Biomedical Engineering Reference
In-Depth Information
Since the rays that form a virtual image are diverging, their vergence must be
designated with a minus sign as follows:
L
′
= −
3.80 D
LINEAR SIGN CONVENTION
Up to now, we've calculated the absolute value of the vergence and then assigned this
vergence a sign depending on whether the light rays are diverging or converging.
Although this approach works just fine, most students prefer not to calculate absolute
values and to instead use a linear sign convention that labels distances as negative or
positive. A linear sign convention provides convenience in solving optical problems,
but it can also undermine an understanding of what is happening and lead to errors.
To minimize these problems, it's a good idea to draw a diagram—it doesn't need
to be anything fancy—so that you understand what is happening to the light rays.
If you keep in mind a few things that we've emphasized up to now—in particular,
that converging light rays have plus vergence and diverging light rays have negative
vergence—you should be in good shape when using a linear sign convention.
In this text, we use a linear sign convention with the following rules:
1. Light is assumed to travel from the left to the right.
2. Object and image distances are measured
from
the refracting, reflecting, or
lens surface.
3. Object and image heights are measured
from
the optical axis.
4. Distances to the left of the surface are designated as negative and those to
the right as positive.
5. Heights above the optical axis are designated as positive and those below
the optical axis as negative.
These rules are summarized in Figure 3-3. Note that when a distance is mea-
sured in the same direction that light travels, it is positive. Distances measured in
the opposite direction are negative.
Let's use this sign convention to calculate the vergence for the object in Fig-
ure 3-1A. Since the object is located to the left of the surface, the linear distance is
−
33.00 cm. The object vergence is calculated as follows:
n
l
L
=
1.00
L
=
=
−
3.03 D
−
0.33 m
Likewise, the vergence for object in Figure 3-1B, which sits in water, is
=
−
4.03 D
L
=
−
0.33 m
