a vrtual mage because you placed a pece o paper at the mage locaton, you wouldn t see any lght. Slde 11 Plane Mrror All you see s what reaches your eyes You thnk object s locaton s where rays appears to come rom. All rays orgnatng rom peak wll appear to come rom same pont behnd mrror! Object q r q Image Slde 12 How to Draw the Image n a Plane Mrror (1) Draw rst ray perpendcular to mrror q = = q r (2) Draw second or thrd ray at angle. q = q r (3) Where the extended lnes appear to ntersect (a dstance d behnd mrror) s the mage locaton. Lght rays don t really converge there, so t s a Vrtual Image q q r d q r q d Vrtual: No lght actually gets here.
Slde 13 How Bg a Mrror?.8 m Slde 14 Queston Why do ambulances have AMBULANCE wrtten backwards? Slde 15 Soluton So you can read t n your rear-vew mrror!
Slde 16 Queston Can you see Fdo s tal n mrror? (You) (Fdo) Slde 17 Soluton Can you see Fdo s tal n mrror? No! You need lght rays rom the tal to bounce o mrror and reach your eye! (You) (Fdo) Slde 18 ACT: Plane Mrrors You are standng n ront o a short lat mrror whch s placed too hgh, so you can see above your head, but only down to your knees. To see your shoes, you must move: (1) closer to the mrror. (2) urther rom the mrror. (3) to another mrror.
Slde 19 ACT: Plane Mrrors You are standng n ront o a short lat mrror whch s placed too hgh, so you can see above your head, but only down to your knees. To see your shoes, you must move: (1) closer to the mrror. (2) urther rom the mrror. (3) to another mrror. Changng dstance doesn t change what you see o yoursel Slde 2 Two Mrrors How many mages o money wll you see (not ncludng the actual money)? Slde 21 Two Mrrors How many mages o money wll you see (not ncludng the actual money)? 2 1 3
Slde 22 R C = Center o Curvature In ront o concave mrror Behnd convex mrror. Curved mrrors A Sphercal Mrror: secton o a sphere. lght ray prncpal axs lght ray C C Concave mrror prncpal axs Convex mrror Slde 23 Understandng An organc chemstry student accdentally drops a glass marble nto a slver ntrate mrrorng soluton, makng the outsde o the marble relectve. What knd o mrror s ths? (1) concave (2) convex (3) lat Slde 24 Prncpal Axs Concave Mrror Rays are bent towards the prncpal axs. Focus =R/2 Rays parallel to prncpal axs and near the prncpal axs ( paraxal rays ) all relect so they pass through the Focus (F). The dstance rom F to the center o the mrror s called the Focal Length (). R 2
Slde 25 What knd o sphercal mrror can be used to start a re? concave convex How ar rom the paper to be gnted should the mrror be held? arther than the ocal length closer than the ocal length at the ocal length Understandng Slde 26 F Concave Mrror Prncpal Axs Rays travelng through ocus beore httng mrror are relected parallel to Prncpal Axs. Rays travelng parallel to Prncpal Axs beore httng mrror are relected through ocus F Slde 27 Convex Mrror Prncpal Axs Focus =-R/2 Rays are bent away rom the prncpal axs. Rays parallel to prncpal axs and near the prncpal axs ( paraxal rays ) all relect so they appear to orgnate rom the Focus (F). The dstance rom F to the center o the mrror s called the Focal Length (). R 2
Slde 28 Concave Mrror Drawng mage Technque 1) Parallel to prncpal axs relects through. 2) Through, relects parallel to prncpal axs. 3) Through center. 4) At the vertex Image s (n ths case): Real or Imagnary Inverted or Uprght Reduced or Enlarged When object s on the outsde o the centre o curvature **Every other ray rom object tp whch hts mrror wll relect through mage tp. You need at least two o the above technques to draw mage #4 #1 #2 #3 c V Slde 29 Concave Mrror Drawng mage When object s on the outsde o the centre o curvature The mage s real The mage s nverted The mage s smaller than the object Slde 3 Concave Mrror-Drawng mages Technque 1) Parallel to prncpal axs relects through. 2) Through, relects parallel to prncpal axs. 3) At the vertex Image s (n ths case): Real or Imagnary Inverted or Uprght Reduced or Enlarged or Same Sze When object s at the centre o curvature c #1 #2 **Every other ray rom object tp whch hts mrror wll relect through mage tp #3 V
