Biomedical Engineering Reference
In-Depth Information
n
l
L
=
n
l
l
=
(100)(1.00)
−
l
=
=
−
13.04 cm
7.67 D
The object is on the same side of the surface as the image (both are to the left
of the surface) but further from the surface than the image. This shouldn't be
surprising—by examining Figure 3-7, you can see that the diverging rays emitted
by the object are further diverged by the negative surface to form a virtual image
that must be closer to the surface.
The lateral magnification is
L
L
M
L
=
′
−
7.67 D
M
L
=
= +
0.61
×
−
12.67 D
The object and image have the same orientation, and the image is smaller. The
object size is calculated as follows:
+
4.00 cm
=
(
+
0.61)(object height)
object height
=
+
6.56 cm
Sample Problem 4: A Flat (Plane) Refracting Surface
A quarter is located at the bottom of an aquarium 38.00 cm from the surface of
the water. In looking down into the aquarium, how far does the quarter appear
to be from the surface? Is it magnified or minified?
If we draw the diagram correctly, as in Figure 3-8, we see that light travels
upward. This is a problem for our linear sign convention, which assumes that light
travels from left to right. There are two ways to get around this and solve the
problem. One solution is to
not
use the linear sign convention and to rely on our
understanding of vergence. The second solution is to turn the aquarium on its
side, pretend that light is traveling from left to right, and then use our linear sign
convention. I'll show you how to use both approaches, and you can decide which
works better for you.
First, let's look at the vergence approach. As can be seen in Figure 3-8, the light
rays coming from the quarter travel in water (the primary medium) and are refracted
at the water-air interface. By drawing normals to the surface and applying Snell's law,
we can see that the rays are refracted away from the normals—they diverge. These
