Seeing Things
in Curved Mirrors
Archimedes's Death Ray
For centuries, it was rumoured that the Greek scientist,
Archimedes, used a "burning glass" to focus the sun’s rays on an
invading Roman fleet which was attacking his home town of
Syracuse around 214 B.C.
From pg 65 The Flying Circus of Physics by Jearl Walkers
Archimedes's Death Ray
For centuries, it was rumoured that the Greek scientist,
Archimedes, used a "burning glass" to focus the sun’s rays on an
invading Roman fleet which was attacking his home town of
Syracuse around 214 B.C.
From pg 65 The Flying Circus of Physics by Jearl Walkers
Archimedse's Death Ray
For centuries, it was rumoured that the Greek scientist,
Archimedes, used a "burning glass" to focus the sun’s rays on an
invading Roman fleet which was attacking his home town of
Syracuse around 214 B.C.
From pg 65 The Flying Circus of Physics by Jearl Walkers
Archimedes's Death Ray
The way that this feat may have been possible was to use many
plane mirrors. (Greek soldiers had copper shields which could be
highly polished.)
From pg 65 The Flying Circus of Physics by Jearl Walkers
Archimedes's Death Ray
Each mirror could be used to reflect a spot of sunlight at the
same object (invading Roman ship).
From pg 65 The Flying Circus of Physics by Jearl Walkers
Archimedes's Death Ray
This might act like a giant magnifying glass.
From pg 65 The Flying Circus of Physics by Jearl Walkers
Archimedes's Death Ray
This might act like a giant magnifying glass and ignite the
target.
From pg 65 The Flying Circus of Physics by Jearl Walkers
Archimedes's Death Ray
The historical record of this possible event is very weak.
It is argued that the feat was impossible given the technology
available to Archimedes.
From pg 65 The Flying Circus of Physics by Jearl Walkers
Archimedes's Death Ray
There is also a problem in aiming all the mirrors at the target
with this.
From pg 65 The Flying Circus of Physics by Jearl Walkers
What technique would have to be used for aiming the
mirrors at distant objects?
Could it be done today?
http://www.youtube.com/watch?v=MDkOaPp_6ug
Click on
Image
to play
Archimedes’s Death Ray
Myth Busters Eat Your Heart Out
Look at the mirrors
only.
The mirrors can be aligned
along a smooth curve so
that they still all reflect
light from the sun to the
same spot.
When light rays come
from a distant source like
the sun, they can be
considered parallel.
All incident light rays
which are parallel to each
other will reflect off any
part of the smooth curve
and pass through the same
spot.
This spot is called the
Focus.
The Curve is called a
Parabola.
The symbol for the Focus
is (F).
Unfortunately, Parabolic
mirrors are expensive to
make.
A circle can be drawn so
that it closely matches
the parabola near the
central region.
Fortunately, Circular (or
in 3D, Spherical)
mirrors are less
expensive to make.
The symbol “C” stands for
Centre of Curvature of
the Spherical mirror.
Most curved mirrors that
are used have a Spherical
instead of the more
expensive (but better)
Parabolic shape.
Only a small portion of the
Spherical mirror is used so
that it closely matches the
properties of a Parabolic
mirror.
This is why curved
mirrors often seem to be
quite “flat”.
The inside of a sphere produces a concave mirror.
The outside produces a convex mirror.
2) The Parts of a Concave Mirror
C  Centre of Curvature
F  Focus
f  Focal Length
V  Vertex
3)Concave Mirror Characteristic Rays
Concave mirrors can produce images but they are
more complicated than plane mirrors.
3) Concave Mirror Characteristic Rays
Certain light rays called “Characteristic Rays” always
reflect the same way from a Concave mirror .
These Characteristic Rays can be used to predict
what the images will look like.
3)Concave Mirror Characteristic Rays
Any incident ray parallel to the principal axis will……
3)Concave Mirror Characteristic Rays
Any incident ray parallel to the principal axis will
reflect through the Focus.
