Biomedical Engineering Reference
In-Depth Information
to the vergence relationship, the vergence of the light rays that form the image is
the sum of the incident vergence and the surface power:
L
′
=
L
+
F
L
′
= −
2.00 D
+
(
+
5.00 D)
= +
3.00 D
Be sure to note that in Figure 3-5 and subsequent figures where we solve opti-
cal problems, the object vergence and surface power are indicated above the
surface. In this case,
L
is
−
2.00 D and
F
is
+
5.00 D. The sum of these, the image
vergence,
L
3.00 D, is given below the refracting element. It's a good
idea to get into the habit of labeling your diagrams like this.
′
, which is
+
Since converging light rays form the image, it is real. Where is it located? The
rays that form the image have an image vergence of
3.00 D.
These rays exist in the
secondary medium
(glass), which has an index of refraction of 1.52. Therefore, to
calculate the distance at which the image rays converge, we use the secondary index
of refraction as follows:
+
n
′
l
′
′
=
L
or
n
L
′
l
′
=
1.52
′
l
=
= +
0.5067 m, or
+5
0.67
cm
3.00 D
Alternatively, the image distance in centimeters may be calculated by placing a
factor of 100 in the numerator
5
:
(100)(1.52)
+
′
l
=
= + 5
0.67 cm
3.00
The image is located 50.67 cm from the surface. Is it to the left (as is the object)
or right? Since the value is positive, our linear sign convention tells us that the
image is located 50.67 cm to the right of the surface. (But we really shouldn't need
to rely on our linear sign convention to tell us this since we know that an image
formed by converging light rays must be located to the right of the surface.)
It is helpful to visualize the light rays in terms of their vergence. In the cur-
rent example, diverging light rays (
+
−
2.00 D) are incident upon a converging surface
(
3.00 D) to form a real image.
To calculate the image size, we need to know the lateral magnification (
M
L
)
produced by the surface, which we defined in Chapter 2 as the ratio of the image
+
5.00 D). Upon refraction they converge (
+
5. If a factor of 1000 is placed in the numerator, the calculated distance would be in millimeters.
