he Nature and

Propagation of Light
- 1 INTRODUCTION Key Concepts
es, ochre deserts, green forests, and multicolored rainbows can
Light is an electromagnetic
r enjoyed byanyone who has eyes with which to see them. But by wave. Its propagation can be
ing the branch of physics called optics, which deals with the behav described by wave fronts or
f lieht and other electromagnetic waves, we can reach a deeper rays. Light also has particle
iation of the visible world. A knowledge of the properties of light
4preciat quantum) aspects.
to understa the blue color of the ský and the design of opti-
alows us
l&ices such telescopes, microscopes, cameras, eyeglasses, and the
as In geometric optics, light is
aneye. The same basic principles of optics also lie at the heart of
ndim developments such as the laser, optical fibers, holograms, opti-
described by rays that travel
in straight lines in a homoge
al computers, and new techniques in medical imaging. neous material. At an
The importance of optics to physics, and to science and engineering interface between two mate-
in general, is so great that we will devote the next five chapters to its rials, a ray is in general pardy
Sudy. In this chapter we begin with a study of the laws of reflection and reflected and party transmit
reiraction and the concepts of dispersion, polarization, and scattering of ted. In special cases a ray
of
hght. Along the way we compare the various possible descriptions may be totally reflected.
ight in terms of particles, rays, or waves, and we introduce Huygens
principle, an important link that connects the ray and wave viewpoints. The optical properties of a
In Chapters 35 and 36 we'll use the ray description of light to understand material are described by its
ow mirrors and lenses work, and we'll see how mirrors and lenses are index of refraction. The
Sed in optical instruments such as cameras, microscdpes, and tele- dependence of index of
Scopes. We'll explore the wave characteristics of light further in Chapters refraction on wavelength is
Si and 38. called dispersion.

Light is a transverse wave

and has polarization. Any light
34-2 THE NATURE OF LIGHT wave can be described as a

Uti the timeoflsaac Newton (1642-1727), most scientists thought that superposition of waves polar-
ized in two perpeFdicúlar
OnSIsted of streams of particles (called corpuscles) emittedtheby light directions. A polarizing filter"
aileo and others tried (unsuccessfully) to measure speed
é to be passes only waves with
a
of
d Around 1665, evidence of wave properties light is a wave began
specific direction of polariza
Ted.
ad
By the early nineteenth century, evidence that light
grown very tion.
In 873, Jamespersuasive. electro-
Clerk Maxwell predicted the existence of
magnetic waves a as we learned The scattering of light by a
in waves and calculated their speed of propagation, depends on wavelength.
hapter 33. This with the experimental
work of gas
development,
Heinrich Hertz starting alongconclusively
in 1887, showed that light is indeed Scattered light is partly polar-
21 electromagnetic wave.
ized.
The
v e picture of light is not the whole story, reveal particle
Several
owever.

Huygens' principle states that

apect, associated
i that the with emission a
energy cariedand
by light wavesofis light
absorption packaged in discrete every point in
a wave front

be considered as the
calledproperties
and partiucle photons or quanta. These parently contradictory wave
have been reconciled since 1930 with the devel-
can
source of secondary
opment wavelets that spread out
from
incudeses ofbothquantumandelectrodynamics,
st wave
a
particle properties.
comprehensive theory that
The propagation of light is
the wave front
with definite

described by a wave
requires a particle model, understand
but emission and absorp- speed.
approach.
 CHAPTER 34 THE NAT

054
The fundamental
sources of radiation are electric
all electromagnetic radiation

accelerated
motion. AIl
dies
bodies emit electromagnetic radiation
this radiation,called nal
charges n
motion of
their molecules; is a radiation, Aturetherof mdia.
mixture
At sutficiently high temperatures, all matter
ferent wavelengths. hot body appears "red hot" or ugh vishle
to be self-luminous, a very "white hot. Thus br
light
matter in any form is a light source. Famili examples are a candle fla
in an electric room
me, hot coals
heater, and an incandescen
campfire, the coils
a

