Electromagnetic
Waves
CHARITY I. MULIG
Def’n: EM Wave
• Energy-carrying wave
emitted by vibrating
charges (often
electrons) that is
composed of
oscillating electric and
magnetic fields that
regenerate one
another.
The EM Spectrum
Range of frequencies over
which electromagnetic
radiation can be
propagated.
fL 
Change in
frequency of
a wave of
sound or
light due to
the motion
of the source
or the
receiver.
v  vo
fo
v  vs
Where
•fl is the apparent frequency
•f0 is the original frequency
•v is the speed of the wave in the medium
•v0 is the speed observer relative to the
medium; positive if the observer is
moving towards the source
•vs is the speed of the source relative to
the medium; positive if the source is
moving away from the observer.
Doppler Effect for EM Waves
Observed Frequency
Change in Frequency
• vs,r = vs – vr is the velocity of the source relative to the
receiver; it is positive when the source and the receiver
are moving further apart.
• λo is the wavelength of the transmitted wave in the
reference frame of the source.
Def’n: Polarization
• Aligning of
vibrations in
a transverse
wave, usually
by filtering
out waves of
other
directions.
Wavefronts vs. Rays
Huygen’s Principle
“The wave fronts of
light waves
spreading out from a
point source can be
regarded as the
overlapped crests of
tiny secondary waves
– wave fronts are
made up of tinier
wave fronts”
Properties of EM Waves
1.
2.
3.
4.
5.
6.
7.
Reflection
Refraction
Diffraction
Dispersion
Scattering
Interference
Polarization
Geometric
Optics
Reflection
Types of Reflection
Specular/Regular
Diffused/Irregular
The open-mesh
parabolic dish is a
diffuse reflector
for shortwavelength light
but a polished
reflector for longwavelength radio
waves.
Law of Reflection
1. The incident,
reflected and
normal ray all
lie in the same
plane.
2. The angle of
incidence is
equal to the
angle of
reflection.
Reflection at a Plane Surface
Locating Plane Mirror Image
Guidelines for Ray Diagrams
Ray Diagram For Concave Mirrors
Ray Diagram for Convex Mirrors
Mirror Equation and
Lateral Magnification
1
1
2
1



d0
di
R
f
hi
di
m

ho
d0
Mirror Equation
Sign Convention
Quantity
Positive
Negative
d0
Real object
Virtual Object
di
Real image
Virtual Image
f
Concave Mirror Convex Mirror
m
Upright/Erect
Inverted
Sample Problems
•A concave mirror forms an image, on a wall 3 m
from the mirror, of the filament of a headlight
The
image
of
a
tree
just
covers
the
lamp 10 cm in front of the mirror. (a) What are the
length
of a plane
4 cmoftall
radius
of curvature
andmirror
focal length
the mirror?
(b)
Whatthe
is the
height is
of held
the image
if the
height of
when
mirror
35 cm
from
the
object
is
5
mm?
the eye. The tree is 28 m from the
•Suppose that in the previous example, the left
mirror.
What
is
its
height?
half of a mirror’s reflecting surface is covered with
non-reflective soot. What effect will this have on
the image of the filament?
Refraction
The direction of
Cause of Refraction
the light waves
- The
change
in the
changes
“The
bending
ofwhen
light
one
part
of
each
average
speed
of
light
as it passes obliquely as
wave slows
enters
a
different
from one medium
to
down before the
medium”
another.” other part.
Definition:
Fermat’s Principle of
Least Time
• Pierre Fermat
• Out of all possible paths that light might travel
to get from one point to another, it travels the
path that requires the shortest time.
Phet
Index of Refraction
• Describes how much light the speed of light
in a material differs from its speed in a
vacuum.
nc v
• The index of refraction of vacuum is 1.
Snell’s Law
When light slows down in
sin

