Download Physics 272 - University of Hawaii Physics Department

Physics 272
April 30
Spring 2015
www.phys.hawaii.edu/~philipvd/pvd_15_spring_272_uhm
go.hawaii.edu/KO
Prof. Philip von Doetinchem
[email protected]
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Thin lenses
http://phet.colorado.edu/en/simulation/geometric-optics
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Object further away than focal point:
– light rays converge and form a real image on the other side of the lens
Object inside focal point:
– Light rays diverge and the image is virtual and larger than the object
Photography: having the sensor at the right focal point is essential for a
sharp image
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The Lensmaker's equation
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The image of the first refracting surface is used as
the object position for the second refracting surface
The sketch shows a distance of d between the two
spherical mirrors → we will set distance to zero
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The Lensmaker's equation
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Image position after the first surface:
Image of first surface acts as object for second surface. In coming light on second
surface is on the opposite side as the image from surface 1: s2=-s1'
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The Lensmaker's equation
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Combining both equations:
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For a lens in air (s1→s, s'2→s', nb = n)
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The Lensmaker's equation
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Focal length on both sides of the object are the
same (set object distance and image distance to
infinity):
Be careful: rays at larger distance from optic axis
are not going to the same focus point → abberation
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Diverging lenses
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Converging lens: thicker in the center than at the edges
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Diverging lens: thicker at the edges than at the center
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Parallel rays are diverged → virtual image in focal point
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For calculations: use negative focal length value for
diverging lens
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The Eye
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The eye works
very much like
a camera
Crystalline index of
refraction has index
of refraction of ~1.437
Eye is filled with substance having similar optical
properties as water (n=1.336)
Muscles change the focal length of the eye by
squeezing the lens → radius gets smaller
Relaxed eye focuses on infinity
Image is projected in retina → connects over optic
nerve to brain
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Defects of vision
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Correcting for farsightedness
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How to correct the near point of a farsighted eye from 100cm to 25cm (standard value)
using a contact lens?
→ form a virtual image of the object at 100cm:
Prescriptions typically use the inverse of the focal length
→ a converging lens of +3.0 diopters would correct this eye
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Correcting for nearsightedness
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Telescopes
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Telescopes are used to magnify objects at large distances
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Objective lens forms a real, reduced image of the object on the sky
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Objects are very far → image nearly perfectly at focal point
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first image serves as object
for the eyepiece lens
→ if at focal point of eyepiece
→ observer can see the
magnified virtual object at infinity
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Telescopes: Hubble in space
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large magnification requires a large focal length f1
large focal length → lower intensity
→ large collecting area needed
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modern telescopes are reflecting telescopes
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Astronomy in space is great, but:
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expensive
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limited in size/weight → intensity limitation
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very limited excess for upgrades
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Mauna Kea's is one of the best sites in the world for astronomical observation
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high altitude → less atmosphere is shielding light from stars
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atmosphere above the volcano is extremely dry (water vapor absorbs radiation)
→ important for near-ultraviolet to mid-infrared observations
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most cloud cover below the summit, free of atmospheric pollution
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summit atmosphere is exceptionally stable
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very dark skies (very little light pollution from the surrounding area)
TMT provides:
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9 times the collecting area of the current largest optical/IR telescopes
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spatial resolution 12.5 times sharper than the Hubble Space Telescope
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3 times sharper than the largest current-generation O/IR telescopes
Primary goals:
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explore first sources of light in the very young
universe
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explore galaxies and large-scale structure in
the young universe
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investigate massive black holes
→ super massive black holes are at the centers
of most or all large galaxies
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explore planet-formation and the
characterize extra-solar planets
secondary
mirror
Courtesy TMT International Observatory
Courtesy TMT International Observatory
Telescopes: Thirty Meter Telescope
tertiary
mirror
scientific
instrument
primary
mirror
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Observation power of a big telescope
credit: F.Marchis
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Simulation of observation of volcanic eruptions on Jupiter moon Io:
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using the current Keck telescope (spatial resolution: 140km)
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upgraded Keck (spatial resolution: 110km)
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Thirty Meter Telescope (spatial resolution: 35km)
→ two young eruptive centers labeled A & B can be detected only on the TMT observations
The arrival of the TMT will provide an increase in angular resolution but also in
sensitivity allowing astronomers to detect fainter and smaller eruptions.
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Additional Material
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Image formation by a concave mirror
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Mirror radius and focal length:
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Magnification:
Source: http://en.wikipedia.org/wiki/Parabolic_mirror
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Image formation by refraction
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Small image in front of a cylindrical glass rod:
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image is inverted and reduced in size
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Image formation by refraction
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Immerse glass rod in water (n=1.33):
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the refracted rays do not converge
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and appear to diverge from a point 21.3cm to the
left from the vertex
The result is a virtual image
Image is still erect and the virtual image appears
magnified
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Converging lens
in front of light
detector
(film or chip)
Lens forms an
inverted image
on the light
detector
Magnification for object at 5m
Cameras: magnification
Focal length [mm]
Good lenses correct for paraxial approximation and
dispersion
Longer focal length → higher absolute magnification
factor (still inverted) → image size on light detector
increases
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Cameras: intensity
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Light intensity on the
detector depends
on field of view
and the aperture
opening
Field of view
scales roughly as
1/f2
Wide aperture allows
more light to enter
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Adjusting
is a typical function of cameras
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Eventually also the exposure time is adjusted
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Cameras: zoom
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Combination of movable converging and diverging
lens make it possible to change the focal length
Real zoom lenses are more complicated than that
and use more than 10 lenses to correct for various
aberrations
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Cameras: depth of focus
small aperture
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large aperture
Introducing an adjustable lens aperture helps
increasing the depth of focus:
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light rays coming from an object further away from a lens
are less refracted than light rays from a closer object
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Extended objects along the optic axis are in focus for a
narrow (wide) region for large (small) apertures
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Cameras: depth of focus
large aperture
short depth of field
object
circle of
confusion
Out of focus: image becomes blurry
● The circle of confusion on the
image side is the size when the
objects starts to appear blurry
(typical: 1 pixel of the sensor)
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long depth of field
object
small aperture
circle of
confusion
http://graphics.stanford.edu/courses/cs178/applets/dof.html
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Cameras: autofocus
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Different autofocus techniques
are available
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Contrast detection
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Assist lamp
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Phase detection:
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Splits incoming light
Analyzes different parts projected on
different sensors in the same plane
Chip compares intensity patterns
Sensor plane is in focus when patterns
are the same
Source: http://en.wikipedia.org/wiki/Autofocus
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The magnifier
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Size of an image depends on size on retina
Moving object closer than near point does not help
→ eye cannot focus
Converging lens:
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Place object at focal point
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Virtual image at infinity has a much larger angular size
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Lateral magnification for virtual image at infinity is not a useful quantity
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The microscope
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Image of one lens can be
used as an object for the
second lens
→ greater magnification
can be reached without
making the lenses too
big
Objects are placed
closely to the focal point
Short focal length of the objective and eyepiece lens
cause a greater magnification
Overall magnification is composed of lateral and
angular magnification
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