Curved Mirrors

• Curved Mirrors have as many different uses as plane mirrors.

• Curved mirrors for this class are spherical mirrors because they have the same curvature as a sphere.

• There are two basic curved mirrors.• Convex mirrors bulge outwards in the middle.• Concave mirrors bulge inwards in the middle.

To help identify the two spherical mirrors, think of the word “cave” in concave. The surface of a concave mirror is curved in like the opening into cave!

Curved Mirror Terminology

Center and Radius of Curvature

• The center of the sphere from which the curved mirrors are from is called the center of curvature (C).

• The distance from the center of the curvature to the surface of the mirror is called the radius of curvature.

Vertex and Principle Axis

• The center of the mirror is called the Vertex (V).

• The line that passes through the center of curvature and the vertex is called the principal axis (P).

V

Vertex

• Any other line that passes from the center of curvature (c) to the surface of the mirror is called a secondary axis.

• Secondary axis meet the surface of the mirror at 90 degree angles.

• The radius of the circle is an example os a secondary axis.

• The secondary axis and the principle axis are normals to the surface of the mirror.

Secondary axis, also known as a radius

Focal Point

• The point that is half way between the C and the V is called the Focal Point (F).

• The length between the C and F is called the focal length.

Concave Mirrors

When parallel lines shine along the P. Axis of a concave mirror, reflecting rays meet at the Focal point (F).

Concave Mirror

Two Rules of Reflection for Concave Mirrors

• Light always reflects according to the law of reflection, regardless of whether the reflection occurs off a flat surface or a curved surface.

• Using reflection laws enables us to determine the image location for an object.

• The image location is where all reflected light appears to diverge from. To determine this location we need to know how light reflects off a mirror.

• Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection.

• Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.

Step by Step Method for Drawing Ray Diagrams (Concave)

• 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.

• 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. Extend the rays past their point of intersection.

• 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.

Image of Object Beyond C

• When the object is located beyond C, the image will always be located somewhere in between C and F.

• The image will be an inverted image. That is to say, if the object is right-side up, then the image is upside down.

• The image is reduced in size• The image is a real image. Light rays actually

converge at the image location. • If a sheet of paper was placed at the image location,

the actual replica of the object would appear projected upon the sheet of paper.

What if the object is right at C?

• When the object is located at C, the image will also be located C.

• The image will be inverted (a right-side-up object results in an upside-down image).

• The image dimensions are equal to the object dimensions.

•Finally, the image is a real image. Light rays actually converge at the image location.

• The image of the object could be projected upon a sheet of paper

What if the object is between C and F?

• When the object is located in front of C, the image will be located beyond the C.

• The image will be inverted (a right-side-up object results in an upside-down image).

• The image dimensions are larger than the object dimensions.

•The image is a real image. Light rays actually converge at the image location.

• The image of the object could be projected upon a sheet of paper.

What if the image is between F and the mirror?

• When the object is located beyond the focal point, the image will always be located somewhere on the opposite side of the mirror.

• The image will be an upright image. If the object is right-side up, then the image will also be right-side up.

• In this case, the image is magnified

• The image location can only be found by extending the reflected rays backwards beyond the mirror.

• The point of their intersection is the virtual image location. It would appear to any observer as though light from the object were diverging from this location.

What is the image is right on F?

• When the object is located at the focal point, no image is formed.

• Light rays from the same point on the object will reflect off the mirror. They will neither converge nor diverge.

• After reflecting, the light rays are traveling parallel to each other and do not result in the formation of an image

Convex Mirrors

• When parallel lines shine along a principle axis on a convex mirror, the reflected rays diverge from one another.

• If you extend the reflected rays to behind the mirror, they would meet up at a point called the virtual focal point.

Two rules of Reflection for Convex Mirrors

• Any incident ray traveling parallel to the principal axis on the way to a convex mirror will reflect so that its extension will pass through the focal point.

• Any incident ray traveling towards a convex mirror such that its extension passes through the focal point will reflect and travel parallel to the principal axis.

Step by Step Method for Drawing for Ray Diagrams (Convex)

• Pick a point on the top of the object and draw two incident rays traveling towards the mirror.

• Using a ruler, draw one ray so that it travels towards the focal point on the opposite side of the mirror

• Draw the second ray so that it travels exactly parallel to the principal axis. Place arrowheads upon the rays to indicate their direction of travel.

• Once these incident rays strike the mirror, reflect them according to the two rules of reflection for convex mirrors.

• The ray that travels towards the focal point will reflect and travel parallel to the principal axis. Use a straight edge to accurately draw its path.

• The ray that traveled parallel to the principal axis on the way to the mirror will reflect and travel in the direction of the focal point. Align a straight edge with the point of incidence and the focal point, and draw the second reflected ray.

• Locate and mark the image of the top of the object.

• The top of the image is the point where the two reflected rays intersect. Since the two reflected rays are diverging, they must be extended behind the mirror in order to intersect.

• Using a straight edge, extend each of the rays using dashed lines. Draw the extensions until they intersect.

• The point of intersection is the top of the image.

• All images produced by convex mirrors produce images with the following characteristics:

• located behind the convex mirror • a virtual image • an upright image