ECEG105 & ECEU646 Optics for Engineers Course Notes Part 2: Geometric Optics (Reflection, Refraction, Thin Lenses) Prof. Charles A. DiMarzio Northeastern University Fall 2003 July 2003 Chuck DiMarzio, Northeastern University

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 2003 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 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Snell’s Law (1) Use Fermat’s Principle Assume Correct Path to Start Find Differential Path Length for Change ds Index = n Q Index = n’ Index = n q’’ s’ q P s Index = n’ -ds’ July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Snell’s Law (2) ds Index = n’ Index = n s’ s -ds’ July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Reflection q q July 2003 Chuck DiMarzio, Northeastern University

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 q’’ q July 2003 Chuck DiMarzio, Northeastern University

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 July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Sign Definitions B Object Distance, s Positive to Left Image Distance, s’ For Refraction Positive to Right For Reflection Notation Capital Letter; Point Lower Case; Distance (Almost Always) A’ F A F’ f B’ s s’ s s’ July 2003 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 July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University The Plane Mirror (1) Point Object Extended Object q B B’ q q h x’ x A A’ A A’ s -s’ July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University The Plane Mirror (2) Image is Virtual (Dotted lines converge) Erect (m>0), Perverted (can not rotate to object) but not distorted (|m|=|mz|) Transverse Magnification x’=x m=x’/x=1 Longitudinal Magnification dy’ dx’ ds’ ds’=-ds mz=ds’/ds=-1 Angular Magnification q’’=q ma=q’’/q =1 dx (refer to picture on left side of previous page) dy ds July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University The Retroreflector 2-D Example 3 Mirrors at 90 deg. Low-Cost Configuration Flat Plastic Front Corner-Cube Patterned Back Total Internal Reflection 3-D Retroreflector or Corner Cube July 2003 Chuck DiMarzio, Northeastern University

The Spherical Mirror (1) Exterior Angles of Triangles g=a+q b=g+q a+b=2g Tangents of Angles tan a=h/(s-d), tan b = h/(s’-d), tan g = h/(R-d) d q h q b a g A C A’ Small-Angle Approximation s’ R Conjugate Planes s July 2003 Chuck DiMarzio, Northeastern University

The Spherical Mirror (2) B s’ x’ q A’ x A q B’ Transverse Magnification ma=b/a =s/s’= |1/m| July 2003 Chuck DiMarzio, Northeastern University

The Spherical Mirror (3) Longitudinal Magnification Compare Transverse Image Equation Differentiate Image is Real (Converging Rays), Inverted (m<0), Distorted (mz=-m2), but Not Perverted (sign(m)=sign(mz)) July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Focal Length Defined C F F’ A’ Object at Infinity Definition Application July 2003 Chuck DiMarzio, Northeastern University

Refracting Surfaces (1) Snell’s Law 50 Air to Water n n’ 45 Air to Glass Air to ZnSe (10 m m) 40 Air to Ge (10 m m) 35 q’’ 30 q Angle of Refraction 25 20 15 10 5 10 20 30 40 50 60 70 80 90 Angle of Incidence July 2003 Chuck DiMarzio, Northeastern University

Refracting Surfaces (2) Snell’s Law 90 Water to Air n n’ 80 Glass to Air ZnSe to Air (10 m m) 70 Ge to Air(10 m m) 60 q 50 q’ Angle of Refraction 40 30 20 10 Critical Angle 10 20 30 40 50 60 70 80 90 Angle of Incidence July 2003 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 July 2003 Chuck DiMarzio, Northeastern University

The Single Plane Surface (1) Angles Snell’s Law Point Object (n’>n as shown) q’ Small-Angle Approximation q h A’ A s -s’ July 2003 Chuck DiMarzio, Northeastern University

The Single Plane Surface (2) Snell’s Law Angles Extended Object Small-Angle Approximation B’ B x’ x q Transverse Magnification A’ A q’ s -s’ mz, ma and summary left for the interested student July 2003 Chuck DiMarzio, Northeastern University

The Spherical Surface (1) d Exterior Angles of Triangles q h q’ a g b A C A’ Tangents of Angles s R Small-Angle Approximation s’ July 2003 Chuck DiMarzio, Northeastern University

The Spherical Surface (2) Back Focal Point Object at Infinity Front Focus Image at Infinity Optical Power Units: m-1 = diopeters F’ f’ F f July 2003 Chuck DiMarzio, Northeastern University

The Spherical Surface (3) Angles B x A’ q A q’ -x’ s B’ s’ Snell’s Law & Small Angles Transverse Magnification July 2003 Chuck DiMarzio, Northeastern University

The Spherical Surface Summary Focal Length Front Back Optical Power Magnification Transverse Longitudinal July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University The Simple Lens (1) Two Surfaces: Air-Glass Glass-Air A1 A1’ A2 1 Find Image from First Surface: s1 R1 s1’ July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University The Simple Lens (2) 2 Object Distance for Second Surface: n2’ n1 n1’ = n2 -s2+d = s1’ s2 = d-s1’ A2’ Find Image from Second Surface: A1’ A2 3 Note Virtual Object R2 s’2 -s2 d s1’ July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University The Simple Lens (3) 4 Summarize n2’ n1 n1’ = n2 Note, w for working distance instead of s. This is important later A2’ A1 s1 w s2 = d-s1’ s’2 w’ d July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University The Thin Lens (1) July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University The Thin Lens (2) Back Focal Length Front Focal Length f f’ July 2003 Chuck DiMarzio, Northeastern University

Special Case: Thin Lens in Air f f’ Lens Equation Lens Makers Equation with d = 0 July 2003 Chuck DiMarzio, Northeastern University