Unit 2 Notes

Physics 30S
Unit 2
The Nature of Light

Unit 2 – The Nature of Light


Inference is the act or process of deriving a
conclusion based solely on what one already
knows.
A model is a pattern, plan, representation
(especially in miniature), or description designed
to show the main object or workings of an object,
system, or concept.
In science a theory is a testable model of the
manner of interaction of a set of natural
phenomena, capable of predicting future
occurrences or observations of the same kind,
and capable of being tested through experiment
or otherwise verified through empirical
observation.


Models, Theories & Laws
• Scientists give the title law to certain concise but
general statements about how nature behaves.
• The law is a summary of the results of our
observations. It is a description of nature without
an explanation of why nature behaves that way.
• To be called a law, a statement must be found
experimentally valid over a wide range of
observed phenomena.
• The law in a sense bring unity to many
observations.
• For less general statements, the term principle
is often used.


• Scientific observations and laws are like
pieces of a jigsaw puzzle. When enough
pieces have fallen into place, a meaningful
pattern emerges. This pattern is a theory.
• A theory provides a general explanation for
the observations, and is created to explain
these observations. These observations may
be made by many scientists over a long
period of time.
• Theories are inspirations that come from the
minds of human beings.
• An important aspect of any theory is how well
it can quantitatively predict phenomena.


• Scientists often make use of models to help them
interpret their observations. A scientific model is not
like a model airplane or a globe.
• A scientific model is a mental picture that helps us
understand something we cannot see or experience
directly. The model may include an analogy with
something we are already familiar with.
• The purpose of a model is to give us a mental or
visual picture, something to hold onto, when we
cannot see what is actually happening.
• Models give us a deeper understanding.
• Scientific models change as new discoveries are
made.


Modeling Video


Black Box Activity


The Scientific Method
• The scientific method is an
orderly and systematic approach to
gather knowledge. With this
approach, new ideas about the
world are constantly checked
against reality. We can also think of
the scientific method as a way of
answering questions about the
world we live in.

• A brief outline of the scientific method might include the
following.
– First the scientist makes observations, or records
facts of what is seen.
– The observation leads to a question. (Sometimes the
question may come before the observations are
made.)
– Thinking about the question produces a hypothesis, a
tentative answer to the question.
– The scientist tests the hypothesis with a carefully
designed procedure, an experiment. As part of the
experiment, the scientist carefully records and
analyzes data, or information, gathered in the
experiment.
– The experiment produces a result, or conclusion,
which the scientists interprets carefully. From the
interpretation, or inference, the result may raise new
questions and lead to new hypotheses and new
experiments.


– After a number of experiments, the scientist may
be able to summarize the results in a natural law,
which describes how nature behaves but does not
explain why nature behaves in that particular way.
It often takes a mathematical form.
– Finally the scientist may be able to formulate a
theory. The theory explains why nature behaves
in the way described by the natural law. It answers
the original questions and also any other
questions that were raised during the process.
The theory also predicts the results of further
experiments and this is how the theory is checked.
A model could also be formed at this point along
with or instead of the theory. The model is a
mental picture that helps us to understand what it
is that we are observing


"I'm All Thumbs"

• What makes a "Class Champion" thumb
wrestler? Does thumb diameter, length, or
wrist diameter have an effect on the
overall chances of winning a thumb
wrestling match? In this investigation we
will develop a hypothesis based on
physical data collected from our
classmates. We will then test this
hypothesis by conducting a thumb
wrestling tournament to determine an
overall "Class Champion".


Knowledge Claims

“I believe that Coke is the best
soft drink.”

• A knowledge claim is a declaration of
conviction consisting of a sentence of the
type "I know that … " or "I believe that".


Knowledge Claims
• Knowledge claims are supported by evidence whose
nature depends on the training and the experiment
of the claimer. Evidence can be first hand
observations, deference to authority, or plausible
explanations. Deference to authority can range from
naive acceptance of the authority to a more careful
consideration of evidence.
• To be convincing, the claimer must formulate a
relevant argument with the intended audience.
Sometimes the evidence is given in the form of a
critical experiment that is overwhelmingly
convincing. An argument based on good evidence
can be referred to as evidential argument.


