1. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-1 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

2. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-2 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

3. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-3 Basic Geometric Optics Reflection and Refraction Imaging –Real and Virtual –Image Location; Conjugate Planes –Magnification Transverse, Angular, Longitudinal Reflecting Optics Refracting Optics

4. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-4 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

5. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-5 Snell’s Law (2) s s’ Index = n Index = n’ ds -ds’ Jan 2005 n’>n means bending toward normal July 2007

6. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-6 Reflection  

7. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-7 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

8. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-8 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

9. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-9 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

10. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-10 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

11. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-11 Real and Virtual Images Dec 2004

12. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-12 The Plane Mirror (1) Point Object Extended Object   AA’ -s’ s  AA’ BB’ h x x’

13. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-13 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

14. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-14 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

15. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-15 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

16. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-16 Refracting Surfaces (1) Snell’s Law ’’’’  n n’ 0102030405060708090 0 5 10 15 20 25 30 35 40 45 50 Angle of Incidence Angle of Refraction Air to Water Air to Glass Air to ZnSe (10  m) Air to Ge (10  m)

17. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-17 Refracting Surfaces (2) Snell’s Law ’’  n n’ 0102030405060708090 0 10 20 30 40 50 60 70 80 90 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

18. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-18 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

19. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-19 The Spherical Surface (1) A A’ ’’     s s’ R C  h Exterior Angles of Triangles Small-Angle Approximation Tangents of Angles V Jan 2005

20. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-20 The Spherical Surface (2) Focal Length Front Back Optical Power Magnification Transverse Longitudinal

21. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-21 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

22. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-22 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

23. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-23 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

24. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-24 The Thin Lens (1) n1n1 n2n2 n’ 1 n’ 2 Dec 2004

25. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-25 The Thin Lens (2) Front Focal LengthBack Focal Length ff’ Jan 2005

26. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-26 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

27. July 2003+ © Chuck DiMarzio, Northeastern University 11270-02-27 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 * * *