(which usually operates

at temperature of about 3000°C).
a filamen
Light is also produced during electrical discharges through ionized es
light of mercury-arc lamps, the orange-yellow of jum-vapor lamps, and The bluirsh
the vanions
are familiar. A variation mercury-arc lamn is he fluorer
of the
colors of "neon" signs
cent lamp. This light source uses a material called a phosphor to convert the ultraviole
radiation from a mercury arc into visible light. This conversion makes fluoresce
more efficient than incandescent lamps in converting electrical energy into light tla-
A light source that has attained prominence in the last thirty years is the ln
most light sources, light is emitted independently by different atoms within the so
in a laser, by contrast, atoms are induced to0 emit light in a cooperative, coherent fadk
The result is a very narrow beam of radiation that can be enormously intense and th
much more nearly monochromatic, or single-frequency, than light from any th
source. Lasers are used by physicians for microsurgery, in CD players and computern
scan the information encoded on a compact disc or CD-ROM, in industry to cut toa
steel and to fuse high-melting-point materials, and in many other applications.
No matter what its source, electromagnetic radiation of all types travels in vacum
at the speed of light. The first approximate measurement of the speed of light was nac
in 1676by the Danish astronomer Olaf Roemer, from observations of the motion of om
of Jupiter's satellites. The first successful terrestrial measurement was made by te
French scientist Armand Fizeau in 1849, using a reflected light beam interupieii
notched rotating disk. More refined versions of this experiment were caied out e
the nineteenth century by Jean Foucault in France and by Albert A. Micheison in e

United States.
From analysis of all measurements up to 1983, the most probable value for tne sp

of light at that time was

c 2.99792458 x 10 m/s.
As we explained in Section 1-4, the definition of the second based on the cE
is precise to within one part in 10 trillion (10*). Up to 1983 the definitonot
was much less precise, about four parts in a billion (10). Any attempt o
speed of light with greater precision foundered on this limitation. Fortnis the meer

November 1983 the General Conference of Weights and Measures redeins

by defining the speed of light in vacuum to be precisely 299,792,458 ms.
now defined to be the distance traveled by light in a time of 1/299,792.-4>
second defined by the cesium clock.

WAVES, WAVE FRONTS, AND RAYS

often use the We inard
We
this
concept of a wave front to describe wave propag opagation.
o r eg e n e a l ,"

concept in Section 33-3 to describe the vbranine

define a wave front as the locus leading edge of awave
of all adjacent points at which the pr nstant,all
punis

a physical quantity associated with the wave is the same. That is, at any
on a wave front wave

are at the same part of the cycle of their

variation. by
the

When we drop a m e d
tionts

pebble into a calm pool, the expanding circies wave

crests, as well as the circles formed are
Whene
the by wave troughs between n
hem,

Similarly, when sound waves spread out in still air from a

pointlike s
 N AND REFRACTION

diation spreads out from

mmagnetic
is
a

front,
pointlike emitter, any 1055
with the
draw only
source a wave

of
as shown in spherical surface that is
Fig. 34-1.
we usually few wave In
fronts, often diagrams of wave
a
ndon

that have the same phase and thus are one choosing
waterwav
vaves. Similarly, a diagram for
sound waves
wavelength apart, suchconsecutive
as crests
Point
sOurce
rsts h e sSurface
which the pressure
ver might show only the
is
etic wavesnicht show only the"erests
maximum, and "pressure
the electricdiagram
a
on which for electro-
or
mum.

use diagrams that:show the

magnetic fieldis
Wewill often shapes of the wave fronts or
ference For plane. example, when their cross sec-
electromagnetic waves
nonsu ns a

uirce, we can
represent the wave fronts are
by radiated
spherical surfaces concentric
as
S m a t

or. as in Fig. 34-2a, by the

sourc
circular intersections of these surfaces with
Far away from the
of the diagram. Far
source, where
large,section of a spherical surface can be the radii of the spheres have 34-1
a
like those discussed in Sections considered as a plane, and we Spherical wave fronts
a plane wave
33-3 spread out uniformly in all
direc-
describe the directions in wnicn ignt propagates, and
heve
33-4 (Fig. 34-2b). tions from a
it's often convenient to poiut source in a
a light wave by rays rather than by wave fronts. repre- motionless medium, such as still
beforeits wave nature was firmly
Rays were used to
describe lieht air, that is homogeneous and
ng established. In a
particle theory of light, rays are isotropic (that is, has the same
ofthe
paths narticles. From the wave
the particles.
ray viewpoint a is an properties in all regions and in all
tion of travel of the wave. In imaginary line along the
Fig. 34-2a the rays are the radii of the spherical wave directions). Electromagnetic
imnts, and in Fig. 34-2b they are straight ines waves in a vacuum also
perpendicular to the wave fronts. When
as shown here.
spread out
w2ves travel in a homogeneous isotropic material
(a material with the same properties
itnallregions and in all directions), the rays are always straight lines normal to the wave
fronts. At a boundary surface between two materials, such as the
surface of a glass plate
in air, the wave speed and the direction of a
aT and in the glass are straight lines.
ray may change, but the ray segments in the
Rays
The next several chapters will give you
many opportunities to see the interplay of the
ay wave, and particle descriptions of light. The branch of
optics for which the ray
desciption is adequate is called geometric optics; the branch dealing specifically with
wve behavior is called
physical optics. This chapter and the two ones are following Source
COBCerned mostly with
geometric optics. In Chapters 37 and 38 we will study wave phe- Wave frmnts
1omena and
physical optics. (a)

