http://www.ck12.org Chapter 20. Geometric Optics
is met as long as the radius of curvature of the mirror is small compared to the distance that the light travels from the
object to the mirror. For example, rays of sunlight are effectively parallel since the sun is so far away. The image of
the sun would therefore form at the focal pointfof the mirror inFigure20.11.
We can demonstrate, with a bit of geometry, that the radius of curvature is twice the focal length.
r= 2 fâf=r 2
FIGURE 20.10
Constructing ray diagrams for concave mirrors: object located beyond the focal point
We begin with a definition. Images that appear on a screen are calledreal images.Such images are formed by
actual rays, not extensions of rays as in the case of virtual images. Images formed with concave mirrors when the
object is located beyond the focal point are real images.
The Law of Reflection is the basis for constructing ray diagrams for mirrors. However, it is rather time-consuming
and difficult to construct rays by measuring their incidence and reflection angles.
Three principal rays can be drawn to construct ray diagrams for concave mirrors.
Figure20.10 suggests that there is at least one way, as described below, to construct a ray path easily.
SeeFigure20.11 for rays labeled 1, 2, 3 as given below.
Ray 1: A ray parallel to the principal axis will, after reflection, pass through the focal point.
We can assume that the direction of the ray is reversible. In other words, if an object (imagine a small light bulb)
were placed at the focal point of the mirror, all rays would reflect off the mirror parallel to the principal axis.
Ray 2: A ray passing through the focal point will reflect parallel to the principal axis.
Ray 3. A ray that reflects perpendicularly off the mirror (along the normal) will pass through the center of curvature,
since all radii are perpendicular to tangents to the circle.
The point where the rays intersect is the location of the image.
Definitions:
object distance(do): Distance from the object to the mirror.
image distance(di): Distance from the image to the mirror.
Notice that the image formed inFigure20.11 is inverted.