Transcript Electromagnetic waves

WAVES
Study topics
 General Wave characteristics- Wavelength, amplitude, frequency, period.
 Wave Types- Transverse, longitudinal, surface, torsional waves.
 Wave Phenomenon- Sound and Light, reflection, standing waves,
constructive and destructive interference, refraction, effect of media
diffraction, Doppler effect.
 Electromagnetic Waves
 Mechanical Waves
 Wave Characteristics
 Crest- the highest point of a wave. Also called peak.
 Trough- the lowest point of a wave.
 Rest position- the position the wave would be if there are no
disturbances along it
 Wavelength- the distance between two crests or troughs.
 Amplitude- the distance between a crest or trough and the rest position.
 Frequency- the number of times a wavelength passes a point in one
second.
 Period- the time a wave takes to complete a wavelength.
VIBRATIONS

Wiggle – Back and forth

Vibrate

Shake

Oscillate

Example

Bogglehead

Pendulum

Mass Spring
VIBRATIONS .. Contd.

Resting Position – equilibrium
position

Resting force
WAVES
a disturbance that transfers energy
Carries energy from one place to another
 Classified by what they move through

1.
2.
Mechanical Waves
the energy is transferred by vibrations of medium
(medium = matter)
ex/ ocean waves move through water
Electromagnetic waves (EM Waves)
the energy moves through disturbances in the
electromagnetic field.
WAVE STRUCTURE
CREST (peak)
AMPLITUDE
resting to max peak
WAVELENGTH
TROUGH
MECHANICAL WAVES
require a medium (the material through which the
disturbance is moving) to transmit energy
travel through & gradually
lose energy to that
medium
 Examples:


water, sound, rope, &
spring waves
Mechanical Media:

water, air, rope, spring
Making a pulse
MECHANICAL WAVES
Classified by how medium vibrates
Pulse = direction of energy transfer
Vibration = direction of vibration of medium
relative to pulse
3 types: Longitudinal, transverse, surface
MECHANICAL WAVES
Classified by how medium vibrates
Longitudinal Waves:
Vibration is in the same direction as
wave pulse (parallel to wave pulse)
Transverse Waves:
Vibration is at 900 (right angles) to wave pulse
Surface Waves:
Vibration is circular
Ex/ Ocean waves; surface waves
TRANVERSE WAVES
Vibration is perpendicular to the direction of
the motion of the wave


Sideways or up & down
Examples:

S-type earthquake waves

Electromagnetic (EM) or
light waves
LONGITUDINAL WAVES
Vibration is parallel to the
direction of the motion of the wave

Back and forth (compression & rarefraction)

Also called compression or pressure wave

Examples:

P-type earthquake waves

Sound waves
Rarefraction (expansion)
Compression
Waves describe the Earth
P waves move through solids & liquids
S waves move through solids only!!!
Are these MECHANICAL WAVES????
YES!! Seismic waves need a medium (the earth!)
CHARACTERISTICS OF WAVES
Waves are described according
to their

Amplitude
measures DISPLACEMENT
size of the disturbance

Wavelength 
distance of a “repeating unit”
Also called a cycle

Velocity v
speed = how fast wave travels
AMPLITUDE

Distance between “rest & crest” or “rest & trough”

Gives indication of “power”
or “strength” of wave
(magnitude of earthquake =
Richter scale)

Does not affect
velocity of wave

Determines loudness (sound) or brightness (EM wave)
FREQUENCY

ƒ
How often
number of wavelengths that pass any point per second

measured in
wavelengths/second or
cycles/second
Hertz (Hz*) = number of
wavelengths in 1 second
* Heinrich Rudolf Hertz, a 19th century physicist
PERIOD t

How long
Amount of time for one wavelength to pass a point

Related inversely to frequency
Period =
1
Frequency
Frequency =
Note: Inverse relationship
1
Period
Period and Frequency

Watch: World's best clapper

If Tim clapped 780 times in one minute, what’s the
frequency?

