July © Chuck DiMarzio, Northeastern University ECEG105/ECEU646 Optics for Engineers Course Notes Part 2: Geometric Optics (Reflection, Refraction, Thin Lenses) Prof. Charles A. DiMarzio Northeastern University Fall 2008 Dec 2004 Jan 2005Jul 2007 Sep 2008

July © Chuck DiMarzio, Northeastern University Where Are We Going? Geometric Optics –Reflection –Refraction The Thin Lens –Multiple Surfaces –Matrix Optics Principle Planes Effective Thin Lens –Stops Field Aperture –Aberrations Ending with a word about ray tracing and optical design. July 2007

July © Chuck DiMarzio, Northeastern University Basic Geometric Optics Reflection and Refraction Imaging –Real and Virtual –Image Location; Conjugate Planes –Magnification Transverse, Angular, Longitudinal Reflecting Optics Refracting Optics

July © Chuck DiMarzio, Northeastern University Snell’s Law (1) Use Fermat’s Principle Assume Correct Path to Start Find Differential Path Length for Change s s’ Index = n Index = n’ Index = n Index = n’ ds -ds’ ’’’’  P Q

July © Chuck DiMarzio, Northeastern University Snell’s Law (2) s s’ Index = n Index = n’ ds -ds’ Jan 2005 n’>n means bending toward normal July 2007

July © Chuck DiMarzio, Northeastern University Reflection  

July © Chuck DiMarzio, Northeastern University Plane of Incidence ’’’’  Contains Normal Contains Incident Ray And Thus Contains Refracted Ray Is the Plane Shown in the Drawing Angles –Defined from Normal Sep 2008

July © Chuck DiMarzio, Northeastern University Imaging First, Assume a Point Object –Spherical Wavefronts and Radial Rays Define Object Location –Find Image Location –Real or Virtual? Next Assume an Extended Object –Compute Magnification Transverse, Longitudinal, Angular Jan 2005

July © Chuck DiMarzio, Northeastern University Sign Definitions Object Distance, s –Positive to Left Image Distance, s’ –For Refraction Positive to Right –For Reflection Positive to Left Notation –Capital Letter; Point –Lower Case; Distance –(Almost Always) s s’ s A A’ B B’ F F’ f

July © Chuck DiMarzio, Northeastern University Real and Virtual Images Real Image –Rays Converge –Can Image on Paper –Solid Lines in Notes Virtual Image –Extended Rays Converge –Dotted-Lines in notes Examples? Dec 2004 Sep 2008

July © Chuck DiMarzio, Northeastern University Real and Virtual Images Dec 2004

July © Chuck DiMarzio, Northeastern University The Plane Mirror (1) Point Object Extended Object   AA’ -s’ s  AA’ BB’ h x x’

July © Chuck DiMarzio, Northeastern University The Plane Mirror (2) dx’ dy’ds’ ds dy dx x’=x m=x’/x=1 Transverse Magnification ds’=-ds m z =ds’/ds=-1 Longitudinal Magnification  ’’=  m  =  ’’/  =1 Angular Magnification Image is Virtual (Dotted lines converge) Erect (m>0), Perverted (can not rotate to object) but not distorted (|m|=|m z |) (refer to picture on left side of previous page) Sep 2008

July © Chuck DiMarzio, Northeastern University The Retroreflector 3 Mirrors at 90 deg. Low-Cost Configuration –Flat Plastic Front –Corner-Cube Patterned Back Total Internal Reflection 2-D Example 3-D Retroreflector or Corner Cube Sep 2008

July © Chuck DiMarzio, Northeastern University The Spherical Mirror A A’ s s’ B B’ Transverse Magnification m a =s/s’= |1/m| x x’   Image Location Longitudinal Magnification Angular Magnification Jan 2005 Note: The derivation is specific, but these equations are very general. July 2007 Sep 2008

July © Chuck DiMarzio, Northeastern University Refracting Surfaces (1) Snell’s Law ’’’’  n n’ Angle of Incidence Angle of Refraction Air to Water Air to Glass Air to ZnSe (10  m) Air to Ge (10  m)

July © Chuck DiMarzio, Northeastern University Refracting Surfaces (2) Snell’s Law ’’  n n’ Angle of Incidence Angle of Refraction Water to Air Glass to Air ZnSe to Air (10  m) Ge to Air(10  m) Critical Angle Stopped Here Tue, 11 Jan 05

July © Chuck DiMarzio, Northeastern University Roadmap of Refractive Optics Snell’s Law: Refraction at a Plane Surface Refraction at a Spherical Surface –Gaussian Optics: Small-Angle Approximation The Simple Lens –One Glass Element = Two Surfaces –The Thin Lens (Good Approximation & More) Matrix Optics for Complicated Systems –Equivalent Thin Lens Sep 2008

July © Chuck DiMarzio, Northeastern University The Spherical Surface (1) A A’ ’’     s s’ R C  h Exterior Angles of Triangles Small-Angle Approximation Tangents of Angles V Jan 2005

July © Chuck DiMarzio, Northeastern University The Spherical Surface (2) Focal Length Front Back Optical Power Magnification Transverse Longitudinal

July © Chuck DiMarzio, Northeastern University The Simple Lens (1) A1A1 A1’A2A1’A2 s1’s1’ R1R1 s1s1 Two Surfaces: Air-Glass Glass-Air Find Image from First Surface: 1 Glass V1V1 Jan 2005

July © Chuck DiMarzio, Northeastern University d The Simple Lens (2) A1’A2A1’A2 s1’s1’ -s 2 -s 2 +d = s 1 ’ s 2 = d-s 1 ’ Object Distance for Second Surface: n 1 ’ = n 2 n1n1 n2’n2’ 2 3 -R 2 s2’s2’ Find Image from Second Surface: A2’A2’ Note Virtual Object Jan 2005 V2V2

July © Chuck DiMarzio, Northeastern University d The Simple Lens (3) Summarize n 1 ’ = n 2 n1n1 n2’n2’ 4 A2’A2’ A1A1 s1s1 w’ w s’ 2 s 2 = d-s 1 ’ Note, w for working distance instead of s. This is important later V1V1 V2V2 Jan 2005

July © Chuck DiMarzio, Northeastern University The Thin Lens (1) n1n1 n2n2 n’ 1 n’ 2 Dec 2004

July © Chuck DiMarzio, Northeastern University The Thin Lens (2) Front Focal LengthBack Focal Length ff’ Jan 2005

July © Chuck DiMarzio, Northeastern University Special Case: Thin Lens in Air Lens Makers Equation with d = 0Lens Equation ff’ R=Radius of Curvature (>0 if Convex to Source) Jan 2005 Stopped Here Thu, 13 Jan 05

July © Chuck DiMarzio, Northeastern University Things to Remember m a =s/s’= |1/m| July 2007 Equations Concepts –Plane of Incidence –Critical Angle –Retroreflector –Lensmaker's Eqn. –*Eqns. to Left Assume n = n' Corrections Exist * * *