Geometrical Optics 2

For over 100 years, from the time of Newton and
Huygens in the late 1600s, until 1801 when Thomas
Young demonstrated the wave nature of light with his
two slit experiment, it was not clear whether light
consisted of beams of particles as proposed by Newton,
or was a wave phenomenon as put forward by Huygens.
The reason for the confusion is that almost all common
optical phenomena can be explained by tracing light
rays. The wavelength of light is so short compared to
the size of most objects we are familiar with, that light
rays produce sharp shadows and interference and
diffraction effects are negligible.
To see how wave phenomena can be explained by ray
tracing, consider the reflection of a light wave by a
metal surface. When a wave strikes a very small object,
an object much smaller than a wavelength, a circular
scattered wave emerges as shown in the ripple tank
photograph of Figure (36-1) reproduced here. But
when a light wave impinges on a metal surface consisting
of many small atoms, represented by the line of dots
in Figure (36-2), the circular scattered waves all add
up to produce a reflected wave that emerges at an angle
of reflection ?r equal to the angle of incidence ?
i .
Rather than sketching the individual crests and troughs
of the incident wave, and adding up all the scattered
waves, it is much easier to treat the light as a ray that
reflected from the surface. This ray is governed by the
law of reflection, namely ?r = ?
i .
reflected wave
incident wave
angle of
incidence
angle of
reflection
?i ?r
angle of
incidence
mirror
angle of
reflection
?i ?r
Figure 36-2
Reflection of light. In the photograph, we see an incoming plane wave scattered by a small object. If the
object is smaller than a wavelength, the scattered waves are circular. When an incoming light wave strikes
an array of atoms in the surface of a metal, the scattered waves add up to produce a reflected wave that
comes out at an angle of reflection ?r equal to the angle of incidence ?i .
Figure 36-1
An incident
wave passing
over a small
object produces
a circular
scattered wave.
Light ray
reflected
from a
mirror.
incident wave
Optics-2
The subject of geometrical optics is the study of the
behavior of light when the phenomena can be explained
by ray tracing, where shadows are sharp and
interference and diffraction effects can be neglected.
The basic laws for ray tracing are extremely simple. At
a reflecting surface ?r = ??i , as we have just seen. When
a light ray passes between two media of different
indexes of refraction, as in going from air into glass or
air into water, the rule is n1 s in?1 = n2 sin?2 , where
n1 and n2 are constants called indices of refraction,
and ?1 and ?2 are the angles that the rays made with
the line perpendicular to the interface. This is known
as Snell’s law.
This entire chapter is based on the two rules ?r = ??i
and n1 s in?1 = n2 sin?2 . These rules are all that are
needed to understand the function of telescopes, microscopes,
cameras, fiber optics, and the optical components
of the human eye. You can understand the
operation of these instruments without knowing anything
about Newton’s laws, kinetic and potential energy,
electric or magnetic fields, or the particle and
wave nature of matter. In other words, there is no
prerequisite background needed for studying geometrical
optics as long as you accept the two rules
which are easily verified by experiment.
In most introductory texts, geometrical optics appears
after Maxwell’s equations and theory of light. There is
a certain logic to this, first introducing a basic theory
for light and then treating geometrical optics as a
practical application of the theory. But this is clearly
not an historical approach since geometrical optics
was developed centuries before Maxwell’s theory. Nor
is it the only logical approach, because studying lens
systems teaches you nothing more about Maxwell’s
equations than you can learn by deriving Snell’s law.
Geometrical optics is an interesting subject full of
wonderful applications, a subject that can appear
anywhere in an introductory physics course.
We have a preference not to introduce geometrical
optics after Maxwell’s equations. With Maxwell’s
theory, the student is introduced to the wave nature of
one component of matter, namely light. If the focus is
kept on the basic nature of matter, the next step is to look
at the photoelectric effect and the particle nature of
light. You then see that light has both a particle and a
wave nature, which opens the door to the particle-wave
nature of all matter and the subject of quantum mechanics.
We have a strong preference not to interrupt
this focus on the basic nature of matter with a long and
possibly distracting chapter on geometrical optics