Reflection and Mirrors

Mirrors and Reflection

Reflection

The bouncing back of a light ray from a surface.

Law of Reflection

When a light ray is incident upon a reflecting surface, the angle of reflection is equal to the angle of incidence. Both of these angles are measured relative to a normal drawn to the surface. The incident ray, the reflected ray, and the normal all lie in the same plane.

law of reflection

Diffuse reflection

When rays are reflected from a rough surface, they are reflected in many directions and no clear image is formed. None of the normals drawn to the surface (at the point at which the incident light ray strikes the surface) are parallel.

Regular reflection

When rays are reflected from a smooth surface, they are reflected so that a clear image is formed. The reflected rays are nearly parallel. The normals drawn to the surface (at the point at which the incident ray strikes the surface) are nearly parallel.

Types of mirrors:

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:

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:

Object size = image size
Object distance = image distance
Orientation = erect
Always forms a virtual image
Image is reversed, left to right

Steps for drawing a plane mirror ray diagram:

A ray that strikes perpendicular to the mirror surface, reflects perpendicular to the mirror. This reflected ray is extended behind the mirror
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.

Curved mirror terminology: (a concave mirror is drawn as an example)

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

mirror terminology

Concave mirror

the reflecting surface of the mirror is on the inside; the object and focus are located on the same side of the mirror

Characteristics of concave mirrors:

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

Ray diagrams for concave mirrors:

A ray incident upon the mirror that is parallel to the principal axis, reflects through the focus
A ray incident upon the mirror that passes through the focus, reflects parallel to the principal axis

Mathematical prediction of image location:

mirror equation

where f is the focal length (remember to assign it a sign), d_o is the object distance, and d_i is the image distance

Mathematical prediction of image height:

image height formula

where h_i is the image height, h_o is the object height, and d_i is the image distance, and d_o is the object distance

Magnification ratio:

magnification formula

where h_i is the image height, h_o is the object height, and d_i is the image distance, and d_o is the object distance

Convex mirrors

the reflecting surface is on the outside; the object and the focus are on opposite sides of the mirror (remember-the focus is on the "inside" of the circle); the object is located on the outside

Characteristics of convex mirrors:

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

Ray Diagrams for convex mirrors:

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)
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)

Mirrors Sample Problems

Mirrors Homework