Models of Light


Theories of Light
• In the seventeenth century two rival theories of the
nature of light were proposed, the wave theory and the
corpuscular theory.

The Dutch astronomer Huygens (1629-1695) proposed
a wave theory of light. He believed that light was a
longitudinal wave, and that this wave was propagated
through a material called the 'aether'. Since light can
pass through a vacuum and travels very fast Huygens
had to propose some rater strange properties for the
aether: for example; it must fill all space and be
weightless and invisible. For this reason scientists were
sceptical of his theory.


Theories of Light
• In 1690 Newton proposed the corpuscular theory of
light. He believed that light was shot out from a source
in small particles, and this view was accepted for over
a hundred years.

• The quantum theory put forward by Max Planck in
1900 combined the wave theory and the particle
theory, and showed that light can sometimes behave
like a particle and sometimes like a wave. You can find
a much fuller consideration of this in the section on the
quantum theory.


Newton’s Model of Light
• Isaac Newton imagined light as
streams of tiny particles he called
corpuscles that shoot out like
bullets from light sources.
Newton’s theory is commonly
called the Corpuscular Theory of
the Particle Theory of light.


Huygen’s Model of Light
• The wave theory was first proposed
by Robert Hooke in 1665 and then
improved upon by Christian
Huygens. The Wave Theory of
Light tried to explain the following
properties of light.


• Newton proposed his theory and gave the following
arguments to support his theory.

– Rectilinear Propagation - Shadows and light rays
traveling through the clouds showed that light
traveled in straight lines. We know that a bullet shot
from a gun will curve due to the force of gravity.
Newton argued that light particles did not do this
because the traveled at extremely high speeds. He
also argued that they must have an extremely small
mass because they did not exert any noticeable
pressure.


• Rectilinear Propagation


• Newton proposed his theory and gave the
following arguments to support his theory.

– Reflection - Newton demonstrated that in
a perfectly elastic collision between a
particle and a solid surface, the incident
velocity equals the magnitude of the
reflected velocity and the angle of
incidence equals the angle of reflection.


• Reflection



– Refraction - To explain refraction Newton
believed that water attracts approaching
particles of light much in the same way as
gravity attracts a rolling ball on an incline.
He predicted that light would speed up as it
enters a medium with a higher index of
refraction such as water.


• Refraction



– Dispersion - The dispersion of light had
been observed for year. Newton explained
this phenomenon by attributing the different
amounts of refraction to the different masses
of the particles. He said the violet particles
had less mass than the red particles,
therefore showing a greater refraction.


• Dispersion


• Newton proposed his theory and gave
the following arguments to support his
theory.

– Diffraction - Newton explained the
diffraction that occurred when light
passed through two slits was the result
of the particles colliding with one
another and with the edges of the slit.


• Newton proposed his theory and gave
the following arguments to support his
theory.

– Partial Reflection/Partial Refraction -
When light refracts, some of the light is
also reflected. Newton had difficulty
explaining this part.


• Rectilinear Propagation - Early
attempts to explain rectilinear
propagation proved difficult.
Huygens thought of light rays as the
direction of travel of the wave (wave
ray).


• Diffraction - Waves diffract and so
did light. Huygen’s principle is
consistent with diffraction of waves.
It wasn’t until the size of the
wavelengths of light was discovered
that Huygens principle was proven .


• Reflection - The same argument
Newton used holds true for waves.
Waves obey the laws of reflection.


• Refraction - Huygen was able to
predict that light is bent towards the
normal as it enters a more optically
dense material. This indicates that
light slows down as it enters water.
This was not proven till years later.


• Refraction


• Partial Reflection/ Partial
Refraction Waves partially reflect
and partially refract when there is a
change in velocity. The amount of
partial reflection varies with the
angle of incidence. There is a
critical angle for waves and light.
Angles of incidence greater than the
critical angle produce only reflection.


