SPHERICAL MIRRORS

Curved Mirrors  Curved mirrors are also called spherical mirrors because they are part of a sphere (ball)  a portion of the sphere was sliced away and then silvered on one of the sides to form a reflecting surface.  There are two types of spherical mirrors…

Types of Spherical Mirrors  Concave mirrors were silvered on the inside of the sphere  Convex mirrors were silvered on the outside of the sphere

Diagram of Concave Mirror Label the diagram below using the next slides.

Principal Axis  a line passing through the center of the sphere and attaching to the mirror in the exact center of the mirror.

Centre of Curvature  point in the center of the sphere from which the mirror was sliced is known as the center of curvature and is denoted by the letter C in the diagram below.

Vertex  The point on the mirror's surface where the principal axis meets the mirror is known as the vertex and is denoted by the letter A in the diagram below.

Focal Point  Midway between the vertex and the center of curvature is a point known as the focal point; the focal point is denoted by the letter F in the diagram below.

Why is it called a focal point?  Because rays of light parallel to the principal axis all pass through or CONVERGE at the focus or focal point. NOTE that the law of reflection still happens! Don’t copy anything from this slide!

Radius of Curvature  The distance from the vertex to the center of curvature is known as the radius of curvature (represented by R). The radius of curvature is the radius of the sphere from which the mirror was cut.

Focal Length  The distance from the mirror to the focal point is known as the focal length (represented by f).  Since the focal point is the midpoint of the line segment adjoining the vertex and the center of curvature, the focal length would be one-half the radius of curvature.

Using Ray Diagrams to Find the Image - Concave Mirrors  To draw these diagrams, we will use the two RAYS for concave mirrors: 1. Any incident ray traveling parallel to the principal axis on the way to the mirror will reflect through the focal point upon reflection. 2. Any incident ray passing through the focal point on the way to the mirror will reflect parallel to the principal axis upon reflection.

Step-by-Step Method for Drawing Ray Diagrams

Step Pick a point on the top of the object and draw two incident rays traveling towards the mirror.  Using a straight edge, accurately draw one ray so that it passes exactly through the focal point on the way to the mirror. Draw the second ray such that it travels exactly parallel to the principal axis. Place arrowheads upon the rays to indicate their direction of travel.

Step 2 2. Once these incident rays strike the mirror, reflect them according to the two rules of reflection for concave mirrors.  The ray that passes through the focal point on the way to the mirror will reflect and travel parallel to the principal axis. Use a straight edge to accurately draw its path. The ray which traveled parallel to the principal axis on the way to the mirror will reflect and travel through the focal point. Place arrowheads upon the rays to indicate their direction of travel. Mark all reflected rays R.

Step 3 3. Mark the image of the top of the object.  The image point of the top of the object is the point where the two reflected rays intersect. If your were to draw a third pair of incident and reflected rays, then the third reflected ray would also pass through this point. This is merely the point where all light from the top of the object would intersect upon reflecting off the mirror. Of course, the rest of the object has an image as well and it can be found by applying the same three steps to another chosen point.

Step 4 4. Repeat the process for the bottom of the object.  The goal of a ray diagram is to determine the location, size, orientation, and type of image which is formed by the concave mirror. Typically, this requires determining where the image of the upper and lower extreme of the object is located and then tracing the entire image. After completing the first three steps, only the image location of the top extreme of the object has been found. Thus, the process must be repeated for the point on the bottom of the object. If the bottom of the object lies upon the principal axis (as it does in this example), then the image of this point will also lie upon the principal axis and be the same distance from the mirror as the image of the top of the object. At this point the entire image can be filled in.

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 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.

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.

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.

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 !

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.