Page 52 - Modern Optical Engineering The Design of Optical Systems

Chapter
3

Paraxial Optics and Calculations

3.1 Refraction of a Light Ray
at a Single Surface
As mentioned in Chap. 1, the path of a meridional light ray through an
optical system can be calculated from Snell’s law (Eq. 1.3) by the appli-
cation of a modest amount of geometry and trigonometry. Figure 3.1
shows a light ray (GQP) incident on a spherical surface at point Q. The
ray is directed toward point P where it would intersect the optical axis
at a distance L from the surface if the ray were extended. At Q the ray
is refracted by the surface and intersects the axis at P′, a distance L′
from the surface. The surface has a radius R with center of curvature
at C and separates two media of index n on the left and index n′ on the
right. The light ray makes an angle U with the axis before refraction,
U′ after refraction; angle I is the angle between the incident ray and
the normal to the surface (HQC) at point Q, and angle I′ is the angle
between the refracted ray and the normal. Notice that plain or unprimed
symbols are used for quantities before refraction at the surface; after
refraction, the symbols are primed.
The sign conventions which we shall observe are as follows:

1. A radius is positive if the center of curvature lies to the right of the
surface.
2. As before, distances to the right of the surface are positive; to the
left, negative.
3. The angles of incidence and refraction (I and I′) are positive if the
ray is rotated clockwise to reach the normal.

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