CURVED MIRRORSSPHERICAL 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

Uses of Concave and Convex Mirrors

CONCAVE- barber/make-up mirrors- car headlights - light reflects wider- microscopes- dentist mirrors- solar cookers

CONVEX- security/surveillance mirrors- sunglasses- passenger side mirrors in vehicles

Diagram of Concave MirrorLabel 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.

Ray1: Parallel-FOCUS Ray 2: FOCUS-Parallel

Step-by-Step Method for Drawing Ray DiagramsParallel-FOCUS-FOCUS-Parallel

You need 2 incident rays and 2 reflected rays to draw your image.

Incident ray #1: Parallel-FOCUS

PARALLEL: From the top of the object, using a straight edge, accurately draw one ray (incident ray) to the mirror so that it travels exactly parallel to the principal axis. Label it “I” for incident ray and place arrowhead to show direction.

FOCUS: Where the incident ray “touches” the mirror, draw the second ray (reflected ray) such that it passes exactly through the focal point on the way from the mirror. Label it “R” and place an arrowhead upon the ray to show direction.

Incident ray #2: FOCUS-Parallel;

FOCUS: From the top of the object, using a straight edge, accurately draw one ray (incident ray) through the focal point on the way from the mirror until it touches the mirror. Label it “I” and place an arrowhead upon the ray to show direction.

PARALLEL: Where the incident ray “touched” the mirror, using a straight edge, accurately draw one ray (incident ray) from the mirror so that it travels exactly parallel to the principal axis. Label it for reflected ray and place arrowhead to show direction.

Step-by-Step Method for

Drawing Ray Diagrams

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

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 willreflect 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 willreflect 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.