Reflection

Law of Reflection

Normal

Angle of Incidence

Angle of Reflection

Diffuse reflection

Regular reflection

An applet explaining the physics of a rainbow. Rainbow

Types of mirrors:

1. Plane mirrors
   A flat mirror that reflects light rays in the same order as they approach the mirror.

   Concave mirrors

   A converging mirror; light rays that strike the mirror surface are reflected so that they converge, or "come together," at a point

   Convex mirrors

   A diverging mirror; light rays that strike the mirror surface are reflected so that they diverge, or "go apart," and they never come to a point.

Type of images:

1. Real images
   formed by converging light rays; can be projected on a screen; orientation=inverted

   Virtual images

   formed by diverging light rays; cannot be projected on a screen; orientation=erect

Characteristics of plane mirror images:

1. Object size = image size
2. Object distance = image distance
3. Orientation = erect
4. Always forms a virtual image
5. Image is reversed, left to right

A game to play using a plane mirror. Mirror Game

Steps for drawing a plane mirror ray diagram:

1. A ray that strikes perpendicular to the mirror surface, reflects perpendicular to the mirror. This reflected ray is extended behind the mirror
2. A ray that strikes the mirror at any angle reflects so that the angle of incidence equals the angle of reflection; the reflected ray is extended behind the mirror.

center of curvature (C)

the center of the circle of which the mirror represents a small arc

focus (F)

the point where parallel light rays converge; the focus is always found on the inner part of the "circle" of which the mirror is a small arc; the focus of a mirror is one-half the radius

vertex (V)

the point where the mirror crosses the principal axis

Principal axis

a line drawn through the vertex, focus, and center of curvature of the mirror upon which the object rests

focal length (f)

the distance from the focus to the vertex of the mirror; the focal length is one-half the radius of curvature

radius of curvature

the distance from the center of curvature to the vertex of the mirror; it corresponds to the radius of the circle

Concave mirror

Characteristics of concave mirrors:

1. The focal length is positive (because the object and the focus are on the same side of the mirror)
2. The object and the focus are on the same side of the mirror (inside the arc)
3. Real images can be formed by the mirror when the object is outside of the focus; an inverted image is formed
4. Virtual images are formed by the mirror when the object is within the focus; an erect image is formed
5. No image is formed when the object is at the focus
6. When the object is at the center of curvature, an inverted image is formed at the center of curvature

Ray diagrams for concave mirrors:

There are three principal rays. You may locate an image using any two of the principal rays.

1. A ray incident upon the mirror that is parallel to the principal axis, reflects through the focus.
2. A ray incident upon the mirror that passes through the focus, reflects parallel to the principal axis.
3. A ray that connects the top of the object and the center of curvature reflects back upon itself.

An interactive applet that allows you to create images for both mirror types using ray diagrams. This is an excellent way to see how each of the three principal rays for a concave mirror are drawn. You may drawn each individually. You may draw any two to locate the image. Or, you may locate the image using all three. Ray Diagrams

Mathematical prediction of image location:

Mathematical prediction of image height:

Magnification ratio:

Convex mirrors

Characteristics of convex mirrors:

1. The focal length is negative (because the object and the focus are on opposite sides of the mirror)
2. The object and the focus are on opposite sides of the mirror (the focus is on the inside of the mirror and the object is on the outside)
3. Only virtual images are formed; all images are smaller than the object

Ray Diagrams for convex mirrors:

There are three principal rays. You may locate an image using any two of the principal rays.

1. A ray incident on the mirror that is parallel to the principal axis is reflected in a line even with the focus (extend the reflected ray behind the mirror so that it passes through the focus).
2. A ray incident on the mirror that passes through the focus is reflected parallel to the principal axis (extend the reflected ray behind the mirror parallel to the principal axis).
3. A ray that connects the top of the object and the center of curvature reflects back upon itself.

An interactive applet that allows you to create images for both mirror types using ray diagrams. This is an excellent way to see how each of the three principal rays for a convex mirror are drawn. You may drawn each individually. You may draw any two to locate the image. Or, you may locate the image using all three. Ray Diagrams

What happens to image distance if the surface of the mirror is curved? A plane mirror produces a virtual image that is the same size as the object. If the mirror is bent so that it becomes concave, the virtual image distance increases and the virtual image size becomes larger, relative to the object. If the mirror is bent so that it becomes convex, the virtual image distance decreases and the virtual image size becomes smaller, relative to the object.

Focal Length

• f is positive for a concave mirror. The real side of the mirror is the same side as the focus.
• f is negative for a convex mirror. The virtual side of the mirror is the opposite side as the focus.

• d_o is positive for a real object (the object is in front of the mirror)
• d_o is negative for a virtual object (the object is behind the mirror)

• d_i is positive for a real image (the image is in front of the mirror)
• d_i is negative for a virtual image (the image is behind the mirror)

• m is positive for an image whose orientation is the same as the object
• m is negative for an image whose orientation is inverted with respect to the object

Mirrors Applet for AP

Diverging Mirrors Applet for AP

AP Multiple Choice Questions on Mirrors & Reflection

1. Questions deal with the type of image created by a mirror. Which type forms real images? Which type forms virtual images? When are images formed by mirrors smaller than the object? The same size as the object? Larger than the object?
2. They will give you an object in front of a mirror. You must predict the size and orientation of the image relative to the object. You must predict the location of the image.
3. Be able to determine the focal length when given the radius of curvature.
4. Know that parallel light rays (those from a very distant object) converge at the focus.
5. Be able to locate the position of an object formed by a plane mirror. Be able to predict the image's orientation.

AP Free Response Questions on Mirrors & Reflection

1. There have not been many free response questions involving mirrors in recent years.
2. In past years, an object was located in front of a mirror (ususally concave). Be able to use the three principal rays to locate the image when the object is within the focus and outside of the focus. Be able to predict how any ray drawn through the top of the object will reflect (apply the law of reflection).
3. Be able to state whether the image is real or virtual and be able to support your conclusion.
4. Apply the mirror equation to calculate image distance. Calculate image height.
5. In recent years, they combine a question on mirrors with a free response question on lenses. For example, they have a converging lens with an object located on its left. They add a concave mirror on the right of the lens and ask you to locate the final image using a ray diagram.

Mirrors and Billiards shows how to use the law of reflection in pool (a pool game is at the bottom of the page)

Mirrors Sample Problems

Mirrors Homework

AP Reflection & Mirrors Objectives