A pendulum is observed to complete 23 full cycles in 58
seconds. Determine the period and the frequency of the
pendulum
WAVELENGTH


Distance between any two
repeating points on a wave
crest-crest,
trough-trough,
expansion-expansion,
compression-compression

Determines what colors
we see; what notes we hear
(pitch)

Shorter wavelengths have
more cycles per minute
because they aren’t as long
VELOCITY

v
the rate at which the
energy travels;
speed & direction

Depends on medium

Mechanical waves travel
faster through dense
mediums

EM Waves are faster
through less dense
mediums
Calculating Wave Speed
 Speed
= wavelength x
frequency
V = λ x f
 V = velocity (m/s)
 λ = wavelength (m)
 f = frequency (Hz; 1/sec)
Example #1
 What
is the speed of a wave
with a wavelength of 2m
and a frequency of 3 Hz?
V=λxf
V = (2)(3)
V = 6 m/s
Example #2

A wave is traveling at a speed of 12 m/s and its wavelength is 3m.
Calculate the wave’s frequency.
V=λxf
12 = (3)(f)
12 = f
3
4 Hz = f
Do these on your own 

A tuning fork has a frequency of 280 Hertz and the
wavelength of the sound produced is 1.5 meters.
Calculate the velocity of the wave.

A wave is moving toward shore with a velocity of 5.0
m/s. If its frequency is 2.5 hertz, what is its
wavelength?
Amplitude and Energy

Amplitude – the energy carried by a wave or
how high the wave is; related to the amount of
energy
 For
compressional waves it’s the amount of
compression in the wave
 Example: The higher the wave, the more energy
(THINK on ocean waves)
For
transverse waves it’s the
height of the wave (E α A2 )
•
They travel as vibrations in electrical
and magnetic fields.
Have
some magnetic and some electrical
properties to them.

When an electric field changes, so does the magnetic field. The changing
magnetic field causes the electric field to change. When one field vibrates—
so does the other.

RESULT-An electromagnetic wave.
 Electromagnetic
waves travel VERY
FAST – around 300,000 kilometres
per second (the speed of light).
At this speed they can go around the
world 8 times in one second.
Speed of electromagnetic waves in
vaccum:
3 * 108 m/s

Waves or Particles?
•
Electromagnetic radiation has properties of waves but also can be thought
of as a stream of particles.

Example: Light

Light as a wave: Light behaves as a transverse wave which we can filter using polarized
lenses.

Light as particles (photons): When directed at a substance light can knock electrons off
of a substance (Photoelectric effect)
 Electromagnetic
Spectrum—name for the
range of electromagnetic waves when placed
in order of increasing frequency
RADIO
WAVES
INFRARED
RAYS
MICROWAVES
ULTRAVIOLET
RAYS
VISIBLE LIGHT
GAMMA
RAYS
X-RAYS
The Electromagnetic Spectrum
The electromagnetic spectrum represents
the range of energy from low energy, low
frequency radio waves with long
wavelengths up to high energy, high
frequency gamma waves with small
wavelengths.
Visible light is a small portion of this
spectrum. This is the only part of this
energy range that our eyes can
detect. What we see is a rainbow of
colors.
RedOrangeYellowGreenBlueIndigoViolet
ROY G BIV
Frequency Ranges of Visible Light
Red light has a frequency of roughly
4.3 × 1014 Hz, and a wavelength of about
7.0 × 107 m (700nm).
Violet light, at the other end of the
visible range, has nearly double the
frequency—7.5 × 1014 Hz—and (since the
speed of light is the same in either
case) just over half the wavelength—
4.0 × 107 m (400nm).
The radiation to which our eyes are
most sensitive has a wavelength near
the middle of this range, at about
5.5 x 10-7m (550 nm), in the yellowgreen region of the spectrum.
It is no coincidence that this wavelength
falls within the range of wavelengths
at which the Sun emits most of its
electromagnetic energy—our eyes have
evolved to take greatest advantage of
the available light.
The
product of wavelength and
frequency always equals the
speed of light.
C = λν
Why
does this make sense?
 NOTE:
c is a constant value= 3.00 x 108 m/s
PROBLEMS
 Calculate
the wavelength of yellow light
emitted from a sodium lamp if the
frequency is
5.10 x 1014 Hz (5.10 x 1014 s-1)
List the known info List the unknown
c = 3.00 x 1010 cm/s
wavelength (λ) = ? cm
Frequency (v) = 5.10 x 1014 s-1
C = λv
λ=c
v
λ = 3.00 x 1010 cm/s = 5.88 x 10-5 cm
5.10 x 1014 s-1
YOUR TURN
1- What is the wavelength of radiation
with a frequency of 1.50 x 1013 s-1?
What frequency is radiation with a
wavelength of 5.00 x 10-6 cm? In what
region of the electromagnetic
spectrum is this radiation?
3. What is the frequency of red light of
wavelength 632.9 nm?
2-
1
John says,
‘When hunting a fish under water, you
should aim your spear directly at the
fish.’
Do you agree?
Yes, of course.
 No, because the fish is actually located
somewhere else.
No, because size of objects changes when
they are put under water.
2
When sunlight falls on the water surface,
which of the following occur(s)?

