Vern J. Ostdiek
Donald J. Bord
Chapter 9
Optics
(Section 2)
9.2 Mirrors: Plane and Not So Simple
• Most mirrors that we use are plane mirrors: they
are flat, smooth, almost perfect reflectors of light.
•
When we use a mirror to “see ourselves,” light that
is diffusely reflected off our clothes and face strikes
the mirror and undergoes specular reflection.
9.2 Mirrors: Plane and Not So Simple
• Some of the rays leaving the mirror are going in
the proper direction to enter our eyes and give us
an image of ourselves.
•
The image appears to be on the other side of the
mirror.
9.2 Mirrors: Plane and Not So Simple
• Instead of showing every light ray traveling
outward from every point on the person, we show
selected rays that happen to enter the person’s
eyes.
•
The dashed lines from the image show the
apparent paths taken by the rays when traced back
to the image.
9.2 Mirrors: Plane and Not So Simple
• Applying the law of reflection and a little
mathematics, it can be demonstrated that the
image of an object in a plane mirror is as far
behind the mirror’s surface as the object is in front
of the mirror.
9.2 Mirrors: Plane and Not So Simple
• If you want to test this conclusion, point your index
finger in the direction of a mirrored surface, and
slowly move your hand toward the mirror.
•
The image of your finger will approach the mirror’s
surface at the same rate that your real finger does
and will arrive at the surface just as your finger
touches it.
9.2 Mirrors: Plane and Not So Simple
• A number of important, practical devices employ
plane mirrors.
• They are used as optical levers to amplify small
rotations in specialized laboratory instruments.
•
For example, as the mirror rotates through an angle
q, the reflected beam will be turned through an
angle 2q.
9.2 Mirrors: Plane and Not So Simple
• A plane mirror is used in many reflex cameras to
redirect light from the lens to the viewfinder.
•
When the shutter is pressed, the mirror tilts up,
allowing the light to reach the film.
9.2 Mirrors: Plane and Not So Simple
• More recently, micromirrors, small enough to fit
through the eye of needle (0.5 mm or less), have
become indispensable parts of modern
telecommunications networks, where they are
used in high-speed optical switches to control the
flow of information through optical fibers.
9.2 Mirrors: Plane and Not So Simple
“One-Way Mirror”
•
A “one-way mirror” is made by partially coating
glass so that it reflects some of the light and
allows the rest to pass through.
•
This is called a half-silvered mirror.
9.2 Mirrors: Plane and Not So Simple
“One-Way Mirror”
• When used as a window or wall between two
rooms, it will function as a one-way mirror if one of
the rooms is brightly lit and the other is dim.
• It will appear to be an ordinary mirror to anyone in
the bright room, but it will appear to be a window
to anyone in the dim room.
•
This is because, in the bright room, the light
reflected off the half-silvered mirror is much more
intense than the light that passes through from the
other room.
9.2 Mirrors: Plane and Not So Simple
“One-Way Mirror”
• In the dim room, the transmitted light from the
bright room dominates.
•
A person in the dim room can see what is
happening in the bright room without being seen by
anyone in the bright room.
9.2 Mirrors: Plane and Not So Simple
“One-Way Mirror”
• This device is often used in interview and
interrogation rooms and as a means of observing
customers in stores and gambling casinos.
windowpane.
•
Note that if a bright light is turned on in the dimmer
room, the one-way effect is destroyed.
9.2 Mirrors: Plane and Not So Simple
“One-Way Mirror”
• Ordinary window glass is a crude one-way mirror
because it does reflect some of the light that
strikes it.
•
At night, one can see into a brightly lit room through
a window, but anyone in the room has difficulty
seeing out because room light is reflected by the
windowpane.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• Reflectors—mirrors in this case—that are curved
have useful properties.
•
Parallel light rays that reflect off a properly shaped
concave mirror—a mirror that is curved inward—are
focused at a point called the focal point.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• The energy in the light is concentrated at that
point.
•
Sunlight focused by a concave mirror can heat
things to very high temperatures.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• Even when a mirror’s surface is curved, the law of
reflection still holds at each point that a ray strikes
the mirror.
•
If a normal line is drawn at each point (as was done
in the figure below), the angle of incidence equals
the angle of reflection.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• One such normal line is shown in the figure.
• A concave mirror can be used to form images that
are enlarged—magnified.
•
Magnifying makeup and shaving mirrors are
concave mirrors, as are the large mirrors used in
astronomical telescopes.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• The figure shows a magnified image seen in a
concave mirror.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• A convex mirror is one that is curved outward.
•
The image formed by a convex mirror is reduced—it
is smaller than the image formed by a plane mirror.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• The advantage of a convex mirror is that it has a
wide field of view—images of things spread over a
wide area can be viewed in it.
•
The figure shows the fields of view for a convex
mirror and a plane mirror of the same size.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• One glance at a well-
placed convex mirror
on a bike path allows
quick surveillance of a
large area.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• Passenger-side rearview mirrors on cars and
auxiliary “wide-angle” rearview mirrors on trucks
and other vehicles are convex so the driver can
view a large region to the rear.
•
Care must be taken when using such a mirror
because the reduced image makes any object
appear to be farther away than it actually is.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• The largest telescopes used by astronomers to
examine stars, galaxies, and other celestial
objects make use of curved mirrors.
•
The figure shows a common design for such
telescopes.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• Light from the distant source enters the telescope
and reflects off a large concave mirror called the
primary mirror.
