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Electromagnetic Waves
‘LIGHT’
Nature of Light
Is light a wave or a particle?
There is a fair amount of evidence to support both theories!
Electromagnetic vs. Mechanical

Electromagnetic waves :
Transverse only
 Does not require a medium
 Light


Mechanical waves:
Transverse and longitudinal
 Requires a medium
 Sound, earthquake, water

Electromagnetic (E-M) Waves

Electromagnetic (E-M) waves are created by the
vibration of an electric charge.


This vibration creates a wave which has both an
electric and a magnetic component.
An electromagnetic wave transports its energy
through a vacuum at a speed of 3 x 108 m/s (a
speed value commonly represented by the
symbol c).
In 1931, Michelson found c = 2.99774×108m/s
The modern value is c = 2.997925×108m/s

Since E-M waves are indeed transverse
waves our wave equation holds true for all
types of E-M waves
v = fλ

As with any wave, light waves transfer
ENERGY !

All wave phenomena that we previously
discussed hold true for E-M waves
Reflection
 Interference

 Constructive
 Destructive
Doppler Effect
 Diffraction


As well as some new ones that will be
discussed in this unit
Refraction
 Polarization

E-M Spectrum

Electromagnetic waves exist with an
enormous range of frequencies.


This continuous range of frequencies is
known as the electromagnetic spectrum.
The entire range of the spectrum is often
broken into specific regions.

The subdividing of the entire spectrum into
smaller spectra is done mostly on the basis of
how each region of electromagnetic waves
interacts with matter.
Spectrum

The diagram below depicts the electromagnetic
spectrum and its various regions.

The longer wavelength, lower frequency regions are
located on the far left of the spectrum and the shorter
wavelength, higher frequency regions are on the far
right. Two very narrow regions within the spectrum
are the visible light region and the X-ray region.
Electromagnetic Spectrum
Found on your Reference Table
About the Spectrum
AM/FM Waves:
They are found when you listen to the car radio
Microwaves:
Yes they are used in Microwave Ovens

Use a frequency of 2.45 GHz

This frequency is readily absorbed by water molecules (it
makes them resonate)

Excites the water molecules within the material to create heat
Infrared Waves:
Associated with heat.

Hot lamps for keeping food warm

Living things give off IR radiation

Night Goggles are used to detect this type of wave
Visible Light:

The only part of the spectrum our eyes are sensitive to

frequencies are in the range of 1014 Hz
Ultraviolet Waves:
Visible Good: Ultraviolet Bad

Responsible for sunburn, skin cancer

“Black lights” are UV lights- certain materials give off visible
light when exposed to UV light

Ozone layer of atmosphere blocks UV light
X-Rays:
 Called x-rays because no one knew what they were when first
discovered
 Pass readily through skin but absorbed by bone

Anyone see a use for this?
Gamma Rays:

Nearly unstoppable, pass right through concrete walls
Visible Light

Visible light region - the very narrow band of
wavelengths located to the right of the infrared
region and to the left of the ultraviolet region.

Normally when we use the term "light," we are
referring to a type of electromagnetic wave that
stimulates the retina of our eyes.
Visible Light

Each individual wavelength within the spectrum of visible light
wavelengths is representative of a particular color. That is,
when light of that particular wavelength strikes the retina of our
eye, we perceive that specific color sensation.
Transparent vs. Opaque
Transparent
Heat
Infrared waves
Visible light
Visible Light
Ultraviolet waves
Glass

Allows light to pass through. It depends on the frequency of the
incident electromagnetic radiation
Materials such as water and glass are transparent to visible light
Incident Light

Heat
Opaque



Does not allow light to transmit through
Most materials are opaque to visible light
The energy is simply converted into internal energy
Color?
You perceive color…it is simply our minds “take” on certain frequency
electromagnetic waves.
So, why do objects appear to be of a certain color?
Color by Reflection:
Objects appear a certain color because they absorb all the other
colors (the frequencies of those colors causes resonance or near
resonance in the molecules of the material-the energy is absorbed
as heat) but “reflect” (absorbed then reemitted) that particular color.
White Objects:
“Reflects” all colors, absorbs little
Wearing white clothes in the summer
Black Objects:
Absorb all colors, reflect little
Wearing dark colors in the winter
Color by Transmission:
The color of the transparent object depends on the color of the light
it re-emits (transmits)
Why is the sky blue?
Sun
Earth
Not Drawn to Scale
Why are Sunsets Red?
The blue light gets
scattered out- there is
no more left
Only red light
is left
Sun
Earth
Representing Light Waves in Diagrams
Ray: A line drawn to represent the direction of energy flow of a wave
(corresponds to the direction of wave propagation)
Sun
ray
Wavefront: A surface passing through those points of a wave that have
the same phase and amplitude
Wavefront: lines represent
crests
Light Rays

