Students explore the physics behind convex mirrors.
After completing this tutorial, you will be able to complete the following:
Passenger-side mirrors on cars in the United States warn that "objects in mirror are closer than they may appear." This is because the passenger side mirror is a convex mirror, an outward-curving reflective surface, which makes reflected objects appear smaller and thus farther away. A convex mirror is a portion of a parabola or, more often, a sphere. The center of this sphere is the mirror's center of curvature and is marked C, and the principal axis runs horizontally through the sphere. It intersects the mirror surface at the midpoint, or vertex V. Exactly midway between the vertex and the center of curvature is the focal point, F; the distance from the vertex to this point is the focal length.
In optics, tracing special rays of light reflected from a convex mirror helps us understand image formation. When a ray parallel to the principal axis is reflected, the extension of the reflected ray passes through the focal point (F). This result does not change when the location of the object changes. A ray with an extension that passes through the center of curvature (C) is reflected back along the same path as the incoming ray. A ray that strikes the vertex (V) is reflected at an angle reversed along the principal axis. Finally, a ray with an extension that passes through the focal point (F) is reflected parallel to the principal axis.
Ray tracing indicates that the image formed by the reflection of an object in a convex mirror will always be smaller than the object, upright, and located behind the mirror; images located behind a mirror are virtual images. A convex mirror cannot, by itself, produce a real, inverted, or magnified image. As the distance between the object and the mirror decreases, the distance between the virtual image and the mirror also decreases while the size of the virtual image increases.
The relationship among the focal length, object distance, and image distance is given by the equation where f is the focal length, is the distance of the image, and is the distance of the object. The magnification of a mirror, M, is given by the equation where are the heights of the image and object, respectively.
|Approximate Time||20 Minutes|
|Pre-requisite Concepts||Students should be familiar with the concepts of a plane mirror and a virtual image, and be able to describe how light travels in a straight line and is reflected in a planar mirror.|
|Type of Tutorial||Concept Development|
|Key Vocabulary||center of curvature, convex mirrors, diverging mirrors|