•
•
The reflected rays converge onto a much smaller
convex mirror called the secondary mirror.
The rays are reflected back toward the primary
mirror, pass through a hole in its center, and
converge to form an image at the focal point F.
• The primary mirror is the key component of the
telescope.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• Telescope mirrors have as their basic functions
the gathering of light and the concentration of that
light to a point.
•
•
The ability of a mirror to collect light increases with
its surface area.
To acquire enough radiation to study faint objects
adequately, astronomers have sought to build
instruments with larger and larger apertures
(openings) and, hence, larger light-collecting areas.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• The quality of the images produced by telescopes
is greatly affected by the shapes of the mirrors.
• The easiest curved mirror to make is one that has
a surface that has the shape of part of a sphere.
•
But such a spherical mirror is not perfect for the
task of focusing light rays.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• The figure shows that parallel light rays reflecting
off a spherical mirror are not all focused at the
same point.
•
An image formed using such a mirror will be
somewhat blurred.
• This phenomenon is called spherical aberration.
•
As the name implies,
spherical aberration is a
defect associated with
spherical surfaces.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• A concave mirror in the shape of a parabola does
not have this aberration.
•
A parabolic mirror will concentrate all the rays
coming from a distant source at the same point.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• Thus, the ideal surface for a telescope mirror (or
for that matter, reflectors in auto headlamps and
household flashlights) is one shaped like a
parabola.
•
•
Fabricating very large mirrors, some as big as 10
meters (33 feet) in diameter, with the precise
parabolic shape is an enormous technical
challenge.
One technique called spin casting exploits the fact
that the surface of a liquid rotating at a steady rate
has the required parabolic shape.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• Since the 1980s, several telescopes have been
constructed that employ rotating liquid mirrors, the
most ambitious being the 6-meter Large Zenith
Telescope (LZT) in British Columbia.
•
In the simplest designs, a large bowl of mercury is
spun at the proper rate to produce a surface with
the desired parabolic shape.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• Although such liquid mirror telescopes can’t be
tilted and can only examine the sky nearly directly
above them, they are relatively cheap to build:
•
The 6-meter LZT cost only about $1 million, 100
times less than a comparable conventional glass
mirror telescope.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• Shortly after the Hubble Space Telescope (HST)
was placed in orbit on 25 April 1990, scientists
discovered that its primary mirror was afflicted with
a type of spherical aberration.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• At the edge of the 2.4-meter-diameter mirror, its
surface is misshapen by 0.002 millimeters from
what it is supposed to be.
•
This seemingly minuscule error drastically reduced
the telescope’s ability to form sharp images.
• In December 1993, space shuttle astronauts
installed corrective optics on the instrument
platform of the Space Telescope to alleviate this
problem and allow the observatory to perform as
designed.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• The figure shows the dramatic improvement in the
ability of the Space Telescope to resolve fine
detail as a result of the repairs.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• Further improvements in the performance of HST
have occurred with the installation of the
Advanced Camera for Surveys (ACS) in the spring
of 2002.
•
The ACS replaced an earlier camera and, with its
higher resolution, larger field of view, and greater
light collection efficiency, has provided about a
factor-of-ten improvement in the capability of the
Space Telescope.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• From the ground, recent efforts to combat the
blurring effects of Earth’s atmosphere and thereby
to increase the resolution of optical instruments,
have involved the use of “adaptive optics” (AO).
•
Here, elaborate wavefront sensors, fast computers,
and deformable mirrors are used to produce
images so sharp that it’s as though the atmosphere
had disappeared entirely.
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• The figure shows a typical design of an AO
system, similar to those in use with the two 10-m
Keck Telescopes in Hawaii, the 8.2-m Gemini
North (Hawaii) and South (Chile) instruments, and
the Very Large Telescope array (Chile).
9.2 Mirrors: Plane and Not So Simple
Astronomical Telescope Mirrors
• The key optical element is the “rubber mirror”—a
thin glass mirror that has a surface that can be
slightly deformed by up to a hundred tiny actuators
attached to the back.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• If the tiny deformations in the rubber mirror can be
made to counteract the deformations in the
wavefronts from distant sources caused by
turbulence in Earth’s atmosphere, then the
original wavefronts can be restored and the
blurring in the image removed.
•
Fast computers are required to monitor
continuously the rapidly changing conditions in the
atmosphere, compute the necessary corrections,
and signal the accuators to move appropriately.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• This technique normally
uses a bright star in the field
of view of the telescope as
the reference beacon for the
wavefront assessment.
•
In the absence of such a
star, an artificial one can be
created using a high-power,
highly focused laser beam
projected up through the
telescope.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• Called “laser guidestars,”
the light from the beam that
is scattered downward either
from air molecules at
altitudes of 10 to 40 km or
from sodium atoms residing
as high as 90 km produces a
faint but measurable target
for the wavefront sensors.
9.2 Mirrors: Plane and Not So Simple
Curved Mirrors
• As indispensable as AO systems are for
optimizing the light-gathering and resolving power
of large, 10-m class telescopes, still greater
advances will be needed in this field to harness
the full capabilities of the really large telescopes
with 20-m apertures or larger planned for the
future.
•
To meet the challenges, new initiatives described
as “atmospheric tomography”—similar to “medical
tomography” where a 3-D view of a patient is
produced—will be required.
Concept Map 9.1