Law of Reflection: The angle of incidence
is equal to the angle of reflection
Incidence
Reflection
Law of Reflection
Law of Reflection: The angle of incidence is
equal to the angle of reflection.
Incidence
θi
Normal

θr
Reflection
θi = θr
This holds true for every
reflection
Light Wave Phenomena:
Reflection
Regular Reflection
Occurs off of
smooth surfaces
Often produces
glare
Diffuse Reflection
Occurs off of irregular
surfaces
Images
Forming Images:

Light must reach your eye from the object to form an image of
the object

Light travels in straight lines
Camera Obscura: Pin Hole Camera
Image Characteristics
Real: The image is formed by converging light rays
The image can be projected on a screen
Virtual: The image is formed by diverging light rays
The image can not be projected on a screen
Upright: The image has the same vertical orientation as the object
Inverted: The image has the opposite vertical orientation as the object
Reversed: The image is flipped from side to side
Images formed by reflections
Mirror Types:
Plane Mirror:
Concave Mirror (converging mirror):
Convex Mirror: (diverging mirror):
Ray Diagram: Plane Mirrors
The image is always:
Virtual, same size, upright,
reversed
And the object distance =
image distance
Ray Diagram: Concave/Converging Mirrors
R, radius of
curvature
Principle Axis
C, center of
curvature
f, focal
length
Ray Diagram: Concave/Converging Mirrors
If the light ray passes parallel to
the principle axis it reflects
through the focal point
If the light ray passes
through the focal point it
reflects parallel to the
principle axis
Convex/Diverging Mirrors
If the light ray is
directed parallel to the
principle axis, the ray
reflects as if it came
from the virtual focal
point
f
If the light ray is directed
towards the virtual focal
point, it is reflected parallel
to the principle axis
C
Convex/Diverging Mirrors
Images formed by diverging/convex mirrors are always
virtual
upright
smaller
Depending on where
object is located
image will appear
differently
Refraction
The sudden change in direction of a light ray as the light ray passes
from one medium to another. It is caused by a change in speed.
Absolute Index of Refraction:
 The ratio of the speed of light in a vacuum to the speed of light in
the substance
 Depends on the frequency of incident light
 “optical density” – how easy is it for light to travel through the
material
c
n
v
*dimensionless quantity that is always equal to or greater than 1*
*As n increases the speed of light decreases*
Common indices of refraction for yellow light
Substance
Index of refraction
Air
1.00
Diamond
2.42
Fused Quartz
1.46
Crown Glass
1.52
Flint Glass
1.66
Sodium Chloride
1.54
Water
1.33
Lucite
1.50
Corn Oil
1.47
Pyrex Glass
1.468
FOUND ON REFERENCE TABLE
When light passes perpendicular to the surface, no refraction occurs.
The light ray still changes speed, however there is no change in
direction.
n1
n2
n1 = n2 No Refraction
Example:
n1 = glass
n2 = glass
When light passes into a substance for which the
speed of light is the same, light “passes” through
unchanged, it is not refracted
n2 > n1 Ray Bends TOWARD Normal
Example:
n1 = air
n2 = water
When a light ray passes into a substance in which the
speed of light decreases, the refracted ray “bends”
towards the normal
n2 < n1 Ray Bends AWAY Normal
Example:
n1 = water
n2 = air
When a light ray passes into a substance in which the speed
of light increases, the refracted ray “bends” away from the
normal
General Rule of Refraction, a.k.a. Snell’s Law
It can be found experimentally that the ratio of the index of
refraction for the substance the light is leaving to the
index of refraction for the substance the light is entering
is equal to the ratio of the sin of the angle of refraction to
the angle of incidence
n1 sin 

n2 sin 
or more commonly expressed
n1sinθ1 = n2sinθ2
Snell’s Law
What happens to the light wave when it enters a new
medium?
n1
n1= c and v1= f1λ1
v1
n2
n2 = c and v2 = f2λ2
v2
So, if v decreases, the wavelength
decreases
But we know that the
frequency of a wave does
not change when it
changes mediums and the
speed of light in a vacuum
is constant so after some
careful algebra you can
get:
n2 v1 1
 
