Biomedical Engineering Reference
In-Depth Information
2
Principles of
Geometric Optics
2.1
Introduction ........................................................................................29
2.2
Relection .............................................................................................29
2.3
Refraction............................................................................................. 31
2.4
Paraxial Lens Equation ......................................................................32
2.5
hin Lens Equation ............................................................................34
Joel A. Kubby
University of California
at Santa Cruz
2.6
Magniication ......................................................................................39
2.7
Aberrations ..........................................................................................40
2.1 Introduction
In this chapter, we consider geometric optics, which is an approximation to wave optics that can be used
when considering an optical system composed of elements that are much larger than the wavelength of
light going through the system. hen, we can ignore the wave nature of light, aside from its color, and
assume that it will travel in a straight line, which is oten called a ray. Although geometric optics is only
an approximation to wave optics, it is technologically useful for the design and modeling of the adaptive
optical systems that will be considered here. It greatly simpliies the calculations to a point that allows
intuition to guide the design. his is not usually the case when considering the Huygens integral!
To determine the direction in which a light ray will pass through an optical system, we can apply
Fermat's principle of least time or shortest optical path length that was discussed in Chapter 1. Fermat's
principle is that the optical path distance
OPD
between points
A
and
B
given by
B
∫
( )
OPD A,B
(
)
=
n x
d
x
(2.1)
A
is shorter than the optical path length of any other curve that joins these points and lies in its certain
regular neighborhood (Born and Wolf, 2006).
2.2 Relection
We consider the application of Fermat's principle to two simple optical surfaces: a mirror that relects
light and an interface between two media that refracts light. With these two simple optical surfaces,
we can understand the most important aspects of geometrical optics for the design of optical systems.
In
Figure 2.1
,
we show a mirror surface where a light ray starting from point
A
is relected of the mir-
ror surface to reach point
B
. he question is what path will the light ray take? If we assume that the
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