Focal Points of Spherical Mirrors. Spherical Mirrors. A plane mirror is a spherical mirror with an infinite radius of curvature. O Height = I Height
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1 Radus f Curvature Plane Mrrr A plane mrrr s a sphercal mrrr wth an nfnte radus f curvature. O Heght = I Heght phercal Mrrrs Cncave Mrrr: (e.g. make up mrrr) Center f curvature s n frnt f mrrr Feld f vew s smaller than fr plane mrrr Object Heght < Image Heght Cnvex Mrrr: (e.g. survellance mrrr) Center f curvature s behnd mrrr Feld f vew s larger than fr plane mrrr Object Heght > Image Heght DEMO 0/25/ 3 Fcal Pnts f phercal Mrrrs R f = 2 DEMO Cncave: Parallel rays clse t central axs reflect thrugh a cmmn pnt F. F s called the fcal pnt. f s the fcal length (dstance frm center f mrrr t F). Cnvex: The extensns f the reflected rays pass thrugh a cmmn pnt behnd the mrrr. gn Cnventn: r & f are pstve fr cncave mrrr. r & f are negatve fr cnvex mrrr. 0/25/ 4
2 DEMO Images frm phercal Mrrrs (a)! O s nsde the fcal pnt: *mage appears behnd the mrrr * s negatve *vrtual mage *same rentatn (b) O at the fcal pnt: phercal Mrrrs! > 0! Real mages frm n the same sde f a mrrr as the bject ( > 0).! Vrtual mages frm n the ppste sde < 0). ( *mage s ambguus *rays d nt crss t frm mage (c) O s utsde the fcal pnt: *mage s nverted & n frnt f the mrrr * s pstve *real mage + f > 0 f < 0 = f cncave mrrr cnvex mrrr Fr a sphercal mrrr 0/25/ 5 0/25/ 6 Magnfcatn ze f an bject r mage s measured called the mage heght, h. t the mrrr s central axs & s Lcatn f Images by Drawng Rays h - heght f bject h - heght f mage Magnfcatn prduced by a mrrr: h m = h m =! m = If m < 0, mage s nverted. Fr plane mrrr : Image s uprght. =! m = + Fr phercal mrrr: + = " f 0 m =! " f =! f! f m =! f Use wth next slde. 0/25/ 7 0/25/ 8
3 Lcatn f Images by Drawng Rays Fr cncave mrrrs: Yu can graphcally lcate the mage f any ff-axs pnt f the bject by drawng a ray dagram wth any tw f fur specal rays thrugh the pnt:.! A ray that s parallel t the central axs reflects thrugh the fcal pnt F. 2.! A ray that reflects frm the mrrr after passng thrugh the fcal pnt emerges parallel t the central axs. 3.! A ray that reflects frm the mrrr after passng thrugh the center f curvature C returns alng tself. 4.! A ray that reflects frm the mrrr at ts ntersectn wth the central axs s reflected symmetrcally abut that axs. 0/25/ 9 ummary! Equatns fr mrrrs : when the fllwng sgn cnventns are used: Mrrr Type Plane Object Lcatn Image Lcatn Anywhere Oppste sde f mrrr frm bject Cncave Insde F Oppste sde f mrrr frm bject Cncave Cnvex Outsde F ame sde as bject Anywhere Oppste sde f mrrr frm bject + Image Type Image Vrtual Vrtual Orentatn ame rentatn as bject ame rentatn as bject gn f f r s m!! Real Inverted Vrtual ame rentatn as bject /25/ 0 = f m =! Last Lecture: Gemetrc Optcs In stuatns n whch the length scales are >> than the lght s wavelength, lght prpagates as rays Reflectn: Refractn:! =! If n > n 2 then! 2 >! If n 2 > n then! >! 2 r n sn! = n sn! 2 2 ncdent ray reflected ray!! r n! 2 n 2 refracted ray Refracted ray bends away frm nrmal Refracted ray bends tward the nrmal 0/25/ Thn Lenses: Cnvergng Lens!Parallel rays refract twce!cnverge at F 2 a dstance f frm center f lens!f 2 s a real fcal pt because rays pass thrugh!f > 0 fr real fcal pnts ' $ = ( n! ) %! " f & r r2 # n! > 0 because n r > 0 r < 0 2 because bj. facng cnvex surface because bj. facng cncave surface 0/25/ 2 glass > n ar
4 Thn Lenses: Dvergng Lens Ray Tracng Fr Lenses!Rays dverge, never pass thrugh a cmmn pnt!f 2 at a dstance f!f 2 s vrtual fcal pnt f < 0 fr vrtual fcal pnts 0/25/ 3 0/25/ 4 Lens Equatn Extra ldes 0/25/ 5 0/25/ 6
5 phercally Refractng urfaces If the refracted ray s drected tward the central axs, a real mage wll frm n that axs. Real (vrtual) mages are frmed when bj. s relatvely far (near) frm refractng surface If the refracted ray s drected away frm the central axs, t CANNOT frm a real mage. Hwever, backward extensn f the ray can frm a vrtual mage. 0/25/ 7 phercally Refractng urfaces n 2 > n Bends tward nrmal Real mage frmed n < n 2 Bends away frm nrmal Real mage frmed 0/25/ 8 phercally Refractng urfaces n > n 2 Bends away frm nrmal and central axs Vrtual mage frmed n 2 > n Ray drected away frm central axs Vrtual mage frmed 0/25/ 9 ummary: phercally Refractng urfaces.! Real Images frm n the sde f a refractng surface that s ppste the bject. 2.! Vrtual Images frm n the same sde as the bject 3.! Fr lght rays makng nly small angles wth the central axs: n n2 n2! n = = r 4.! When the bject faces a cnvex refractng surface, the radus f curvature s pstve. 5.! When bject faces a cncave surface, radus f curvature s negatve. 0/25/ 20
6 Example: Msqut n Amber A msqut s embedded n amber wth an ndex f refractn f.6. One surface f the amber s sphercally cnvex wth a radus f curvature 3.0 mm. The msqut head happens t be n the central axs f that surface, and when vewed alng the axs appears t be bured 5.0 mm nt the amber. Hw deep s t really? Draw Pcture Example: Msqut n Amber ) =!5 mm b/c bj. and mage are n same sde f refractng surface (mage s vrtual) 2) n =.6 (use cnventn that bj. s n medum wth ndex n ) n 2 = (ar) 3) r =!3 mm (negatve b/c bj. faces cncave surface) n + n 2 = n 2! n r ".6 +!5 =!.6!3 " 0 = 4 mm 0/25/ 2 0/25/ 22
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