1. Chapter 2: Geometrical optics

2. Table of Opticks, from the 1728 Cyclopaedia, Volume 2

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
curved wavefront:
planar wavefront:
obstructed wavefront:
In geometrical optics, this region should be dark (rectilinear propagation).
Ignore the peripheral and back propagating parts!
cDt

5. Huygens’ proof of law of reflection

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

7. shortest path between 2 points
“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 n2 x 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)
object displaced 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: Spherical 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. 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… ~0
> ~l

19. Exercises
M.C. Escher
You are encouraged to solve all problems in the textbook (Pedrotti3).
The following may be covered in the werkcollege on 1 September 2010:
Chapter 1
2, 10, 17
Chapter 2
4, 6, 9, 25, 27, 31