Light & Refraction
• A wave doesn't just stop when it reaches
the end of the medium. The transmitted
wave undergoes refraction (or bending) if
it approaches the boundary at an angle.
• Refraction is the bending of the path of a
light wave as it passes from one material
to another material. The refraction occurs
at the boundary and is caused by a
change in the speed of the light wave
upon crossing the boundary.


Light & Refraction
• The tendency of a ray of light to
bend one direction or another is
dependent upon whether the light
wave speeds up or slows down upon
crossing the boundary.


Light & Refraction
• FST = Fast to Slow, Towards Normal
– If a ray of light passes across the boundary
from a material in which it travels fast into a
material in which travels slower, then the
light ray will bend towards the normal line.
• SFA = Slow to Fast, Away From Normal
– If a ray of light passes across the boundary
from a material in which it travels slow into a
material in which travels faster, then the light
ray will bend away from the normal line.


Snell’ Law & Angle of Refraction
• There is a mathematical equation
relating the angles which the light
rays make with the normal to the
indices (plural for index) of refraction
of the two materials on each side of
the boundary. This mathematical
equation is known as Snell's Law.


• Snell's law will apply to the refraction of
light in any situation, regardless of what
the two media are.
• The study of the refraction of light as it
crosses from one material into a second
material yields a general relationship
between the sines of the angle of
incidence and the angle of refraction.
This general relationship is expressed by
the following equation:
ni *sin(θ i) = nr * sin(θ r)


ni * sin(θ i) = nr * sin(θ r)

– ("θ i") = angle of incidence
– ("θ r") = angle of refraction
– ni = index of refraction of the incident
medium
– nr = index of refraction of the refractive
medium


• Measure, calculate, and draw in the
refracted ray with the calculated
angle of refraction.


• Answer


Refractive Index
• In 1621 Snell found that when the sin of
the angle of incidence is divided by
the sin of the angle of refraction, the
result is a constant value for a given
interface (boundary layer between
specific materials).
• This constant number was named the
Relative Refractive Index and is
specific for each pair of media.
• For an air-to-water interface, the relative
refractive index is 1.33.


Refractive Index
• A more useful quantity is the Absolute
Refractive Index. This is the relative
refractive index for a vacuum-to-
medium interface and is specific for
each medium. The value of the index
for light traveling from air into the
substance is so close to the value of
absolute refractive index that we only
distinguish between them in rare
instances.


Snell’ Law
• Lab 17.2
• Worksheet 2.2.1
• Worksheet 2.2.3
• Worksheet 2.2.4


Total Internal reflection
• Total internal reflection is the reflection of
the total amount of incident light at the
boundary between two medium.


• At angle of incidence close to 0 degrees,
most of the light energy is transmitted
across the boundary and very little of it is
reflected. As the angle is increased to
greater and greater angles, we would begin
to observe less refraction and more
reflection.


• The maximum possible angle of refraction is 90-degrees.
There is some specific value for the angle of incidence
(called the "critical angle") which yields an angle of
refraction of 90-degrees.
• This particular value for the angle of incidence could be
calculated using Snell's Law (ni = 1.33, nr = 1.000, = 90
degrees, = ???) and would be found to be 48.6 degrees. Any
angle of incidence which is greater than 48.6 degrees would
not result in any refraction.
• Instead, when the angles of incidence is greater than 48.6
degrees (the critical angle), all of the energy (the total
energy) carried by the incident wave to the boundary stays
within the water (internal to the original medium) and
undergoes reflection off the boundary. When this happens,
total internal reflection occurs.


• Total internal reflection (TIR) is the
phenomenon which involves the reflection of all
the incident light off the boundary.


• TIR only takes place when both of the following
two conditions are met:
– the light is in the more dense medium and
approaching the less dense medium.
– the angle of incidence is greater than the so-
called critical angle (since light only bends
away from the normal when passing from a
more dense medium into a less dense medium)

• Total internal reflection only occurs with large
angles of incidence. The critical angle is different
for different media.