v
n
1
1
going from one
 medium
 2 to
another
as
sin such
v2goingn1from
2
air to water, it refracts
toward
the normal. When
• aka Snell-Descartes
law
it• speeds
in of
traveling
aka theup
law
from
one medium to
refraction
another, such as going from
• Follow’s from Fermat’s
water to air it refracts away
principle of least time
from the normal.
Few
Phenomena
Due to
Refraction
Because of refraction, the
full root-beer mug appears
to hold more root beer
than it actually does.
TheBecause
apparentofwetness
refraction,
of the
a submerged
road is notobject
reflection
appears
of the
to sky
be by
water
nearer
but,of
to
rather,
the surface
refraction
than
ofitsky
actually
light
through
is.the sun
theiswarmer
Because
atmospheric
refraction,
when
near
and
near the
road
surface.
theless-dense
horizon, it air
appears
to be
higher
in the sky.
Lenses
A prism
A curved prism
A converging lens
Types of Lenses
Ray
Diagrams
Finding the image produced by a THIN
CONVERGING LENS. To emphasize that the mirror
is thin the ray QAQ’ is shown as bent at the
midplane of the lens rather than at the two
surfaces and ray QOQ’ is shown as a straight line.
Graphical Method for Thin Lenses
•A ray parallel to the axis emerges from the lens
ray through
proceeding
toward)
the first
in• aAdirection
that(or
passes
through
the second
focal
point
F1aemerges
parallel
axis. to
focal
point
F2 of
converging
lens,toorthe
appears
come from the second focal point of a diverging
lens.
•A ray through the center of the lens is not
appreciably deviated; at the center of the lens
the two surfaces are parallel, so this ray emerges
at essentially the same angle at which it enters
and along the same line.
Important Equations and Conventions
Quantity
Thin Lens Equation
1 1 1
 
do di f
Positive
Negative
d0
Real object
Virtual Object
di
Real image
Virtual Image
f
Converging Lens
Diverging Lens
R
Converging Lens
Diverging lens
m
Upright Image
Inverted Image
Lensmaker’s Equation
for Thin Lenses
Lateral Magnification for Thin Lenses
 1
1
1 
 n  1  
f
 R1 R2 
hi
di
m

ho
do
Sample Problems
a.
Suppose
the
absolute
values12
of
theto
radii
of
An
object
8
cm
high
is
placed
cm
the
You
are
given
a
thin
diverging
lens.
You
find
A converging lens has a focal
curvature
ofofthe
lens
inlength
a double
left
ofa abeam
converging
lenssurfaces
of focal
cm.
that
parallel
ray
spreads
out8after
length
of
20
cm.
Describe
the
convex
lens
are
both
equal
to
10
cm all
andthe
A
secondthrough
converging
length
6the
cm
passing
the lens
lens,of
asfocal
though
index of
refraction
is right
n = 1.52.
What
islens.
the
image
when
an
object
is
placed
is
placed
36
cm
to
the
of
the
first
rays came from a point 20 cm from the the
focal
length
of the
lens?
Both
lenses
have
the
same
optic
axis.this
Find
following
from
the
lens:
center
of thedistances
lens. You
want
to use
lens
b.Suppose
a double
concave
lens also
has n =
the
position,
size,
and
orientation
of
the
to
form
an erect
virtual
image
thatcm;
is 1/3
(a)1.52,
50and
cm;
(b)
20
cm;
(c)
15
(d)
the
absolute
values
of
the
radii
of
image
produced
by
the two
lenses
inshould
the
height
of
the
object.
(a)
Where
curvature
of its lens surfaces
are also both
40
cm.
Determine
the
combination.
(Combinations
of converging
the
object
be
placed?
(b)
Draw
a principalequal to 10 cm. What is the focal
length of
magnification
in each case.
lenses
are used in telescopes
and
raythis
diagram.
lens?
microscopes.)
Sample Problems
An insect 3.75 mm tall is placed 22.5 cm to
the left of a thin planoconvex lens. The left
surface of this lens is flat, the right surface
has a radius of curvature of magnitude 13
cm, and the index of refraction of the lens
material is 1.70 cm. (a) Calculate the
location and size of the image this lens
forms of the insect. Is it real or virtual?
Erect or inverted? (b) Repeat part (a) if the
lens is reversed.