Thursday, July 13, 2006
Announcements:
- For class participation
credit today, please complete a mid-course evaluation, but do not write your name on it!
Later in the class, you will exchange papers with another student and
write your name on their paper, along with your clicker ID
number. This allows attendance to be taken and double-checked
against clicker responses, while ensuring anonymity for the course
evaluation (pretty clever, eh!).
- Correction on Exam 1:
After
further discussion and analysis, Michael and I agree that the correct
answer to the exam question about the charged spheres that touch and
share their total charge is answer 1 (+100 uC for the larger sphere,
+50
uC for the smaller sphere). The reasoning for this answer is that
when the spheres touch, they must both have the same electrical
potential, and since V = kq/r, the charge on each sphere is inversely
proportional to its radius. If you marked this answer, be sure to
note
this when you submit your test corrections so that an additional 2
points can be added to your exam score. If you answered option 3
(same
charge of +75 uC for each sphere), you will still receive credit since
this is the answer that Michael implied to be correct based on the
example presented in class using
three identical spheres.
- The list of Web
Project groups and topic selections has been revised. If
yours is missing, let me know.
Assignments:
- Read Chapter 28 and submit HW28a before class tomorrow
- HW27b is now due Sunday at midnight
- Exam 1 corrections are due next Monday
- RWP3 (Contact Lenses) is due Monday
- Web Projects are due next Friday
Chapter 27: Optical Instruments
27-1: The Human Eye and the
Camera
The human eye and a camera both form a real,
inverted image that is focused either on the retina or photographic
film.
The eye is focused by the ciliary muscles, which
change the shape of the lens (accommodation).
A camera is focused by moving the lens (with fixed
focal length) closer or farther from the film.
The near point
is the closest distance from the eye that a person can focus.
Typical value: N ~ 25 cm ~ 10 in.
The far point
is the greatest distance from the eye that a person can focus.
For a normal eye, the far point is infinity.
The f-number
of a lens relates the diameter of the aperture, D, to the focal length,
f. f-number = f/D
27-2: Lenses in Combination and
Corrective Optics
When lenses are used in combination, the image
produced by one lens acts as the object for the next lens.
The total
magnification of a system of lenses is the product of the
magnifications produced by each individual lens.
Nearsightedness
is a condition where a person can only focus on objects that are near
(not at infinity), often caused by an elongation of the eyeball
(prolate spheroid) so that the image forms in front of the
retina. Nearsightedness can be corrected by placing a diverging
lens in front of the eye to extend the focal range of the eye.
Farsightedness
is a condition where a person can only focus on objects
that are far away, so that the near point is significantly greater than
the usual 25 cm. This condition tends to occur in most humans as
they get older, sometimes cause by a shortening of the
eyeball (oblate spheroid) or weakened ciliary muscles so that the image
forms behind the
retina. Farsightedness can be corrected by placing a converging
lens
in front of the eye to shorten the focal range of the eye.
Ponderable:
What is the near point for a typical person with myopia?
Ponderable:
What is wrong with the following statement? "My aunt is far
sighted with a far point of about 5.0 m."
The refractive
power of a lens is a measure of the ability of a lens to bend
light and is measured in diopters (1/m): refractive power = 1/f,
where f is in meters.
As is the case for focal lengths, a
positive refractive power indicates a converging lens, while negative
indicates a diverging lens.
27-3: The Magnifying Glass
A magnifying glass is simply a converging lens held
in front of the eye to produce an enlarged virtual image of an object
that is closer than the near-point distance, thereby resulting in an
increased angular size.
Magnification: M = N/f (image at infinity)
or M = 1 + N/f (image at near point)
T/F:
A magnifying glass produces an image that is closer than the near point.
27-4: The Compound Microscope
A compound microscope uses two lenses in combination
(an objective and an eyepiece) to produce a magnified image.
The object to be viewed is placed just beyond the
focal length of the objective. The image formed by the objective
is then viewed by the eyepiece to yield an increased
magnification: M = -di*N/(fobjective*feyepiece)
27-5: Telescopes
A telescope produces magnified views of distant
objects using two lenses or mirrors. The objective lens or mirror
focuses incoming light to its focal point (since the objects are very
far away), and the eyepiece magnifies the image formed by the objective.
The total magnification is: M =
fobjective/feyepiece
The length of a Galilean telesope is L = fobjective
+ feyepiece, but this length can be reduced by "folding" the light
path, as is the case for most large telescopes and many telescopes used
by amateur astronomers.
27-6: Lens Aberrations
Any deviation of a lens from ideal behavior is
referred to as an aberration.
Spherical
aberration results from light passing through different parts of
a lens not passing through a single focal point. This aberration
can be reduced by limiting the aperture size or using an aspherical
lens that is specially shaped to avoid this problem.
Chromatic
aberration results from dispersion within a refracting material,
so that different colors of light focus at different points.
Achromatic lenses are made to correct this problem by combining two or
more lenses with different refractive properties.
Concept
Tests