Transcript
Magnifying glassPurpose: 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 lensand so < f
Largest image without aid:
Magnifying glassMagnifying 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:
u
aMP
a - aided, u - unaided
Near point, do :closest point at which image can be brought into focusStandard observer: do=0.25 m
Magnifying glass
u
aMP
Lyia /
oou dy /
Using paraxial approximation and lens equation (page 211):
lLLdMP o D1
f1
D
DoL dMP
unaided viewaided view
Standard observer: do=0.25 m
If D=10, MP=2.5, notation 2.5XTypically limited to 2.5X - 3X
Most common case: so=f, L=
Eyepiece (ocular)Eyepiece is essentially a magnifying glass that is designed to magnify image created by the previous optical system.
The Huygens eyepiece
Virtual object!Virtual image at Center of exit pupil -
at eye plane
More complex:
M1 M2
Image plane #1
Eye-piece
Objective Image plane #2
Microscopes goal: to magnify objects that are really close.
When two lenses are used, it’s called a compound microscope.
Microscopes
Compound microscope
~1595, Zacharias Janssen: compound microscope
~1660, Robert Hooke’smicroscope,
~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 lengthAssuming standard tube length and standard viewing distance 25 cm:
eo fmm
fmmMP 250160
Respective powers are marked as 10X, 20X etc.
Compound microscope
Amount of light (brightness of image) depends on numerical aperture of the objective:NA = nisinmax
Power = 40X
NA=0.65
Maximum NA in air is 1Can be as large as 1.4 - in oil
The pinhole camera
Object
Image
Pinhole
If all light rays are directed through a pinhole, it forms an image with an infinite depth of field.
The first person to mention this idea was Aristotle.
The concept of the focal length is inappropriate for a pinhole lens. The magnification is still –di/do.
With their low cost, small size and huge depth of field, they’re useful in security applications.
1769
Camera obscuraLatin: dark room
pinhole cameraPortable tent version
1620
Inside camera obscura Central Park, 1877
1665:VermeerThe Girl with the Red HatProbably used camera obscura
http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html
Photography lenses
Double Gauss Petzval
Photography lenses are complex! Especially zoom lenses.
These are older designs.
Photography lenses
Modern lenses can have up to 20 elements!
Canon EF 600mm f/4L IS USM Super Telephoto Lens17 elements in 13 groups$12,000
Canon 17-85mm f/3.5-4.5 zoom
Modern SLR Camerasingle lens reflex
Diaphragm=variable aperture stopcontrols f-number, or amount of light
For sharp image lens is moved back and forth - changing sichanges so
Film size is fixed (field stop) -changing f can change angular field of view.f=6-40 mm - wide-anglef~50 mm - normal anglef=80-1000 - telephoto lens
Telescopes
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.
M1 M2
Image plane #1
Image plane #2
Keplerian telescope
The telescopetele-skopos (Greek) - seeing at a distance
1608, Hans Lippershey tried to patent “kijker”
1609: Galileo, two lenses and an organ pipe
“looker” (Dutch)
Refracting telescope
Notes:image is invertedobject is typically at infinity
Angular magnification:e
o
u
a
ffMP
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 lightD - diameter of lens (or mirror)
ExerciseA friend tells you that the government is using Hubble telescope to read car license plates. Is it possible?
Assume best case scenario: the car’s license plate faces up
Solution: To resolve license plate number need ~2 cm resolution
Dnm 50022.1
m 000,600cm 2
must have D 20 m
Orbit height 600 km, aperture 2.4 m
Hubble
2.4 m telescope could resolve ~15 cmNote: atmospheric turbulence will most probably lower the resolving power below theoretical limit
Refracting telescope aperture
Lens versus mirror:- harder to make (need large diameter to collect more light)- focal length depends on wavelength: n=n()
Largest refracting telescope (~1900): 40” doublet, 500 pounds. Net weight: 20 tonsYerkes, Williams Bay, WI
http://www.wavian.com/aip/cosmology/tools/tools-refractors.htm
Reflecting telescope
prime focus
1661: Invented by Scottsman James Gregory
1668: Constructed successfully by Newton
Newtonian telescope
The Cassegrain TelescopeTelescopes 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
Liquid mercury mirror3m NASA’s Debris Observatory
Spinning liquid in equilibrium: parabolic surface
grz
2
22
• 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
r
z
6 m liquid mercury telescope f/1.5
http://www.astro.ubc.ca/LMT/lzt/gallery.html
mirror support
Zenith telescope70 km East of Vancouver
f/1.5, f=10 m
Correcting aberrationsSpherical mirrors do not work:spherical aberrations and coma
Aplanatic reflectors:Both primary and secondary mirrors are hyperbolic
Example: Hubble telescope
Catadioptric systems:Correct spherical aberrations using specially profiled lens
Wavefront shapingLenses, mirrors - reshape wavefronts, designed to work with spherical or plane wavesMore complex elements - more complex wavefronts
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
Wavefront distortions
Phys 322Lecture 16
Phase conjugation
If we could at the same instant turn the wave direction backwards we can restore the initial (plane) wave shapeThe light propagation is reversible.
1972: Zeldovich et al.Use Stimulated Brillouin Scattering
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Intense electric field increases n at minima and maxima (sound wave) - constructive backward scattering (simplified view)
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