Chapter 2: Geometrical optics

1. Chapter 2: Geometrical optics

3. All of geometrical optics boils down to… normal Law of reflection: qi qr n1 n2 qt Law of refraction “Snell’s Law”: Incident, reflected, refracted, and normal in same plane Easy to prove by two concepts: Huygens’ principle Fermat’s principle

4. Huygens’ principle every point on a wavefront may be regarded as a secondary source of wavelets planar wavefront: obstructed wavefront: curved wavefront: cDt In geometrical optics, this region should be dark (rectilinear propagation). Ignore the peripheral and back propagating parts!

5. L Huygens’ proof of law of reflection

6. Huygens’ proof of law of refraction viDt vi= c/ni qi vt= c/nt qt vtDt L

7. “Economy of nature” shortest path between 2 points Hero—least distance: Fermat—least time: Fermat’s principle the path a beam of light takes between two points is the one which is traversed in the least time

8. Fermat’s proof of law of refraction normal A qi a n1 O x n2 b qt B c

9. Huygens’- and Fermat’s principles: provide qualitative (and quantitative) proof of the law of reflection and refraction within the limit of geometrical optics.

10. Principle of reversibility • In life • If you don’t use it, you lose it (i.e. fitness; calculus) • If you can take it apart you should be able to put it back together • Do unto others as you would have them do to you • … • In optics • Rays in optics take the same path backward or forwards

11. Reflections from plane surfaces retroreflector

12. Image formation in plane mirrors point object extended object image point; SN = SN′ Note: virtual images (cannot be projected on screen) objectdisplaced from mirror multiple images in perperdicular mirrors

13. Imaging by an optical system conjugate points Fermat’s principle: every ray from O to I has same transit time (isochronous) Principle of reversibility: I and O are interchangeable (conjugate) Perfect imaging: Cartesian surfaces (i.e. ellipsoid; hyperbolic lens) Practical imaging: Spehrical surfaces

14. Reflections from spherical surfaces virtual image Chicago focal length: mirror equation: magnification:

15. Ray tracing three principle rays determine image location Starting from object point P: (1) parallel—focal point (2) focal point—parallel (3) center of curavature—same Image at point of intersection P′ Concave: real (for objects outside focal point) Convex: virtual

16. Ray tracing for (thin) lenses converging lens diverging lens magnification:

17. Simple lens systems

18. ~0 Is geometrical optics the whole story? No. -neglects the phase -implies that we could focus a beam to a point with zero diameter and so obtain infinite intensity and infinitely good spatial resolution. The smallest possible focal spot is ~l. Same for the best spatial resolution of an image. This is fundamentally due to the wave nature of light. To be continued… > ~l

19. Exercises You are encouraged to solve all problems in the textbook (Pedrotti3). The following may be covered in the werkcollege on 7 September 2011: Chapter 1 2, 10, 17 Chapter 2 4, 6, 9, 25, 27, 31 M.C. Escher