34-3 REFLECTION AND REFRACTION Rays

s Section we'll use the ray model of light to explore two of the most important
2spectshght propagation: reflection and refraction. When a light wave strikes a
and
glascthac SCparating two transparent materials (such as air and glass or water the nd

e Wave is in general partly reflected and partly refracted (transmitted) into

ate al, as shown in Fig, 34-3a (page 1056). For example, when you look into Wave fronts
ind window from the street, vou see a reflection of the street scene, but a person
(b)
reaches
urant can look out through the window at the same scene light
as
nim by refraction. 34-2 Wave fronts and rays.
The s bundles of (a) When the fronts are
wave

rays forming O plane waves shown in Fig. 34-3a can be represented by radiate out from
beams of draw only one ray in spherical, the rays
h beam ( ig. 34-3c).ght (Fig. 34-3b). For simplicity we often of geo the center of the spheres. (b) When
TDetric Represer
Senting these waves in
terms of rays is the basis
fronts are planes, the
NeCGptics. egin our study with the behavior of an individual
the wave
ray. are paraile.
rays
refracted (transmitted) rays
incident, reflected, and
of the
mooth interface between
ons
two materials in terms
of the angles they make
normal to the surface at theoptical
point of incidence, as shown in Fig. 34-3c. Ifthe
1S rough, both the transmitted light and the reflected light are scattered in yar-
Ous directions, and a
reflection. Retflection at
definite angle from a
n o Single angle of transmission reflection (from
or
the Latin
very
a y Smooth surface is called specular
 Incident

rays

Incident
wave

Refrncel
tays
Rcfracted
wave Reflected
rays a b
Reflected
wave (b)

SHOP Incident
ray

Normal

(a)
Refracted
ay
34-3 (a) A plane wave is in pat
reflected and in part refracted at Reflected
a b
the boundary between two media ray
(in this case, air and glass). The (c)
light that reaches the inside of the
coffee shop is refracted twice,
word for "mirror"); scattered reflection from a rough surface is called diffuse reflection
once when it enters the glass and
This distinction is shown in Fig. 34-4. Both kinds of reflection can occur with either
once when it exits the glass. (b)
The waves in the outside air and in transparent materials or opaque materials that do not transmit light. (In Section 33-6e
glass in (a) are represented by described why metals are opaque.) The vast majority of objects in your environmem
Trays. (c) For simplicity, only one (including clothing, plants, other people, and this book) are visible to you because hey
example of an incident ray, a reflect light in a diffuse manner from their surfaces. Our primary concerm, however, wi
reflected ray, and a refracted ray is be with specular reflection from a very smooth surface such as highly polished glas.
drawn. For the case shown here, plastic, or metal. Unless stated otherwise, when referring to "reflection" we will aways
material b has a greater index of
mean specular reflection.
refraction that material a (n, > n,)
The index of refraction of an optical material (also called the refractive inder.
and the angle 0, is smaller than e denoted by n, plays a central role in geometric optics. It is the ratio of the speed of g
c in vacuum to the speed v in the material:

n =
Cindex of refraction). 4-1

W
LIght always travels more slowly in a material than in vacuum, so the value ot n na

thing other other than a vacuum is always greater than unity. For vacuum, n=1. >
eofn
1s of
aratio two speeds, it is a pure number without units. (The elation of the
to the electric and -6.)
ane
magnetic properties of a material is described
in
Section the
CAUTION> Keep in mind that the wave speed v is inversely
(a) index of refraction n. The prop r the
greater the index of refraction in a material, tne o
wave speed in that material.
Failure to remember this point can lead to no
fusion!