• To calculate the critical angle, a
modification of Snell’s Law equation can
be used:
ni * sineθi = nr * sine θr
ni * sineθcrit = nr * sine (90 degrees)
ni * sineθcrit = nr
sineθcrit = nr/ni
θcrit = sine-1 (nr/ni)


Young’s Experiment
• The research by Thomas Young
(1773 – 1829) into the interference
of light was critical in demonstrating
that light has wave like properties.
His famous experiment has become
known as “Young’s Experiment”.


Young’s Experiment –
Simulation Activity


• Instead of using two sources, he used only one
source of light directing it through two pinholes
placed very close together.
• The light was diffracted through each pinhole so
that each acted as a point source of light.
• Since the sources were close together, the
spacing between the nodal lines was great enough
that the pattern could be seen.
• Because the light from the two pinholes came from
the same source, the two interfering beams of light
were always in phase and a single, fixed
interference patter could be created on the screen.
• A series of bright and dark bands called
interference fringes were produced.


• We will look at interference in
Young’s Experiment at three
different angles. In the diagrams on
the following slides, light waves in
phase are passing through the slits
S1 and S2 which are a distance d
apart. The waves spread out in all
directions through the slits.


• In this diagram, both waves that reach the
centre of the screen are in phase because they
travel the same distance. Constructive
interference occurs and there is a bright spot
on the screen.


• In this diagram, the waves from S2 travel an extra
1/2 λ to reach the screen. When they do so, they
are exactly out of phase. This means that the
crest from the wave of S1 meets the trough from
the wave of S2. Destructive interference occurs
and the screen is dark at this point. This
corresponds to nodal point 1.


• In this diagram, the point P is moving further
away from the center of the screen. A point is
reached where the path difference is one
wavelength and the waves are once again in
phase.


Young's Experiment and His Useful Equation

• For the interference of light from two point
sources, the equation below can be used.

• In this equation,
λ is the wavelength of the light,
∆ x is the distance between adjacent nodal lines on
a screen,
– d is the separation between the slits
– L is the perpendicular distance from the slits to the
screen.


Electromagnetic Waves
• Electromagnetic waves are waves which
can travel through the vacuum of outer
space.
• Mechanical waves, unlike
electromagnetic waves, require the
presence of a material medium in order
to transport their energy from one
location to another.
• Sound waves are examples of
mechanical waves while light waves are
examples of electromagnetic waves.


• Electromagnetic 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
3.00 x 108 m/s (commonly known as "c").
• The propagation of an electromagnetic
wave through a material medium occurs
at a net speed which is less than 3.00 x
108 m/s.


• The propagation of an electromagnetic
wave through a material medium occurs
at a net speed which is less than 3.00 x
108 m/s.


• Electromagnetic waves are
produced by a vibrating electric
charge and as such, they consist of
both an electric and a magnetic
component.


Electromagnetic 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.


Electromagnetic Spectrum
• 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 with the spectrum are the
visible light region and the X-ray region.


Visible Light Spectrum
• Though electromagnetic waves exist in a vast
range of wavelengths, our eyes are sensitive to
only a very narrow band. Since this narrow
band of wavelengths is the means by which
humans see, we refer to it as the visible light
spectrum.
• This visible light region consists of a spectrum
of wavelengths, which range from
approximately 700 nanometers (abbreviated
nm) to approximately 400 nm; that would be 7
x 10-7 m to 4 x 10-7 m. This narrow band of
visible light is affectionately known as
ROYGBIV.


Visible Light Spectrum


The Photoelectric Effect
• Heinrich Hertz noticed that when one
exposes certain metal surfaces to an
ultraviolet light, negative charges were
emitted from the metal. How can we
explain the emission of negative
charges?
What is the Photoelectric Effect?
• The photoelectric effect refers to the
emission, or ejection, of electrons
from the surface of, generally, a metal
in response to incident light.