It is reflected back to the air.


It refracts into the water.
It is absorbed by water and
turned into heat.
Introduction
Refraction is the bending of light
when the light passes from one medium
to another.
air
glass
Introduction
Useful words to describe refraction of light
angle of
incidence
air
glass
normal
angle of
refraction
Introduction
From a less dense to a denser medium
• e.g. from air to glass
normal
air
glass
• Light is bent towards the normal.
Introduction
From a denser to a less dense medium
• e.g. from water to air
normal
water
air
• Light is bent away from the normal.
Laws of refraction
• The incident ray, the refracted ray,
and the normalall lie in the same plane.
normal
air
glass
glass
Q1 A boy shines a torch under…
A boy shines a torch under water as shown.
Which one shows the correct path of the light
ray?
A
B
Path X.
Path Y.
C
Path Z.
D
All of them.
Q4 True or false: When light is…
True or false: When light is incident on a
surface along the normal, only refraction
occurs; there is no reflection.
(T/F)
Q5 Statements:...
1st statement
Light is bent
towards the normal
when it passes from
air to glass.
2nd statement
Glass has a greater
refractive index than
air.
true?
Yes
true?
Yes
4
Examples of refraction of light
a
Bent chopstick
• The chopstick appears bent because
of refraction
4
Examples of refraction of light
c
Flickering objects in hot air
• The object you see through the
unstable hot air appears blurred and
flickering.
Q1 True or false: Light slows…
True or false: Light slows down when it enters
a material from air.
(T/F)
Q3 True or false: If light travel…
True or false: If light travel at the same speed
in all materials, refraction would still occur
when it passes from air to water.
(T/F)
Refraction
-
Light Bends
when coming at
an angle
-
Light slows down
or speeds up
-
Wavelength
changes
-
Frequency
remains the
same
Example
Incident
Ray
Less Rigid
Medium
More Rigid
Medium
Refracted ray
bends
towards
Refracted Ray
the normal.
Index of Refraction, n
n=c/v

c : the speed of light in a vacuum,
3 x 108 m/sec

v : speed of light in the medium.

n : medium's index of refraction
Q2 True or false: The refractive…
True or false: The refractive index cannot be
smaller than 1.
(T/F)
Indices of Refraction
Vacuum
Air
1.00
1.0003
Water
1.33
Ethanol
1.36
Crown glass 1.52
Quartz
1.52
Diamond
2.42
Note

The speed of light has a lower speed in a more optically
dense medium.
Problem

What is the speed of light in quartz?

Answer: 1.97 x 10
8
m/s
Refraction
n1- from
n2 - into

When a wave slows down it bends closer to the normal.
{less to more – toward} n2>n1

When a wave speed up it bends away from the normal.
{BLA – Big ―› Little – Away} n2<n1
Q5 Sketch a ray diagram for the...
Sketch a ray diagram for the tip of the
chopstick to show why the chopstick looks
bent when dipped into water.
4
Examples of refraction of light
b
Shallower in water
• The depth that the object is
actually at is called the real
depth.
I
O
real
depth
Apparent Depth
R – Real Depth
A – Apparent Depth

Diverging rays enter
your eyes.

You “think” in
Straight Lines.

A virtual image
appears to come from
point y
Apparent Depth

If the chest is 20 m below the surface at what depth will the image
appear? Assume nsea water = 1.34
Snell’s Law

n1 sin q1 = n2 sin q2
Example
A monochromatic light ray f= 5.09 x 1014 Hz is
incident on medium X at 55˚. The absolute
index of refraction for material X is 1.66
1.
2.
3.
What is material X?
Determine the angle
of refraction.
Determine the
speed of light in
medium X.
Ex: Solution
The index of 1.66 is Flint Glass
To find the angle of
refraction use
Snell’s Law.
θ2= 30˚
To find the speed use
n=c/v.
v = 1.8 x 108 m/s
Problem

What is the angle of refraction when a ray from air with
an angle of incidence of 25 o is incident to water?