n1 v2 2
Dispersion
The process of separating light into its component colors due to the
dependency of the index of refraction on wavelength/frequency.
Dispersive Materials: Materials for which the index of refraction
varies with wavelength (examples: water, glass, diamond)
Non-Dispersive Materials: Materials for which the index of
refraction does not vary with wavelength (examples: vacuum, air)
For dispersive materials the index of refraction varies with wavelength,
therefore the angle of refraction varies with wavelength.
In general, as frequency increases, wavelength decreases, the
index of refraction increases
Prisms: Dispersion
Red light has the longest
wavelength, therefore the
smallest index of refraction: it
bends the least and it travels the
fastest through the substance
Violet light has the
shortest wavelength,
therefore the highest
index of refraction: it
bends the most and
travels the slowest
Dispersion in Motion
Total Internal Reflection


As light passes from a substance with a higher index of refraction to
a substance with a lower index of refraction, the light ray bends
away from the normal.
Eventually, as the incident angle increases, the angle of refraction
increases as well approaching 90o, after which none of the light
escapes.

This is called total internal reflection (TIR)
Critical Angle (θc)
The angle of incidence for which the angle of refraction is equal to 90o
From the general rule for refraction:
n1sinθc = n2sin90
n2
sin  c 
n1
only works when n1 > n2
When the angle of incidence exceeds the critical angle, TIR occurs
As the ratio between n2 and n1 increases, the critical angle decreases
(its easier to “trap” light inside the substance)
Forming Converging Lenses
Forming Diverging Lenses
Ray Diagram: Converging lenses
A light ray directed
parallel to the principle
axis is refracted
through the focal point
R=2f
f
A light ray directed
through the focal
point is refracted
parallel to the
principle axis
f
A light ray directed
through optical
center passes
straight through
R=2f
Ray Diagram: Diverging Lens
A light ray directed
parallel to the
principle axis is
refracted such that
is appears to
originate at the
virtual focal point
2f
f’
A light ray directed
towards optical center,
“passes” straight
through
f’
2f
Images formed by diverging
lenses are always virtual,
upright, and smaller
Ray Diagram Practice
Problems with spherical lenses and mirrors
Spherical Aberration:

The focal point of light rays far from the principle axis of a spherical
lens/mirror are different from the focal points of the light rays close
to the principle axis. The result is a blurry image.
Corrective Procedure: Minimize the amount of lens/mirror being
used around the principle axis
ex) Adjustable aperture on a camera
Chromatic Aberration



A problem only with lenses
Based on the dependency of the index of refraction on frequency
The focal points of different colors of light are different
White light
Red light focal
point
Violet light focal
point
Interference of light waves:
Constructive interference
Results in bright light
Destructive interference
Results in dim light
Conditions for sustained interference patterns produced by light waves
1) The light sources must be coherent
2) The waves must have identical wavelengths
Two speakers driven by a single amplifier can produce a sustained
interference pattern
Two light sources will not
However, never you worry.
I can produce “two sources” from one by way of a screen with two small
holes cut into it.
Double Slit interference pattern
obstruction
Viewing
surface
Laser
Pattern of light
and dark
spots
How is that possible?
Diffraction
Diffraction:
 A general wave phenomena (happens with all waves)
 The bending of a wave around a barrier or obstruction
Some useful information about diffraction as seen on the video disc
Classic diagram
Wave
fronts
The larger the wavelength the more
diffraction the wave undergoes
The smaller the “opening” the more
diffraction the wave undergoes
Conclusions From Young’s Double Slit Experiment
y = mLλ
d
As L increases,
y increases
As d decreases,
y increases
As λ increases,
y increases
where y is the distance from the central
maximum to the bright fringes
Diffraction Gratings
Wave
Fronts
Viewing
Screen
The more openings there are, the harder (less likely) that the conditions
will be right between all of the “sources” to result in an interference
pattern. The result, the pattern of light and dark bands “spreads”
out.
Polarization
Light is said to be polarized if the variances in the electric
field all occur in the same plane.
The fact that light can be polarized provides evidence that,
not only is light a wave, but it is a transverse wave
Head on view of electric
fields for unpolarized light
Head on view of electric
fields for polarized light
E
E
(a)
So, how do you go from (a) to (b)?
(b)
Polaroid Filter
The most common method of polarization
involves the use of a Polaroid filter.
 Polaroid filters are made of a special
material that is capable of blocking one of
the two planes of vibration of an
electromagnetic wave.