3)Concave Mirror Characteristic Rays
Any incident ray passing through the Focus will……
3)Concave Mirror Characteristic Rays
Any incident ray passing through the Focus will
reflect parallel to the principal axis.
3)Concave Mirror Characteristic Rays
Any incident ray passing through the Centre of Curvature
will……
3)Concave Mirror Characteristic Rays
Any incident ray passing through the Centre of Curvature
will reflect back upon itself.
3)Concave Mirror Characteristic Rays
Any incident ray striking the Vertex will……
3)Concave Mirror Characteristic Rays
Any incident ray striking the Vertex will reflect
such that i = r.
Predicting Images in a Concave Mirror
Predicting Images in a Concave Mirror
Any incident ray parallel to the principal axis will……
Predicting Images in a Concave Mirror
Any incident ray parallel to the principal axis will
reflect through the Focus.
Predicting Images in a Concave Mirror
Any incident ray passing through the Focus will……
Predicting Images in a Concave Mirror
Any incident ray passing through the Focus will
reflect parallel to the principal axis.
Predicting Images in a Concave Mirror
Any incident ray passing through the Centre of Curvature
will……
Predicting Images in a Concave Mirror
Any incident ray passing through the Centre of Curvature
will reflect back upon itself.
Predicting Images in a Concave Mirror
Any incident ray striking the Vertex will……
Predicting Images in a Concave Mirror
Any incident ray striking the Vertex will reflect
such that i = r.
Predicting Images in a Concave Mirror
Where is the image?
Predicting Images in a Concave Mirror
The object is located where the rays appear to come from.
Predicting Images in a Concave Mirror
The image is also located where the rays appear
to come from.
NOTE: Light rays originating from any point on the object,
and reflecting off the mirror, will pass through a
corresponding point on the image. Characteristic rays
simply help predict image location and characteristics.
NOTE: The bottom of the object could be below the
principal axis. The bottom of the image would be found the
same way as the top.
For simplicity, we place the bottom of the object on the
principal axis.
Predicting Images in a Concave Mirror
Your Turn
Continue with
L6 Concave Mirrors - Student Notes
Predicting Images in a Concave Mirror
L6 Concave Mirrors - Student Notes
Answers Follow
Predicting Images in a Concave Mirror
Object is at the Centre of Curvature.
When the Object is at C
Any incident ray parallel to the principal axis will……
Any incident ray parallel to the principal axis will
reflect through the Focus.
Any incident ray passing through the Focus will……
Any incident ray passing through the Focus will
reflect parallel to the principal axis.
Any incident ray passing through the Centre of Curvature
will……
Any incident ray passing through the Centre of Curvature
will reflect back upon itself.
Any incident ray striking the Vertex will……
Any incident ray striking the Vertex will reflect such
that i = r.
Where is the image?
The object is where all incident rays appear to come
from.
The image is where all reflected rays appear to come from.
When the Object is Between C and F
Any incident ray parallel to the principal axis will……
Any incident ray parallel to the principal axis will
reflect through the Focus.
Any incident ray passing through the Focus will……
Any incident ray passing through the Focus will
reflect parallel to the principal axis.
Any incident ray in a direction the same as if it had passed
through the C will……
Any incident ray in a direction the same as if it had passed
through the C will reflect back upon itself.
Any incident ray striking the Vertex will……
Any incident ray striking the Vertex will reflect such
that i = r.
The object is where all incident rays appear to meet or come
from.
The image is where all reflected rays appear to meet.
When the Object is at F
Any incident ray parallel to the principal axis will……
Any incident ray parallel to the principal axis will
reflect through the Focus.
Any incident ray passing through the Focus will
miss the mirror because it is parallel to it.
Any incident ray in a direction the same as if it had passed
through the C will……
Any incident ray in a direction the same as if it had passed
through the C will reflect back upon itself.
