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

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?

Archimedes’s Death Ray Myth Busters Eat Your Heart Out Could it be done today? Click on Image to play

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.

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. 3)Concave Mirror Characteristic Rays

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.

and the parts which are between F and C. 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,

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 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, Or view Try to “see it” in your mind.