what people ordinarily think of as “magnified.”
Now, on to the equations. The mirror equations are very useful for designing equipment
such as cameras and telescopes because they enable engineers to correctly focus an
image at a required point (for example, at the surface of a photographic film, or in a
digital camera, at the surface of a “charge-coupled device”). The formula in Equation 1
shows the relationship of object and image distance to the focal length of a mirror. It is
valid when the incident rays from the object are paraxial.
The next two equations, shown in Equation 2, are used to define and calculate
magnification. The first equation defines magnification: It is the ratio of the image and
object heights. The magnification can also be calculated as the negative of the ratio of
image distance to object distance.
If you now refer back to the table in Concept 1 for signs, you may see one entry that
surprises you: an object with a negative distance. Such a “virtual object” can be created
by a configuration of two mirrors, or by a lens and a mirror, as shown in the illustration
below.Incident rays from the original real object first reflect off some mirror, or pass through
some lens, which is not shown in the illustration, being off screen to the left. As a result,
converging rays come in from the left and strike the convex mirror in the diagram. The
image they create would be a real image “behind” the location of the mirror if the mirror
were not there. Since the mirror is there, the convergence point of the virtual rays on the
right defines the location of a virtual object, whose distance from the mirror is negative.
The incident rays reflect off the front of the mirror to create a real image, with a positive
image distance, as shown. Since optical instruments such as telescopes and
microscopes often rely on a combination of lenses and mirrors, negative object
distances are not rare.Mirror equation
di= image distance
do = object distance
f = focal length
Magnification equations
m = magnification of image
hi = height of image
ho = height of object
(^588) Copyright 2007 Kinetic Books Co. Chapter 31