Download Inleiding Optica 2010

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Schneider Kreuznach wikipedia, lookup

Nonlinear optics wikipedia, lookup

Confocal microscopy wikipedia, lookup

Chemical imaging wikipedia, lookup

Preclinical imaging wikipedia, lookup

Anti-reflective coating wikipedia, lookup

F-number wikipedia, lookup

Fourier optics wikipedia, lookup

Ray tracing (graphics) wikipedia, lookup

Christiaan Huygens wikipedia, lookup

Lens (optics) wikipedia, lookup

Image stabilization wikipedia, lookup

Superlens wikipedia, lookup

Retroreflector wikipedia, lookup

Reflecting telescope wikipedia, lookup

Optical aberration wikipedia, lookup

Nonimaging optics wikipedia, lookup

Harold Hopkins (physicist) wikipedia, lookup

Transcript
Chapter 2: Geometrical optics
All of geometrical optics boils down to…
normal
i
Law of reflection:
i   r
Law of refraction
“Snell’s Law”:
sin  i  n2

sin  t  n1
r
n1
n2
t
Incident, reflected, refracted, and normal in same plane
Easy to prove by two concepts:
Huygens’ principle
Fermat’s principle
Huygens’ principle
every point on a wavefront may be regarded as a secondary source of wavelets
curved
wavefront:
planar
wavefront:
c Dt
obstructed
wavefront:
In geometrical optics, this
region should be dark
(rectilinear propagation).
Ignore the peripheral and
back propagating parts!
Huygens’ proof of law of reflection
r
i
90   r
cos90   i  
cDt
L
cos90   r  
cDt
L
90  i
 θi   r
L
Huygens’ proof of law of refraction
vi Dt
sin  i 
L
v Dt
sin  t  t
L
vi sin t  vt sin i
i
ni sin i  nt sin t
vi = c/ni
vt = c/nt
t
L
“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
Fermat’s proof of law of refraction
t
normal
AO OB

vi
vt
b 2  c  x 
a2  x2
t

vi
vt
2
A
i
a
n1
n2
dt
x
cx


0
2
2
2
2
dx vi a  x
vt b  c  x 
sin  i 
O
x
a2  x2
sin t 
cx
b 2  c  x 
dt sin  i sin  t


0
dx
vi
vt
b
t
c
x
B
ni sin i  nt sin t
2
Huygens’- and Fermat’s principles:
provide qualitative (and quantitative) proof of
the law of reflection and refraction within the
limit of geometrical optics.
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
Reflections from plane surfaces
retroreflector
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
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:
Practical imaging:
Cartesian surfaces (i.e. ellipsoid; hyperbolic lens)
Spherical surfaces
Reflections from spherical surfaces
virtual image
Chicago
focal length:
f 
R   0, concave mirror

2   0, convex mirror
1 1
1


mirror equation:
s s
f
magnification:
m
hi s

ho s
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
Ray tracing for (thin) lenses
converging lens
diverging lens
magnification:
hi
s
m

ho
s
Simple lens systems
Is geometrical optics the whole story?
No.
-neglects the phase
~0
-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
Exercises
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
M.C. Escher
Chapter 2
4, 6, 9, 25, 27, 31