LAWS OF REFLECTION AND

REFRACTION
Experimental studies of the directions of the incident, reflected, and refractcu
Smooth interface between usions:
twooptical materials lead to the following conc
1. The incident, a lle
(b) reflected, and refracted rays and the norma mal to the
surfac
plane ne
in the same of
34-4 (a) plane. The plane of the three rays is perpendicular to the
Specular reflection. boundary surface between the two materials. We
Cndicular u ms so
(b) Diffuse reflection. the incident, always draw ray alag
reflected, and refracted rays are in the plane of the diagra
 NEPLECTTON AND REFRACTION

of reflection
6, is equal to the angle of 1057
2 Theangle
incidence 0, for all
nd for any pair ofmaterials. That is, in Fig. 34-3e, wavelengths
e, =. (law of reflection).
(34-2)
This
lation,
e l together with the observation that the
incident and reflected
in the same plane, is called the law of
liein rays and
the norma
all reflection. Incident
nochromatic light and for a given pair of materials, a and b, on opposite sides
3 .Formonochr

ray
the ratio of the sines of the angles
the interface. th
0, and e,, where both
are easured from the normal to the surface, is equal to the inverse ratio angles
of
Normal
of the
_

wo
indexes of refraction:
Refracted
sine Reflected
ray
sin 6, (34-3) ray
h

S i n ea = n, Sin e, (law of refraction). 34-5 Reflection and refraction in

(34-4) the case in which material b has a
This experimental result, together with the observation that the incident and refracted smaller index of refraction than

normal all lie in the same plane, is called the law of refraction or Snell's material a, so n, < n, The
ravs and the refracted angle 6, is greater than
scientist Willebrord Snell (1591-1626). There is some doubt
law, after the Dutch the incident angle Compare to
thatSnell actually discovered it. The discovery that n clo came much later.
=

Fig. 34-3c, which shows the situ-

from one material (a) into ation for n,> na
Bquations (34-3) and (34-4) show that when a ray passes
index of refraction (n, >n,) and hence a slower wave
another material (b) having a larger
normal is smaller in the second material than the angle 0, in
speed, the angle 6, with the
toward the normal (Fig. 34-3c). When the second
mate-
the first; hence the ray is bent
material (n, < n,) and hence a faster
ri2l has smaller index of refraction than the first
a
the nor1mal (Fig. 34-5). This explains why par-
a
wave speed, the ray is bent away from
from below the
straw appears bent; light rays coming
tially submerged ruler or drinking so the rays appear to be coming
surface change in direction at the air-water interface,
34-6).
from a position above their actual point of origin (Fig.
interface between vacuum,
An important special case is
refraction that occurs at an
When a ray passes
0r which the index of refraction is unity by
definition, and a material.
bent toward
vacuum into a material (b), so that n,
= l and n,> 1, the ray is always
Om > I and n,
=
1,
from a material into vacuum, so that n,
e Dormal. When a ray passes
e ray is always bent away from the normal.
transmitted ray is not
either side of the interface, the
NO matter what the materials on incident ray is perpen-
incidence, in which the 34-6
(a) This ruleris actualy
normal this m e a n s that 6,
a t all in the special case of sin 0,= 0. From Eq. (34-4) straight, but it appears
to bend at

that 6, =0 and of the water (b) Light

L h e interface so is also perpendicular to the intertace. the surface
s transmitted ray the interface object
u a l to zero, so the regardless of which side of rays
from any submerged
and refraction apply 34-3c or from the normal when
laws of reflection approaches the interface in Fig. bend away
into the air. As
seen
comes from. If a ray
of light reflected and refracted they emerge
E dent ray rather than from
the left, there
are again
observer above the surfare
O m
the right by an to
water, the object appears
of the surface than
closer to the
Observer be much
it actually is.

, (air) I.00
Apparent pasition
nwater) = 1.33
ofnuler
of end
Actual position

ofruler
of end

(b)
 the incident ray, and
the normal to the surface again lie i
surfa.

rays:
these two rays,
the
refracted ray
path of a ref
is reversible; it foll the same
the same path
to b. (You can
Furthermore,

when going from.

plane.
from b to a as incident verify this usino
when going rays make tthe same angle with the
4).) Since
reflected and
mal, the path
(34
of a reflected ray is
also reversible.
That s why
when you
omeone's eyes in
see someone
a
mir.
can also see you.
or, they rays depend on the angle of
and retracted
The intensities of the
reflected incidence
oe :

and the polarization (that is, the directi n of the

indexes of refraction,
the two
ray. The fraction reflectedis smallest at norma electhic
ficld vector) of the incident 4% lor an aif-glass intertace. This fraction in incidence
( = 0°). where it is about reases with
incidence to 100% lence, when , =90°.
at grazing inciden
increasing angle of
we have described
the laws of retlection and refraction as exma.
Although
also be derived from
a wave model using Maxwell's. erimental
they
polarizatic This
results, can
the amplitude, intensity, phase, and
analysis also enables us predict
to
waves. This beyond our scope, howedes
analysis is
of the reflected and refracted
The index of refraction depends not only on the substance but also on the wavel
jelength
of the light. The dependence on wavelength 1s called dispersion; we will considerrit in
Section 34-5. Indexes of refraction for several solids and liquids are given in Table 34-|

for aparticular wavelength of yellow light.