• Energy contained within the incident light
is absorbed by electrons within the metal,
giving the electrons sufficient energy to
be "knocked" out of, that is, emitted from,
the surface of the metal.


The Photoelectric Effect: Wave
Model or Particle Model
• The wave model predicts that the energy, which is
distributed along the wave, will eventually build up and
release a bunch of electrons at the same time. According
to the wave model, light of any frequency should
demonstrate the photoelectric effect. Lower frequencies
would just take longer to build up enough energy to
release the electrons. A low frequency wave with high
intensity should eventually be able to dislodge an
electron. However this is not the case, it is observed that
only certain frequencies emit electrons. The wave
model fails to accurately predict the photoelectric
phenomenon.


• Einstein (1905) successfully resolved this
paradox by proposing that the incident light
consisted of individual quanta, called photons,
that interacted with the electrons in the metal
like discrete particles, rather than as continuous
waves.


• Einstein proposed that the light consists of packets of
energy called "photons" and that the quantity of energy
of each photon is fixed and depends on its frequency.
• The higher the frequency, the greater the energy
contained in the photon. Thus, the particle model
predicts that individual photons knock out electrons and
that only photons with enough energy (above the
threshold frequency) can do this.
• Einstein’s theory explained the existence of a threshold
frequency. A photon must have a minimum energy to
eject an electron from a metal. This minimum energy
depends on the threshold frequency, fo, of the light.


• If the photon has a frequency below fo, then it does not
have the energy needed to eject an electron. Light with a
frequency greater than fo has more energy than needed to
eject the electron. The excess energy make the electron
move, and is converted to kinetic energy of the moving
electron.
• When the frequency of the incident light is too low, the
photon does not give the absorbing electron sufficient
energy and it remains bound to the surface. The intensity
(brightness) of the light is only a measure of the rate at
which the photons strike the surface, not the energy of the
photon. This explains why the kinetic energy of the
emitted photoelectrons and the threshold frequency do not
depend on the intensity of the incident light.


• Notice that an electron cannot simply accumulate
photons until it has enough energy. Only one photon
interacts with one electron. The photon either has
enough energy to eject the electron or it does not. Thus,
the photon behaves more like a particle than a wave.
• The photoelectric effect is perhaps the most direct and
convincing evidence of the existence of photons and the
"corpuscular" nature of light and electromagnetic
radiation.
• Albert Einstein received the Nobel Prize in physics in
1921 for explaining the photoelectric effect and for his
contributions to theoretical physics.


The Principle of
Complementarity and Light
• As we evaluate the predictions of the particle
and wave models of light we find that each
model explains some phenomenon and each
model has difficulty explaining other
phenomenon.
• The photoelectric effect reveals that light has a
particle nature. For properties such as reflection,
refraction, diffraction and interference light
behaves more like a wave.


The Principle of
• It has become obvious that light is not just a
wave and not just a particle. It has a dual nature,
a property referred to by physicists as a wave-
particle duality. We can come to this
conclusion because both theories of light have
been shown to be valid based on very strong
experimental evidence. It is clear that light is a
much more complex phenomenon than just a
beam of particles or just a simple wave.


The Principle of
• The Principle of Complementarity, proposed by
Neils Bohr, stated that understanding both the
wave and particle properties of light is essential
if one is to have a full understanding of light. In
other words, the two aspects of light
complement one another.


Modern Theory of Light


The Speed of Light


The Speed of Light
• Measuring the speed of light has always been a
challenge.
• Galileo was one of the first who attempted to calcualte
the speed of light.
• Then in the 1600s Roemer and Huygens used similar
approaches by looking at the eclipses and orbits of
Jupiter and one of its moons, Io.
• Then in the 1800s Fizeau and Foucault used rotating
wheels and mirrors to measure the speed of light.
• In the 1900s, Michelson improved on Foucault’s
technique and obtained a very accurate measurement of
the speed of light.

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