Physics 272
May 1
Spring 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html
Prof. Philip von Doetinchem
philipvd@hawaii.edu
Phys272 - Spring 14 - von Doetinchem - 441
Summary
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Lens in air:
Phys272 - Spring 14 - von Doetinchem - 442
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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
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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)
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 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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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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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
Modern telescopes are reflecting telescopes
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Telescopes: Hubble in space
Hubble Ultra deep field:
At this time the universe was
only 800 Million years old
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Large magnification requires a large focal length f1
Large focal length → lower intensity
→ large collecting area needed
Modern telescopes are reflecting telescopes
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Telescopes: Keck on Mauna Kea
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Review
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Reflection and refraction at a plane surface:
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Important difference between virtual and real image
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Only for a real image the light rays actually cross the
image point
Magnifcation: is defined in lateral and angular
direction
Focal point describes the point where parallel light
rays converge in a concave mirror
(light rays emerging from the focal point of a convex
mirror are parallel after reflection)
Thin lens find wide applications and consist of the
combination of two spherical refracting surfaces
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Physics 272
Review of second part
Spring 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html
Prof. Philip von Doetinchem
philipvd@hawaii.edu
Phys272 - Spring 14 - von Doetinchem - 462
Final May 15
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Thursday 5/15: 9:45am-11:45am, WAT112
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Will focus on chapters 28-34 of the textbook
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Is the exam cumulative?
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No supplemental materials allowed:
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The final will cover all chapters 21-34
Bu the focus is on chapters 28-34 (understanding of chapters 21-27 is essential)
For instance: understanding of electric fields (ch21) is absolutely essential for
understanding electromagnetic waves (ch32)
Just bring paper and calculator
Study suggestions:
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Make sure to understand old homework:
mastering physics and hand-in
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The final exam will again have conceptual questions that do not require long
calculations, but qualitative understanding:
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Work with “test your understanding” questions and discussion questions from the book
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Maxwell's equations of electromagnetism
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Gauss's law for electric fields (surface integral)
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Electric field is related to total charge in an enclosed
surface
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Electric charges are sources of magnetic fields
Gauss's law for magnetism (surface integral)
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No magnetic monopoles exist
→ magnetic flux through closed surface is always zero
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Maxwell's equations of electromagnetism
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Ampere's law (line integral)
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Conducting and displacement current act as sources of
magnetic fields
Faraday's law (line integral)
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A changing magnetic field or magnetic flux induces an
electric field
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Moving charges as sources of magnetic fields
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Magnetic field of a moving charge:
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Magnetic field of a conductor (law of Biot-Savart)
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Magnetic field of a long, straight, current-carrying
conductor
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Forces between two moving protons
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Two protons moving in the same direction.
Magnetic force on
the upper proton
from the magnetic
field of the lower
proton: attractive
Magnetic force on
the lower proton
from the magnetic
field of the upper
proton: attractive
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Magnetic field on the axis of a coil
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Magnetic field on axis
of the loop along the
x axis at a certain
distance x using
Biot-Savart
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Magnetic field on the axis of a coil
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Stack a number of N loops on top of each other
Assume that each loop is planar and that the loops
are very closely spaced
Also assume that the distance from the center of
each loop is the same to the point along the coil
axis under study
Superposition principle at work:
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