The index of refraction of air at standard temperature and pressure is about 10003
and we will usually take it to be exactly unity. The index of refraction of a gas incTeas
as its density increases. Most glasses used in optical instruments have indexes ofretae
tion between about 1.5 and 2.0. A few substances have larger indexes; two examples are
diamond, with 2.417, and rutile (a crystalline form of titanium dioxide), with 2.62.

INDEX OF REFRACTION AND THE WAVE ASPECTS OF LIGHT

We have discussed how the direction of a light ray changes when it passes from one
material to another material with a different index of refraction. It's also important to see
what happens to the wave characteristics of the light when this happens.
.First, the frequency fof the wave does not change when passing from one matenal
to another. That is, the number of wave cycles arriving per unit time must equal the nu

ber leaving per unit time, this is a statement that the boundary surface cannot craare or
destroy waves.
Second, the wavelength A of the wave is different in general in different nals

TABLE 34-1
INDEXOF REFRACTION FOR YELLOW SODIUM LIGHT (A, =589 nm)
INDEX OF INDEN OF
SUBSTANCE REFRACTION, n SUBSTANCE REFRACTON,

Solids
lce (H,0)
Liquids at 20°C
1.309 Methanol (CH,OH) .329
Fluorite (CaF) 1.434
Polystyrene 49
Water (H,0) .333

Rock salt (NaC)) Ethanol (C,H,OH) 1.36

1.544 Carbon tetrachloride (CCL) 460
Quartz (Sj0,) 1.544
Turpentine 1472
Zircon (Zr0, Sio,) 1.923
Diamond (C) Glycerine I.473
2.417 Benzene
Fabulite (STiO,) .501
2.4 Carbon disulfide (CS.)
Rutile (Ti0,) I.628
Glasses (1ypical values) 2.62
Crown
Lighi fint I.52
Medium flint T.58
Dense flint 1.62
1.66
Lanthanum flint
 34-3
REFLECTION AND
REFRACTION
because
in any material, v =Af; since f is the same in any 1059
his
is
than the wave speed e in vacuum, 2 is material as in vacuum
of Ilight in a material is less thañ alsó
ecth AA of
wavelength reduced. corespondingly
the
Thos
the
From the
ahr
discussion,. f= clà, vla. wavelength A, of the
= same
Combining
v a c u u m .

in this with Eq
hht we find

4-1).m=ct,
(wavelength of light in a
material).
(34-5)
passesffrom
ASSes
When&wave one material into a second
material with larger index
n, and the wave speed
of refrac.
so that n,
> creases, the wavelength
d material is shorter than the wavele 2, = A,/n, in the first A, An/n,
=
material. in the
If instead
d material has a smaller dex of refraction than the first material, so
t hs n c o n d

ndthewave speed increases, the velength A, in the second material thatthan

is longer <r
n, <n,
the
in the first material. This makes intuitive sense; the waves
wZVelen
get "squeezed"
the wavelength gets shorter)if the wave speed decreases and get "stretched" (the wave
kngth gets longer)
if the wave speed increases.

Probiem-Solving Strategy
REFLECTION AND REFRACTION
1. n geometric optics problems involving rays and angles, 3. You will often have to
aheays start by drawing a large, neat diagram. Label all
use some
simple geometry or
trigonometry in working out angular relations. The sum
known angles and indexes of refraction. of the interior angles in a triangie is 180°, an angle and
2 Remember to always measure the angles of incidence, its complement add to 90°, and so on. Ask yourself
reflecion, and refraction from the normal to the surface "What information am I given?" "What do I need to
where the reflection and refraction occur, never from the know to find this angle?" or "What other angles or other
surface itself. quantities can I compute using the information given in
the problem?"

ELAMPLE 34-1
ecion and refraction In Fig. 34-7, material a is water and Normal
aeial bis a glass with index of
refraction 152. If the incident
makes an angle of 60° with the normal, find the directions of
te reflected 60°1
and refracted rays.
133
n, (water) =
LUTON According to Eq. (34-2), the angle the reflected ray b ,glass)
cs with the normal is the same as that of the incident ray, so
,0 60.0.
id the direction of the refracted ray, we use Snell's 1aw
4), with n, = 1.33,n= 1.52, and , = 60.0°. We find refraction of light passing trom water to
34-7 Reflection and
n,sin 8, n, sin 6, glass.
refractive index than the first;
The second material has larger normal as the
a
51n 6, wave slows
=
sin 6, 2 sin 60.0
= =
0.758,
the refracted ray is
bent toward the
1.52 material.
second
6, = 49.30 down upon entering the