Way to Think

A picket-fence analogy is often used to
explain how this dual-filter demonstration
works.
Polarization by reflection

When a beam of light is reflected off a surface, the light can be
completely polarized, partially polarized or not polarized depending
on the angle of incidence

For incidence angles of 0o and 90o
No polarization occurs

For incident angles between 0o and 90o
The light will be partially polarized horizontally

Hence, hitherto, and therefore…
polarized sunglasses are worth the extra cash!
(This is paid for by our sponsors at RayBan®)
Anatomy of the Eye

The eye is essentially an opaque eyeball
filled with a water-like fluid. In the front of
the eyeball is a transparent opening known
as the cornea.


The cornea is a thin membrane that has an
index of refraction of approximately 1.38.
The cornea has the dual purpose of
protecting the eye and refracting light as it
enters the eye.
After light passes through the cornea, a
portion of it passes through an opening
known as the pupil.

Rather than being an actual part of the
eye's anatomy, the pupil is merely an
opening. The pupil is the black portion in
the middle of the eyeball. Its black
appearance is attributed to the fact that the
light that the pupil allows to enter the eye is
absorbed on the retina (and elsewhere) and
does not exit the eye. Thus, as you sight at
another person's pupil opening, no light is
exiting their pupil and coming to your eye;
subsequently, the pupil appears black.
Anatomy of the Eye

Like the aperture of a camera, the size of the pupil opening can be
adjusted by the dilation of the iris.



The iris is the colored part of the eye - being blue for some people and
brown for others (and so forth); it is a diaphragm that is capable of
stretching and reducing the size of the opening. In bright-light situations,
the iris adjusts its size to reduce the pupil opening and limit the amount
of light that enters the eye. And in dim-light situations, the iris adjusts so
as to maximize the size of the pupil opening and increase the amount of
light that enters the eye.
Light that passes through the pupil opening, will enter the
crystalline lens. The crystalline lens is made of layers of a fibrous
material that has an index of refraction of roughly 1.40. Unlike the
lens on a camera, the lens of the eye is able to change its shape
and thus serves to fine-tune the vision process.
The lens is attached to the ciliary muscles. These muscles relax
and contract in order to change the shape of the lens. By carefully
adjusting the lenses shape, the ciliary muscles assist the eye in the
critical task of producing an image on the back of the eyeball.
Anatomy of the Eye

The inner surface of the eye is known as the
retina. The retina contains the rods and cones
that serve the task of detecting the intensity and
the frequency of the incoming light.

An adult eye is typically equipped with up to 120
million rods that detect the intensity of light and about
6 million cones that detect the frequency of light.
These rods and cones send nerve impulses to the
brain. The nerve impulses travel through a network of
nerve cells. There are as many as one million neural
pathways from the rods and cones to the brain. This
network of nerve cells is bundled together to form the
optic nerve on the very back of the eyeball.
Image Formation


In order to facilitate the ability to see, each part must
enable the eye to refract light so that is produces a
focused image on the retina.
It is a surprise to most people to find out that the lens of
the eye is not where all the refraction of incoming light
rays takes place. Most of the refraction occurs at the
cornea.

The cornea is the outer membrane of the eyeball that has an
index of refraction of 1.38. The index of refraction of the cornea
is significantly greater than the index of refraction of the
surrounding air. This difference in optical density between the air
the corneal material combined with the fact that the cornea has
the shape of a converging lens is what explains the ability of the
cornea to do most of the refracting of incoming light rays.
Image Formation

The use of the lens equation and magnification
equation can provide an idea of the quantitative
relationship between the object distance, image
distance and focal length.
Problem

The varying distance between the
observer and the object poses some
potential problems for the human eye.

Objects located varying distances from a lens
system with a fixed focal length produce
images that are varying distances from the
lens. Yet, the eye must always produce an
image on the retina - a location that is always
the same distance away from the cornea. The
eye cannot afford to allow changes in the
image distance.
Questions

So how does an eye always focus images
with the same dimage regardless of the fact
that the dobject is different? How can an
object 100 meters away be focused the
same distance from the cornea-lens
system as an object that is 1 meter away?
Answer

The cornea-lens system is able to change
its focal length. The ciliary muscles of the
eye serve to contract and relax, thus
changing the shape of the lens. This
serves to allow the eye to change its focal
length and thus appropriately focus
images of objects that are both close up
and far away.
Farsightedness

Farsightedness or hyperopia is the inability of the eye
to focus on nearby objects. The farsighted eye has no
difficulty viewing distant objects.
Nearsightedness

Nearsightedness or myopia is the inability of the eye to
focus on distant objects. The nearsighted eye has no
difficulty viewing nearby objects. But the ability to view
distant objects requires that the light be refracted less.