Biomedical Engineering Reference
In-Depth Information
2
Refraction at Spherical
Surfaces
CONVERGING AND DIVERGING
SPHERICAL SURFACES
In clinical practice, we are concerned mostly with lenses, not surfaces. But lenses
have surfaces, and this is where the action—in our case, refraction—occurs. This
chapter will help you understand how light is refracted by surfaces to form images.
It will give you a foundation for understanding lenses used in clinical practice.
Refraction does not always occur when light travels from one optical medium to
another. Figure 2-1A shows parallel light rays striking a plane (flat) glass surface.
Although there is a change in the index of refraction as the light rays travel from
the primary medium (air) to the optically denser secondary medium (glass), the
angle of incidence is zero and refraction does not occur (Snell's law). As illustrated
in Figure 2-1B, the same holds true when light rays are directed toward the
center
of curvature
(C) of the spherical surface of a glass rod; rays strike perpendicular to
the surface and are not refracted.
Now, consider parallel light rays (originating from an object located at infinity)
that are incident upon a spherical convex front surface of a crown glass rod. These
are drawn as solid lines in Figure 2-2. The dotted lines in this figure are radii that
originate at the sphere's center of curvature. The radii are normal (perpendicular)
to the sphere's surface. Rays 1, 2, 4, and 5 are each refracted toward the normal to
the surface. The amount of refraction, as given by Snell's law, is greater for those
rays that have a larger angle of incidence. Hence, ray 1 is refracted more than ray
2, and ray 5 is refracted more than ray 4. Ray 3 is not refracted at all (it is not devi-
ated) because it is normal to the glass surface and has an angle of incidence of zero
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