EXAMPLE 34-2 in air and v a c u u m are

the
that the wavelengths material is
rom a refraction in the eye The wavelen of the red light
so we a s s u m e
A in the
given by Eq.
queoushelium-
Then the wavelength
laser is 633 in airbut nm 474 nm in the
same.

humor inside (34-5)

your yeball. Calculate the index of 633 om 1.34,
he of the aqueous humor =

light in this and the speed and frequency of n 474 nm

substance. as for water.
Then

OLUTION The index

index of refraction
refraction

same
index of
ne which is about the
of air is very close to
unny
 CHAPTER 34 THE NA
1060
Note that while the speed and
wavelen have
n = clv gives in air and in the aqueous humor,
frequency differen
S00 X10 S 2.25 x 10 m/s. same as the frequency f in the in
aqueous humor: air, f, is
valves
= =
=
the
I.34
So 3.00x 10 m/s =
4.74 x 10"
Finally, from U = Af. 633x 10 m Hz
2.25 x 10" m/s = 4,74 x 10'" Hz.
f 474 x 10 m

EXAMPLE 34-3
perpendicular to cach
Two mirors are
A twice-reflected ray
to both mirrors is
other. A ray traveling
in a plane perpendicular
then the other, as shown in Fig. 34-8.
reflected from one mimor,
What is the final direction relative to its original direction?
ray's
sOLUTION For mirror 1 the angle of
incidence is e,, and this

equalsthe angle of reflection. The sum of interior angles in the 90°-67

90-0,
triangle shown in the figure is 180°, so we see that the angles of
incidence and reflection for mirror 2 are both 90° ,.The
total
reflections is therefore Mirror 2
change in direction of the ray after both
180°. That is, the ray's final direction is
2(90° 8,)+28, =

opposite its original direction.

to
An alternative viewpoint is that specular reflection reverses
the sign of the component of light velocity perpendicular to the 90-,
surface but leaves the other components unchanged. We invite
Miiror 28
you to verify this in detail. You should also be able to use this
result to show that when a ray of light is successively reflected
by three mimors forming a corner of a cube (a "corner reflec 34-8 A ray moving in the xy-plane. The first reflection changes
tor"), its final direction is again opposite to its original direction. the sign of the y-component of its velocity, and the second
This principle is widely used in tail-light lenses and highway reflection changes the sign of the x-component. For a difteret
signs to improve their night-time visibility. Apollo astronauts ray with a z-component of velocity, a third miror (perpendiuls
placed arrays of corner reflectors on the moon. By use of laser to the two shown) could be used to change the sign of that com
beams reflected from these arrays, the earth-moon distance has ponent.
been measured to within 0.15 m.

34-4 TOTAL INTERNAL REFLECTION

Lnter

We have described how light is partially reflected and partially transmitted ara
certaun

face between two materials with different indexes of refraction. Under wh

interface.
circumstances, however, all of the light can be reflected back fron
rom the
Figux
none of it being transmitted, even though the second material is transparcit s O u Y

34-9a shows how this can occur. Several rays are shown radiating from a p o n t
Pin material a with index of refraction n. The rays strike thesurface
: ofa second
váterand

rial b with index n, where n, >n,. (For instance, materials a and b coula
air, respectively.) From Snell's law of refraction,
sin 6, = sin , .
n
Because bent awaya w
nJn, is greater than unity, sin 6, is ray is
larger than sin , the ray
the normal. Thus there must be some value of
6, less than 90° for whicn
esjiust

gives sin 6,=1 and e, 90°. This is shown by ray 3 in the diagram, W Fig
= A-9

in Fig.
in
grazing the surface at an angle ofrefraction of 90°. Compare the diagram a m

to the photograph of
light rays in Fig. 34-9b.
 Ci

(a) (b)

34-9 (a) Total internal teflection.