Slde 31 Concave Mrror-Drawng mages Technque When object s between the centre o curvature and the ocus 1) Parallel to prncpal axs relects through. 2) Through, relects parallel to prncpal axs. 3) At the vertex Image s (n ths case): Real or Imagnary Inverted or Uprght Reduced or Enlarged #1 c #2 **Every other ray rom object tp whch hts mrror wll relect through mage tp #3 V Slde 32 Technque Concave Mrror Prncpal Rays 1) Parallel to prncpal axs relects through. 2) Through, relects parallel to prncpal axs. #1 3) At the vertex Image s (n ths case): Real or Imagnary Inverted or Uprght Reduced or Enlarged When object s between the ocus and the Vertex **Every other ray rom object tp whch hts mrror wll relect through mage tp #3 c #2 V Slde 33 Concave Mrror Prncpal Rays When object s between the ocus and the Vertex The mage s vrtual The mage s uprght The mage s larger than the object
Slde 34 Understandng Whch ray s NOT correct? p.a. R 1) 2) 3) Ray through centre should relect back on sel. Slde 35 Mrror Focal Lengths A concave mrror has a postve ocal length > A convex mrror has a negatve ocal length < What s the ocal length o a lat mrror? (1) = (2) = The latter the mrror, the larger the radus o curvature, (e.g. the earth s round, but looks lat) Slde 36 Concave Mrror Image Locaton Yep, no mage
Slde 37 Mrror Equaton d d d o = dstance object s rom mrror: Postve: object s In ront o mrror Negatve: object s behnd mrror d = dstance mage s rom mrror: d o O c I d Postve: nverted mage s In ront o mrror Inverted Negatve: uprght mage s behnd mrror uprght = ocal length mrror: Postve: concave mrror Concave In Front Negatve: convex mrror Convex Behnd Slde 38 Understandng The mage produced by a concave mrror o a real object s: 1) Always Real 2) Always Vrtual 3) Sometmes Real, Sometmes Vrtual In a concave mrror the ocal length,, s > Real Object means n ront o mrror: d o > Thereore d can be postve or negatve Mrror Equaton d d d d Slde 39 Practce: Concave Mrror Where n ront o a concave mrror should you place an object so that the mage s vrtual? 1) Close to mrror 2) Far rom mrror 3) Ether close or ar 4) Not Possble In a concave mrror the ocal length,, s > Object n ront o mrror: d o > Vrtual mage means behnd mrror: d < When d o < then d < : vrtual mage. Mrror Equaton: d d d d
Slde 4 Magncaton Equaton h m h o h o = heght o object: d d Postve: Always h = heght o mage: Postve: uprght Negatve: nverted m = magncaton: Postve / Negatve: same as or h < 1: mage s reduced > 1: mage s enlarged o ho h tan(q ) d d o h h o O Angle o ncdence q d q d o q d o I q d Angle o relecton Slde 41 Practce Solvng Equatons A candle s placed 6 cm n ront o a concave mrror wth ocal length =2 cm. Determne the mage locaton. Real Image! 1 6cm 2cm d 2 2 3cm 6cm d 2cm d 12cm 12cm (n ront o mrror) d d 1 1 d 2cm 6cm 3cm Compared to the candle, the mage wll be: Larger Smaller Same Sze Note: mage s 3 cm n ront o mrror, thereore 1 cm to the let o the ocus d p.a. C Slde 42 Practce: Magncaton A 4 nch arrow pontng down s placed n ront o a mrror that creates an mage wth a magncaton o 2. What s the sze o the mage? 1) 2 nches 2) 4 nches 3) 8 nches What drecton wll the mage arrow pont? 1) Up 2) Down (-) sgn tells us t s nverted rom object h m h o 4 nches Magntude gves us sze. h mh 24" 8"
