Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii...
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Transcript of Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii...
![Page 1: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/1.jpg)
Chapter 2: Geometrical optics
![Page 2: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/2.jpg)
![Page 3: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/3.jpg)
All of geometrical optics boils down to…
Law of reflection: ri
i
normal
n1
n2
r
t Law of refraction“Snell’s Law”:
1
2
sin
sin
n
n
t
i
Easy to prove by two concepts:Huygens’ principleFermat’s principle
Incident, reflected, refracted, and normal in same plane
![Page 4: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/4.jpg)
Huygens’ principleevery point on a wavefront may be regarded as a secondary source of wavelets
planar wavefront:
ct
curved wavefront:
In geometrical optics, this region should be dark (rectilinear propagation).
Ignore the peripheral and back propagating parts!
obstructed wavefront:
![Page 5: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/5.jpg)
Huygens’ proof of law of reflection
L
L
tci
90cos
r90 i90
L
tcr
90cos
ri
riθ
![Page 6: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/6.jpg)
vt t
vi t
i
L
t
L
tvii
sin
L
tvtt
sin
itti vv sinsin
Huygens’ proof of law of refraction
ttii nn sinsin vi = c/ni
vt = c/nt
![Page 7: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/7.jpg)
“Economy of nature”shortest path between 2 points
Hero—least distance: Fermat—least time:
Fermat’s principlethe path a beam of light takes between two points is the one which is traversed in the least time
![Page 8: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/8.jpg)
n1n2
O
a
b
c
x
Fermat’s proof of law of refraction
ti v
OB
v
AOt
ti v
xcb
v
xat
2222
0
2222
xcbv
xc
xav
x
dx
dt
ti
0sinsin
t
t
i
i
vvdx
dt
A
B
i
normal
t
22sin
xa
xi
22sin
xcb
xct
ttii nn sinsin
![Page 9: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/9.jpg)
provide qualitative (and quantitative) proof of the law of reflection and refraction within the limit of geometrical optics.
Huygens’- and Fermat’s principles:
![Page 10: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/10.jpg)
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
![Page 11: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/11.jpg)
Reflections from plane surfaces
retroreflector
![Page 12: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/12.jpg)
Image formation in plane mirrors
Note: virtual images (cannot be projected on screen)
point object extended object
object displaced from mirror multiple images in perperdicular mirrors
image point; SN = SN′
![Page 13: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/13.jpg)
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
Imaging by an optical system
![Page 14: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/14.jpg)
Reflections from spherical surfaces
virtual image
mirror convex 0,
mirror concave 0,
2
Rffocal length:
mirror equation:fss
1
1
1
s
s
o
i
h
hmmagnification:
Chicago
![Page 15: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/15.jpg)
Ray tracingthree 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
![Page 16: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/16.jpg)
Ray tracing for (thin) lenses
converging lens
diverging lens
magnification: s
s
h
hm
o
i
![Page 17: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/17.jpg)
Simple lens systems
![Page 18: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/18.jpg)
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 ~. Same for the best spatial resolution of an image. This is fundamentally due to the wave nature of light.
To be continued…
> ~
~0
![Page 19: Chapter 2: Geometrical optics. All of geometrical optics boils down to… Law of reflection: ii normal n1n1 n2n2 rr tt Law of refraction “Snell’s.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649eac5503460f94bb2695/html5/thumbnails/19.jpg)
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
Exercises
M.C. Escher