Biomedical Engineering Reference
In-Depth Information
n
L
′
′
=
l
(100)(
1.52
)
+
′
=
l
= +
126.67 cm
1.20 D
If the back surface did not exist, a real image would be located 126.67 cm to
the right of the front surface (and situated in glass). However, this image is never
formed—it serves as a virtual object for the back surface. What is the object ver-
gence at the back surface? Taking into account the thickness of the lens, we cal-
culate that the virtual object is located 124.67 cm to the right of the back surface
(126.67
124.67 cm).
The rays that form this virtual object exist in
glass.
Therefore the object vergence at the back surface is
−
2.00 cm
=
n
l
L
=
(100)(
1.52
)
+
L
=
= +
1.22 D
124.67 cm
The vergence relationship is used to calculate the image vergence produced by
the back surface:
L
′
=
L
+
F
11.62 D
Since the rays are converging, the image is real. Where is it located?
The light
rays that form the image live (i.e., exist) in air; therefore, we use the index of
refraction of air to locate the image:
L
′
=
+
1.22 D
+
(
+10
.40 D)
= +
n
′
′ =
L
′
l
n
L
l
′ =
′
(100)(
1.00
)
+
′ =
= +
8.61 cm
l
11.62 D
The final image is located 8.61 cm to the right of the second surface.
The total lateral magnification of the thick lens is calculated by multiplying the
lateral magnification produced by the first surface by the lateral magnification pro-
duced by the second surface:
Total lateral magnification
=
(
M
L
for first surface)(
M
L
for second surface)
−
4.00 D
+
1.22 D
⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
Total lateral magnification
=
= −
0.35
×
+
1.20 D
+
11.62 D