for which the retracted ray emerges tangent to the surface is
The angle of incidence The angle of incidence for which

d the critical angle, denoted by eri (A more detailed analysis using Max well's the angle of refraction is 90° is
callec

shows that as the angle approaches the critical angle, the transmitted
ident called the critical angle; this is the

zero.) If the angleotincidence is greaterthan the critical angle, the case for ray 3. The reflected por
equations

approache;
intensity tions of rays 1, 2, and 3 are
sineofthe angleof refraction,as computed by Snell's law, would have to begreaterthan omitted for clarity. (b) Rays of
Beyond the. critical angle, the rav cannot pass into theupper
nity, which isimpossible. reflected at the boundary
laser light enter the water in the
material; it is trapped in the lower materta-and-is completely
internal reflection, occurs, only when a raV Is inci
fishbowl from above:; they are
Tface. This Situation, caied total reflected at the bottom by mirors
material whose index of refraction is smaller than
ent on the interface with a second tited at slightly different angles.
and one ray undergoes total inter-
thatofthe material in which the ray is travetng.materials 90° (sin 0, l)
by setting 0, =
nal reflection at the air-water
we can find thecritical angle for íwo gíven
=

interface.
in Snell's law. We then have

Sinr i t 2 (critical angle for total internal reflection). (34-6)

na
Total internal reflection will occur if the angle of incidence 0, is greater than or equal

AS an example, for a glass-air surface with n = 1.52 for the glass,

ri 1.52=
Ocrit41.1°.
sin .ri
sin 0.658,

if it strikes the glass-air sur

pagating within this glass will be totally reflected is than 45, t
Because the critical angle slightly less
c angle of 41.1° or greater. surtace. As
d

te o prism with angles of 45°45°-90° as a totally reflecting

use a
metallic surtaces sueh as
Grd Otally reflecting prisms have some advantages over
100% of the light inC
dent ed-glass mirrors. While no metallic surface reflects
dent on it, lightcan be totally reflected by a prism. The reflecting properties of a prism
and unaffected by tarnishing.
A 45MOdadvantages of being
permanent
445-90° prism, used as in Fig. 34-10a (page 1062), is called r ch
Light enters and leaves at the hypotenuse and is totally
reflected at each
ofthe shorter faces. The rightchange
total angles of direction
to of the rays is 180°. Binoculars often
lse
combinations oftwo Porro prisms, as in Fig. 34-10b.
index of refraction
rilliance
n =2.417) and of diamond is due in rge measure to its very high is
diamond
angle. Light entering
a cut
totally internally ndingly high critical
surface, then emerges
from the ftront
Surface. "Imitation diamond"
drom gems, such as cubic zirconia, are made from less expen
facets on its back
siveve crystalline
materials
When a beam of lightwith
enters one endindexes
atparable
com of refraction.
of a transparent rod (Fig. 34-1D, the light
can be
totally refle tCrnally if the index of refraction of
than unat
the rod is greater
 CHAPTER 34 THE NATURE AND PROPAGATION OF LIGHT
1062

b) 34-11 A transparent rod with refractive index greater

(a) than ths
of the surrounding material. A light ray is "rapped" bv intem
34-10 (a) Total intenal reflection in a Porro prism. (b) A com- reflections within the rod, provided that the angles shown exce
bination of tuwo Pomo prisms in binoculars.
the critical angle.

of the surrounding material. The light is "trapped'"' within the rod even if thedd
curved., provided that the curvature is not too great. Such a rod is sometimescale
light pipe. A bundle of fine glass or plastic fibers behaves in the same way and has te
advantage of being flexible. A bundle may consist of thousands of individual fibers.eah
of the order of 0.002 to 0.01 mm in diameter. If the fibers are assembled in the bundle
so that the relative positions of the ends are the same (or mirror images) at both ends, te

bundle can transmit an image, as shown in Fig. 34-12.

Fiber-optic devices have found a wide range of medical applications in insæumei
called endoscopes, which can be inserted directly into the bronchial tubes, the biai
the colon, and so on for direct visual examination. A bundle of fibers can be encaseu
a hypodermic needle for study of tissues and bood vessels far beneath the sian
Fiber optics also have applications in communication systems, in which Dry
can
used to transmit a modulated laser beam. The rate at which informaüon
mitted by a wave (light, radio, or whatever) is proportional to the frequeu

34-12 Image ransmission by a

bundle of optical fibers.
 34-5 DIsPERSION 1063

this is so, modulating (modifying) the wave by chopping off

consider
tively why with a chopped-
f the wave
crests. Suppose cach crest represents a binary digit,
a zero and an unmodified The number of
cres representing a one.
esenting
S o n

o f fc r e s t r e p r e s e

unit time is thus proportional to the frequency of the

Odigits we can transmit per
have much higher frequency than do radio waves,
fafrared and visible-light waves information through a
madulated laser beam can transmit an enormous amount of
s0 a
For example, the Carnegie-Mellon University computer system,
ale fiber-optic cable.
single
several thousand networked personal computers and work stations, is
hich includes
1tnked partly by fiber-optic cables. Many telephone systems are connected by fiber
optics.
cables is that they are electrical insulators. They are
Another advantage of fiber-optic
interference from lightning and other sources, and they don't allow
immune to electrical
immu
between source and receiver. They are secure and difficult to ""bug,"
unwanted currents
also difficult to splice and tap into.
but they are

