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Phys 322
Lecture 16
Chapter 5
Geometrical Optics
Optical systems
Magnifying glass
Purpose:
enlarge a nearby object by increasing its image size on retina
Requirements:
• Image should not be inverted
• Image should be magnified
• Rays entering eye should not be converging
Use positive lens
and so < f
Magnifying glass
Magnifying power MP, or angular magnification
- the ratio of the size of the retinal image as seen through the
instrument to that as seen by bare eye at a normal viewing distance:
MP 
a
u
a
- aided,
u
- unaided
Standard observer: do=0.25 m
Largest image without aid:
Near point, do :
closest point at
which image can be
brought into focus
Magnifying glass
a
MP 
u
unaided view
aided view
 a  yi / L
 u  yo / d o
Using paraxial approximation
and lens equation (page 211):
do
MP  1  D L  l 
L
1
D
f
Most common case: so=f, L=
MP L  d oD
Standard observer:
do=0.25 m
If D=10, MP=2.5, notation 2.5X
Typically limited to 2.5X - 3X
Eyepiece (ocular)
Eyepiece is essentially a magnifying glass that is designed to
magnify image created by the previous optical system.
Virtual object!
Virtual image at 
Center of exit pupil at eye plane
The Huygens eyepiece
More complex:
Microscopes
Image
plane #1
Objective
M1
Eyepiece
Image
plane #2
M2
Microscopes goal: to magnify objects that are really close.
When two lenses are used, it’s called a compound microscope.
Compound microscope
~1595, Zacharias Janssen:
compound microscope
~1660, Robert Hooke’s
microscope,
~30X magnification
~1700, Anton Van
Leeuwenhoek microscope
(single lens)
270X magnification
“Father of microscope”
Compound microscope
Total magnification:
MP = MTo MAe
angular magnification of eyepiece
Transverse magnification of objective
Standard design: L = 160 mm
Tube length
Assuming standard tube length and
standard viewing distance 25 cm:
 160mm  250mm 


MP   
f o  f e 

Respective powers are marked as 10X, 20X etc.
Compound microscope
Amount of light (brightness of image)
depends on numerical aperture of the
objective:
NA = nisinmax
Power = 40X
NA=0.65
Maximum NA in air is 1
Can be as large as 1.4 - in oil
Microscope
summary
If all light rays are directed through
a pinhole, it forms an image with
an infinite depth of field.
The pinhole
camera
The concept of the
focal length is
inappropriate for a
pinhole lens. The
magnification is still –
di/do.
Pinhole
Image
Object
The first person to
mention this idea
was Aristotle.
With their low cost, small size
and huge depth of field,
they’re useful in security
applications.
Camera obscura
Latin: dark room
pinhole camera
1769
1665:Vermeer
The Girl with the Red Hat
Inside camera obscura
Central Park, 1877
http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html
Probably used
camera obscura
Portable tent version
1620
Camera
1826: First photograph by Joseph Nicephore Niepce
Exposure time: 8 hours!
Photography
lenses
Photography lenses are complex! Especially zoom lenses.
Double Gauss
These are older designs.
Petzval
Photography
lenses
Modern lenses can
have up to 20
elements!
Canon 17-85mm
f/3.5-4.5 zoom
Canon EF 600mm f/4L IS USM
Super Telephoto Lens
17 elements in 13 groups
$12,000
Modern SLR Camera
single lens reflex
For sharp image lens is moved
back and forth - changing si
changes so
Film size is fixed (field stop) changing f can change angular
field of view.
f=6-40 mm - wide-angle
f~50 mm - normal angle
f=80-1000 - telephoto lens
Diaphragm=variable aperture stop
controls f-number, or amount of light
Telescopes
Keplerian telescope
A telescope should image an object, but, because the object will
have a very small solid angle, it should also increase its solid angle
significantly, so it looks bigger.
Image
plane #1
M1
Image
plane #2
M2
The telescope
tele-skopos (Greek) - seeing at a distance
1608, Hans Lippershey tried to patent “kijker”
“looker” (Dutch)
1609: Galileo,
two lenses and an organ pipe
Telescope Terminology
Refracting telescope
Notes:
image is inverted
object is typically at infinity
a
fo

Angular magnification: MP 
u
fe
Terrestrial (non-inverting) telescope
Binoculars
Telescope aperture
Telescope aperture:
* determines amount of light collected
more light - more low-brightness distant stars could be seen
* determines the angular resolution
diffraction limited angle is 1.22/D radians (chapter 10)
 - wavelength of light
D - diameter of lens (or mirror)
Exercise
A friend tells you that the government is using Hubble telescope
to read car license plates. Is it possible?
Orbit height 600 km, aperture 2.4 m
Hubble
Assume best case scenario: the car’s license plate faces up
Solution: To resolve license plate number need ~2 cm resolution
2 cm
1.22  500 nm

must have D  20 m
600,000 m
D
2.4 m telescope could resolve ~15 cm
Note: atmospheric turbulence will most probably lower the resolving power
below theoretical limit
Refracting telescope aperture
Largest refracting telescope (~1900): 40” doublet, 500 pounds. Net weight: 20 tons
Yerkes, Williams Bay, WI
http://www.wavian.com/aip/cosmology/tools/tools-refractors.htm
Lens versus mirror:
- harder to make (need large diameter to collect more light)
- focal length depends on wavelength: n=n()
Reflecting telescopes
Keck 10 m telescope
Hawaii, 1993
Arecibo Observatory
305 m radio telescope
Reflecting telescope
1661: Invented by Scottsman James Gregory
prime focus
1668: Constructed successfully by Newton
Newtonian telescope
The Cassegrain Telescope
Telescopes must collect as much light as possible from the generally
very dim objects many light-years away.
It’s easier to create large mirrors than large lenses (only the surface
needs to be very precise).
Object
It may seem like the
image will have a
hole in it, but only if
it’s out of focus.
Liquid mercury telescope
z

r
Spinning liquid in equilibrium:
parabolic surface
z
Liquid mercury mirror
3m NASA’s Debris Observatory
•
•
•
•
•
•
 2r 2
2g
One turn in ~10 seconds
 must be maintained at 10-6 level
~30 L of Hg for 6 m mirror
Surface smoothness ~10-7 (.3mm bump on Earth)
Points only up
Costs $1M instead of $100M
6 m liquid mercury telescope f/1.5
Zenith telescope
70 km East of Vancouver
f/1.5, f=10 m
mirror support
http://www.astro.ubc.ca/LMT/lzt/gallery.html
Correcting aberrations
Spherical mirrors do not work:
spherical aberrations and coma
Catadioptric systems:
Aplanatic reflectors:
Both primary and secondary
mirrors are hyperbolic
Example: Hubble telescope
Correct spherical aberrations
using specially profiled lens
Wavefront shaping
Phys 322
Lecture 16
Lenses, mirrors - reshape wavefronts, designed to work with
spherical or plane waves
More complex elements - more complex wavefronts
Wavefront distortions
Light from star passes turbulent air wavefront is not plane anymore, it has few
m distortions (> ~0.5 m)
In a good night, the planar area of the wave
from distant star is ~20 cm - no matter how
large the telescope is resolution is the same
as that of 20 cm telescope!
Need techniques that could
constantly adapt optical elements to
restore plane wave:
Adaptive optics
Adaptive optics
Phase conjugation
If we could at the same instant turn
the wave direction backwards we
can restore the initial (plane) wave
shape
The light propagation is reversible.
1972: Zeldovich et al.
Use Stimulated Brillouin
Scattering
Intense electric field increases n at minima and
maxima (sound wave) - constructive backward
scattering (simplified view)
/2