Slde 43 Technque Convex Mrror Rays 1) Parallel to prncpal axs relects through. 2) Through center. 3) Through, relects parallel to prncpal axs. O #3 #1 #2 I Image s: Vrtual (lght rays don t really cross) Uprght (same drecton as object) Reduced (smaller than object) (always true or convex mrrors!): c Slde 44 Convex Mrror Rays The mage s vrtual The mage s uprght The mage s smaller than the object Slde 45 Convex Mrror Images Unlke Concave Mrrors, convex mrrors always produce mages whch share these characterstcs. The locaton o the object does not aect the characterstcs o the mage. As such, the characterstcs o the mages ormed by convex mrrors are easly predctable The dagrams below shows that n each case: the mage s located behnd the convex mrror a vrtual mage an uprght mage reduced n sze (.e., smaller than the object)
Next tme Today Last Tme Slde 46 Relecton: Reracton: Absorpton q = q r Overvew Flat Mrror: mage equdstant behnd Sphercal Mrrors: Concave or Convex n 1 sn(q 1 )= n 2 sn(q 2 ) Flat Lens: Wndow Sphercal Lenses: Concave or Convex q q r q 1 n 1 n 2 q 2 Slde 47 Solvng Problems A candle s placed 6 cm n ront o a convex mrror wth ocal length =-3 cm. Determne the mage locaton. d d 6cm d 3cm Determne the magncaton o the candle. m d 2cm 1 m d 6cm 3 d = - 2 cm (behnd mrror) Vrtual Image! I the candle s 9 cm tall, how tall does the mage candle appear to be? h mh h m 1 9 h cm 3 3cm Image s Uprght! Slde 48 Problem Where should you place an object n ront o a convex mrror to produce a real mage? 1) Object close to mrror 2) Object ar rom mrror 3) Ether close or ar 4) You can t Convex mrror: < Object n ront o mrror: d o > Real mage means d > d s negatve! Mrror Equaton: 1 d o 1 d 1 d d d o s s negatve postve
Slde 49 Problem A concave mrror has a radus o curvature o 24. cm. An object 2.5 cm hgh s placed 4. cm n ront o the mrror. a) At What dstance rom the mrror wll the mage be ormed? b) What s the heght o the mage? 2.5cm C 4.cm 24.cm Slde 5 Problem A concave mrror has a radus o curvature o 24. cm. An object 2.5 cm hgh s placed 4. cm n ront o the mrror. a) At What dstance rom the mrror wll the mage be ormed? b) What s the heght o the mage? d d R 2 12.cm 4. cm d 12.cm 4.cm d 7 1 12cm d d 17.14 cm 24.cm 2 12.cm 2.5cm The mage s 17 cm n ront o the mrror C 4.cm 24.cm Slde 51 Problem A concave mrror has a radus o curvature o 24. cm. An object 2.5 cm hgh s placed 4. cm n ront o the mrror. a) At What dstance rom the mrror wll the mage be ormed? b) What s the heght o the mage? h d m h d h 17.14 cm 2.5cm 4.cm 17.14cm h 2.5cm 4.cm 1.7 cm 2.5 cm The heght o the nverted mage s 1.1 cm C 4.cm 24.cm
Slde 52 Problem A convex mrror has a radus o curvature o 8. cm. An object 1.7 m hgh s placed 4.5 m n ront o the mrror. a) At What dstance rom the mrror wll the mage be ormed? b) What s the heght o the mage? 1.7 m 4.5m 8.cm C Slde 53 Problem A convex mrror has a radus o curvature o 8. cm. An object 1.7 m hgh s placed 4.5 m n ront o the mrror. a) At What dstance rom the mrror wll the mage be ormed? b) What s the heght o the mage? d d.4m 4.5m d d.4m 4.5m 1 4.9m d 1.8m d.37m R 1.7 m 2.8m 2.4m 4.5m Thereore the mage s.37 m behnd the mrror.37m.4m 8.cm C Slde 54 Problem A convex mrror has a radus o curvature o 8. cm. An object 1.7 m hgh s placed 4.5 m n ront o the mrror. a) At What dstance rom the mrror wll the mage be ormed? b) What s the heght o the mage? h d m h d h d h d h d h d.37m 1.7m 4.5m.14m 1.7 m 4.5m.37m.4m 8.cm C
Slde 55 Mrror Summary Angle o ncdence = Angle o Relecton Prncpal Rays Parallel to P.A.: Relects through ocus Through ocus: Relects parallel to P.A. Through center: Relects back on sel = R/2 1 1 1 d o d h m ho d d o