Any incident ray striking the Vertex will……
Any incident ray striking the Vertex will reflect such
that i = r.
The reflected rays are parallel !
This property is used in headlights and flashlights.
A bulb located at the Focus produces a parallel beam
which travels a long way without diverging and
becoming less intense.
But, where is the image?
Choose a point just a little closer to C or between C
and F. The final ray diagram looks like the one above.
The reflected rays are no longer parallel and meet far
away.
When the Object is Between F and V
Any incident ray parallel to the principal axis will……
Any incident ray parallel to the principal axis will
reflect through the Focus.
Any incident ray in a direction the same as if it had passed
through F will……
Any incident ray in a direction the same as if it had passed
through F will reflect parallel to the principal axis.
Any incident ray in a direction the same as if it had passed
through C will……
Any incident ray in a direction the same as if it had passed
through C will reflect back upon itself.
Any incident ray striking the Vertex will……
Any incident ray striking the Vertex will reflect such
that i = r.
The reflected rays diverge!
This property is used in “low beam” headlights .
A bulb located above the axis, between the Focus and
Vertex, produces a less intense, diverging beam which
spreads out and down.
But, where is the image?
The image is where all reflected rays appear to meet.
This property is used in Make-Up or Shaving Mirrors.
A face located between the Focus and Vertex produces
a large erect image .
Looking back to when the object was at F:
-part of it was between F and V and the reflected
rays diverged slightly.
The image is behind the mirror where all reflected
rays appear to meet.
When the object was at F, part of it was close, but
between F and C. The reflected rays converged
slightly.
And the reflected rays meet far away.
When the object is
at F, there are two
images which are
formed by the
parts of the object
which are between
F and O,
and the parts
which are between
F and C.
The reflected rays are not parallel when they produce
a distant image, but they are close to being parallel.
If the image were an object, the rays could be just
turned around. Then an image would be formed at the
Focus.
When the object is FAR beyond the Centre of
Curvature, it cannot be seen on the ray diagram.
When the object is FAR beyond the Centre of
Curvature, it cannot be seen on the ray diagram.
As usual though, any incident ray passing through
the Focus will……
When the object is FAR beyond the Centre of
Curvature, it cannot be seen on the ray diagram.
As usual though, any incident ray passing through
the Focus will reflect parallel to the principal axis.
When the object is FAR beyond the Centre of
Curvature, any incident ray parallel to the principal axis
cannot be seen because it is far below the ray diagram.
But for the purpose of locating the image, we can
still consider it reflecting through the Focus.
Any incident ray passing through the Centre of Curvature
will……
Any incident ray passing through the Centre of Curvature
will reflect back upon itself.
Any incident ray striking the Vertex will……
Any incident ray striking the Vertex will reflect such
that i = r.
The image is formed at the Focus where the reflected
rays meet.
This fact can be used to find the Focus and focal
length of a mirror when it is not known.
Light rays from a distant luminous object (like a
window) will be almost parallel and will form an image at
the Focus.
Note that the image is smaller and inverted.
5) If the OBJECT IS MOVED far beyond the Centre of
Curvature, the image will move toward the Focus.
6) If the OBJECT IS MOVED close toward the Focus,
the image will move far beyond the Centre of
Curvature.
7) In order to produce a VIRTUAL IMAGE with
CONCAVE MIRROR, an object must be placed
between the Focus and the Vertex.
8) In order to produce a REAL IMAGE with CONCAVE
MIRROR, an object must be placed beyond the Focus
(away from the mirror).
9) In order to produce an ERECT IMAGE with CONCAVE
MIRROR, an object must be placed between the
Focus and the Vertex.
10)In order to produce the LARGEST IMAGE POSSIBLE
with CONCAVE MIRROR, an object must be placed at
the Focus.
Now that you are an expert, check out the simulation,
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=48.0
Or view
http://www.exploratorium.edu/media/index.php?project=&program=0
0000944
Try to “see it” in your mind.