Draw the ray diagram.

Answer: 18.5 o
Which angle is larger?

A light ray is emerging from glass to air. Which angle is
larger, in glass or in the air ?
normal
glass
Or this?
AIR
This?
Which angle is larger?

A light ray is emerging from glass to air. Which angle is
larger, in glass or in the air ?
normal
glass
Or this?
AIR
This?
Critical angle (1)

For glass-air interface, the angle of refraction in air >
incident angle
glass
Angle of refraction
normal
Partial
reflection
Incident angle
AIR
Which angle first?
If the angle of incidence increases, which angle will reach 90o first, the
angle of incidence or the angle of refraction?
A
B
Angle of incidence (from glass)
Angle of refraction (in the air)
Critical angle (2)

When we increase the angle of incidence (i), the angle of refraction (r)
increases until ......
normal
glass
i
r
AIR
Critical angle (3)

when the angle of refraction is 90o, the incident angle is
called the critical angle (C).
normal
glass
iC
90or
AIR
Critical angle (4)

For glass-air interface, the critical angle is 42o.

At critical angle, angle of refraction is 90o, so, by the laws of refraction,
sin r
1sin
n=
=
sin i
90o
n x sin C = 1 sin C
1
sin C =
n
What is the critical angle...
… for water-air interface?
The refractive index of water is 1.33
1 ÷ 1.33 = 0.75
sin-1 0.75 = 48.8o
=>
C = 48.8
o
Check :
sin
C = sin 48.8 = 0.75
o
1 ÷ 0.75 = 1.33
1
sin C =
n
I can do it,
so can you!
Critical angle (5)
For glass, the refractive index is 1.5;
C = sin-1 (1÷1.5)
Critical angle = 42o
For water, the refractive index is 1.33;
C = sin-1 (1÷1.33)
Critical angle = 48.8o
Csin
= sin
C -1
=
)
11
(
nn
What if ...
… the angle of incidence (from glass) is larger than the critical angle?
A
B
C
The angle of refraction will become
smaller again.
There will be no refracted ray.
The light ray will be reflected the
same way back.
Next
Total internal reflection (1)

When the light ray (from water) is emerging at the critical angle, the
refracted ray will be along the interface.
along
along
AIR
water
Total internal reflection (2)

When the incident angle is larger than the critical angle,
total internal reflection will occur (at the interface).
AIR
water
Next
Total internal reflection (3)

View under water!!
AIR
water
Total Internal Reflection

Can occur when ray goes from higher n to lower n.

Above a Critical angle (of incidence) the ray is
reflected, not refracted

For problems, set the angle of refraction to 90, and
solve for critical angle
Problem

Find the critical angle for a light ray that is incident
from water to air.

Answer: 48.8
o
Dispersion

The separation of light into colors arranged according to their
frequency, by interaction with a prism or diffraction grating.
Rainbows

White light separates into different colors
(wavelengths) on entering the raindrop
because red light is refracted by a lesser
angle than blue light. On leaving the
raindrop, the red rays have turned through a
smaller angle than the blue rays, producing a
rainbow.
Q4 True or false: If the speed of…
True or false: If the speed of light in raindrop
is equal to that in air, there would be no
rainbows.
(T/F)
Lenses
Converging Lens
Rules For Converging Lenses
1)
Any incident ray traveling parallel to the
principal axis of a converging lens will
refract through the lens and travel through
the focal point on the opposite side of the
lens.
2)
Any incident ray traveling through the focal
point on the way to the lens will refract
through the lens and travel parallel to the
principal axis.
3)
An incident ray which passes through the
center of the lens will in effect continue in
the same direction that it had when it
Image Formation by Converging
Lens
Diverging Lens
Rules For Diverging Lenses
1)
Any incident ray traveling parallel to the
principal axis of a diverging lens will refract
through the lens and travel in line with the
focal point (i.e., in a direction such that its
extension will pass through the focal point).
2)
Any incident ray traveling towards the focal
point on the way to the lens will refract
through the lens and travel parallel to the
principal axis.
3)
An incident ray which passes through the
center of the lens will in effect continue in
the same direction that it had when it
Diverging Lens Image Formation
Always Virtual, Smaller, and Right-Side Up
Problem
The index of refraction for crown glass for red light is
1.514.
What is the speed of red light in crown glass?
Answer: 1.98 x 10
8
m/s