EXAMPLE 34E4
Aleaky periscope A perisuope for a submarine uses two totally ertarcsin 61.0°
reflecting 45°-45°-90° prisms with total internal reflection on
the sides adjacent to the 45° angles. It springs a leak, and the The 45° angle of incidence for a totally reflecting prism is less
bottom prism is covered with water. Explain why the periscope than the 61° critical angle, so total internal reflection does not
no longer works. occur at the glass-water boundary. Most of the light is transmit-
ted into the water, and very little is reflected back into the prism
SOLUTION The critical angle for water (n, = 1.33) on glass
n = 1.52) is

Index ol retracti0n ( )

34-5 DiSPERSIONN
Ordinary white light is a superposition of waves with wavelengths extending throughout
the visible spectrum. The speed of light iu vacuum is the same for all wavelengths, but Silicate flint glass
ne speed in a material substance is different for different wavelengths. Therefore the
Borate flint glass
an4refraction of a material depends on wavelength. The dependence of wave speed
d
index of refraction on wavelength is called dispersion. Quartz
r e 4-13 shows the variation of index of refraction n wavelength for a few
with
o n optical materials. Note that the horizontal axis of this figure refers tothe wave Silicate crown gl

e ght in vacuum, Ap; the wavelength in the material is given by Eq. (34-5), and
1.5

decrer nost materials the value ofn decreases with increasing wavelength Fused quartz
re
easing frequency,
ncy, and thus n increases with decreasing wavelength and increasing
Fluorite
shotyn such a has greater speed than light oft
shorter wavelength. material, light of longer wavelength
of idired
Quene 414 shows
produced byathe
rayprism
of white light incident
increases on a prism.
with increasing The
index deviation (change
of refraction and fre 500 600 70%
Wavelength in vacuum (nm)

least, otdecreasing wavelength. Vioiet light is deviated most, and red is deviated 34-13 Variation of index of
is spread OTS are in intermediate positions.. When it comes out of the prism, the light refraction n with wavelength for
to be
Pectrum, T a fan-shaped
of
beam, asshown. The ight is said
between the
dispersed into
a

refractive
different transparent materials.
The horizontal axis shows the
r nt dispersion depends on the difference
Such as fluo n t and for red light. From Fig, 34-13 we can see that for a substance wavelengh A, of the light in vac-
dispersi the difference between the indexes for red and violet is small, and the uum; the wavelength in the
also be small. A better choice of material for a prism whose purpose I material is equal to A = a,/n.
 Deviation of
White
lighi yellow light

Measure of
dlpersion

34-14 Dispersion of light by a prism. The band of colors is called a spectrum.

to produce a spectrum would be silicate flint glass, for which there is a larger diference
in the value of n between red and violet.
As we mentioned in Section 34-4, the brilliance of diamond is due in part to tt
unusually large refractive index; another important factor is its large dispersion, which
-causes white light entering a diamond to emerge as a multicolored spectrum. Crystals of
rutile and of strontium titanate, which can de produced synthetically, have about eighs
times the dispersion of diamond.
When you experience the beauty of a rainbow, you are seeing the combined effecs
of dispersion, refraction, and reflection (Fig. 34-15). Sunlight comes from behind you
is refracted into a water droplet, is (partially) reflected from the back surfaceor
droplet, and is refracted again upon exiting the droplet (Fig. 34-15a). Dispersion causs
different colors to be refracted at different angles. hen you see a second. slightly larg
rainbow with its colors reversed, you are seeing the results of dispersion and wo r e
tions from the back surface of the droplet (Fig. 34-15b). Both of these rainbows (cae
the primary and secondary bows) can be seen in Fig. 34-15c.

34-6 PoLARIZATiON
Polarization is a characteristic of all transverse waves. This chaptei is abour
introduce some basic polarization concepts, let's go back to the transvene the.r-us
string that we studied in Chapter 19. For a string that in equilibrium along
lies along
r i u m lies

Sunlight

40.8 (viole) Sunlight

o 42.5° (red)

50.1 (red)
w 53.2 (violet

(a)
(b c)
34-16 Rainbows (a) T
are formed drops.
by
or the primary bow is red.refractio
ion, reflecuon, and dispersion in water
r p
ouLsjue red. (c)A
(b) The inside of the fainter secondary bw is
ograph showing the primary and D
secondary bows.