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Seeing Things inCurved Mirrors


Archimedes's Death RayFor 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. Frompg 65 The Flying Circus of Physics by Jearl Walkers


Archimedes's Death RayFor 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. Frompg 65 The Flying Circus of Physics by Jearl Walkers


Archimedse's Death RayFor 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. Frompg 65 The Flying Circus of Physics by Jearl Walkers


Archimedes's Death RayThe way that this feat may have been possible was to use many plane mirrors. (Greek soldiers had copper shields which could be highly polished.)Frompg 65 The Flying Circus of Physics by Jearl Walkers


Archimedes's Death RayEach mirror could be used to reflect a spot of sunlight at the same object (invading Roman ship). Frompg 65 The Flying Circus of Physics by Jearl Walkers


Archimedes's Death RayThis might act like a giant magnifying glass. Frompg 65 The Flying Circus of Physics by Jearl Walkers


Archimedes's Death RayThis might act like a giant magnifying glass and ignite the target. Frompg 65 The Flying Circus of Physics by Jearl Walkers


Archimedes's Death RayThe historical record of this possible event is very weak. It is argued that the feat was impossible given the technology available to Archimedes. Frompg 65 The Flying Circus of Physics by Jearl Walkers


Archimedes's Death RayThere is also a problem in aiming all the mirrors at the target with this. Frompg 65 The Flying Circus of Physics by Jearl WalkersWhat 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



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. will reflect off any part of the smooth curve and pass through the same spot.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.



The inside of a sphere produces a concave mirror. “flat”.

The outside produces a convex mirror.


The Parts of a Concave Mirror “flat”.

C  Centre of Curvature

F  Focus

f  Focal Length

V  Vertex


Concave Mirror Characteristic Rays “flat”.

Concave mirrors can produce images but they are more complicated than plane mirrors.


Concave Mirror Characteristic Rays “flat”.

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.


Concave Mirror Characteristic Rays “flat”.

Any incident ray parallel to the principal axis will……


Concave Mirror Characteristic Rays “flat”.

Any incident ray parallel to the principal axis will

reflect through the Focus.


Concave Mirror Characteristic Rays “flat”.

Any incident ray passing through the Focus will……


Concave Mirror Characteristic Rays “flat”.

Any incident ray passing through the Focus will

reflect parallel to the principal axis.


Concave Mirror Characteristic Rays “flat”.

Any incident ray passing through the Centre of Curvature

will……


Concave Mirror Characteristic Rays “flat”.

Any incident ray passing through the Centre of Curvature

will reflect back upon itself.


Concave Mirror Characteristic Rays “flat”.

Any incident ray striking the Vertex will……


Concave Mirror Characteristic Rays “flat”.

Any incident ray striking the Vertex will reflect

such that i =r.



Predicting Images in a Concave Mirror “flat”.

Any incident ray parallel to the principal axis will……


Predicting Images in a Concave Mirror “flat”.

Any incident ray parallel to the principal axis will

reflect through the Focus.


Predicting Images in a Concave Mirror “flat”.

Any incident ray passing through the Focus will……


Predicting Images in a Concave Mirror “flat”.

Any incident ray passing through the Focus will

reflect parallel to the principal axis.


Predicting Images in a Concave Mirror “flat”.

Any incident ray striking the Vertex will reflect

such that i =r.


Predicting Images in a Concave Mirror “flat”.

Where is the image?


Predicting Images in a Concave Mirror “flat”.

The object is located where the rays appear to come from.


Predicting Images in a Concave Mirror “flat”.

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 axis. The bottom of the image would be found the same way as the top.

Your Turn

Continue with

Concave Mirrors - Handouts


Predicting Images in a Concave Mirror axis. The bottom of the image would be found the same way as the top.

Object is at the Centre of Curvature.


When the Object is at C axis. The bottom of the image would be found the same way as the top.

Any incident ray parallel to the principal axis will……


Any incident ray parallel to the principal axis will axis. The bottom of the image would be found the same way as the top.

reflect through the Focus.


Any incident ray passing through the Focus will…… axis. The bottom of the image would be found the same way as the top.


Any incident ray passing through the Focus will axis. The bottom of the image would be found the same way as the top.

reflect parallel to the principal axis.








Any incident ray passing through the focus will

reflect parallel






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 reflect back upon itself.


Any incident ray striking the Vertex will…… through the C will reflect back upon itself.




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. The final ray diagram looks like the one above.


When the Object is Between F and V The final ray diagram looks like the one above.


Any incident ray parallel to the principal axis will…… The final ray diagram looks like the one above.


Any incident ray parallel to the principal axis will The final ray diagram looks like the one above.

reflect through the Focus.



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 striking the Vertex will…… through F will reflect parallel to the principal axis.




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?



This property is used in Make-Up or Shaving Mirrors.

A face located between the Focus and Vertex produces a large image .


Looking back to when the object was at F:

-part of it was between F and V and the reflected rays diverged slightly.



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. F and C. The reflected rays converged slightly.


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.

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 consider it reflecting through the Focus.

will……


Any incident ray passing through the Centre of Curvature consider it reflecting through the Focus.

will reflect back upon itself.


Any incident ray striking the Vertex will…… consider it reflecting through the Focus.


Any incident ray striking the Vertex will reflect such that consider it reflecting through the Focus.i =r.



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.


If the OBJECT IS MOVED far beyond the Centre of Curvature, the image will move toward the Focus.

If the OBJECT IS MOVED close toward the Focus, the image will move far beyond the Centre of Curvature.

In order to produce a VIRTUAL IMAGE with CONCAVE MIRROR, an object must be placed between the Focus and the Vertex.


7) In the image will move order to produce a REAL IMAGE with CONCAVE MIRROR, an object must be placed beyond the Focus (away from the mirror).

8) In order to produce an UPRIGHT IMAGE with CONCAVE MIRROR, an object must be placed between the Focus and the Vertex.

In order to produce the LARGEST IMAGE POSSIBLE with CONCAVE MIRROR, an object must be placed at the Focus.


http://www.exploratorium.edu/media/index.php?project=&program=00000944http://www.exploratorium.edu/media/index.php?project=&program=00000944

Try to “see it” in your mind.


Why is it important to study optics?http://www.exploratorium.edu/media/index.php?project=&program=00000944

Walkie Talkie Building

http://www.youtube.com/watch?v=BTBm9LwzIAw


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