Transcript Chapter 14

Chapter 14
Light and Reflection
Chapter 14 Objectives
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Identify the nature of light
Calculate the speed of light
Law of Reflection
Ray Diagrams
– Flat mirrors
– Concave mirrors
– Convex mirrors
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Mirror Equation
Magnification Equation
Color
Polarization
What is Light?
• Sir Isaac Newton first proposed that light was a tiny
stream of particles emitted by the light source.
• Thomas Young noticed that given light under certain
conditions it could cancel itself due to interference.
– Interference is a wave property!
• Einstein took it one step further to explain the
photoelectric effect.
– Thus creating photons, or tiny particles of energy that
are transferred by a light wave.
Electromagnetic Wave
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For much of our introductory purpose, we will only consider
the wave property of light.
Since we can cancel out the wave property of light but still
have energy emitted, there must be more to the wave than
just the light.
This leads to light fitting being an electromagnetic wave.
– That is it contains perpendicular electric fields and magnetic
fields that oscillate perpendicular to the wave flow.
• So light waves travel as transverse waves.
Speed of Light
• Armand H. L. Fizeau developed the first
successful method for measuring the speed
of light.
– By bouncing a laser off a mirror and
calculating the time it takes to return to the
source.
• He also used a toothed wheel to separate the
continuous laser into countable pulses.
• v = c = 3 x 108 m/s
c represents the speed of light
Modeling Light Waves
• For our purposes, we will model a light wave as a ray, or
vector.
– So that is to draw an arrow.
• Sometimes it may be necessary to model light as a set of rays.
• What we do know…
– Light will continue in a straight line until it encounters a
boundary between two different materials.
– When light encounters that new boundary, anything could
happen!
Intensity of Spherical Light Waves
• Since the waves will travel as a spherical shell, the
area that it approaches is equal to the area of a sphere
– 4r2
• Due to the spherical nature, as the wave travels the
intensity dissipates by a factor of r2.
I
P
=
4r2
Law of Reflection
• Any time a light ray encounters the surface of a new
medium, part of the light ray is reflected.
– In a mirror, some light is reflected upon entering the glass
and the rest is reflected when it hits the metallic backing.
• The new light rays will now travel parallel together, assuming
the surfaces were smooth.
– Reflection from a smooth surface is often called specular
reflection.
– Reflection from a rough surface such as cloth or wood is often
called diffuse reflection.
Angle of Reflection
•
From observation, the angle of reflection is equal to the
angle of incidence.
– Incidence indicates the original path of entry.
•
However, the angle is measured from a line perpendicular to
the surface that we call the normal.
– We use the perpendicular line because using the mirror
itself could vary based on the shape and surface quality of
the mirror at the incidence point.
1 1’
Red Eye
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Red eye is often seen in photographs taken with a flash.
This shows an example of retroreflection.
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Retroreflection is reflection that travels back along its original
direction.
So what you are seeing is the light reflecting off the blood vessels
in the retina of your eye and returning back out the lens of the eye.
Reflection Notation
• When investigating reflections, there is some notation to
account for:
– The original item that is being reflected is called the object.
• The object distance, or the distance the object is from the
mirror, is represented by the variable p.
• With a height of h.
– The observed reflection of the object is called the image.
• The image distance is represented by the letter q.
• With a height of h’.
p
h
o
q
i
h’
Real vs Virtual
The images formed through any alteration of light can be classified in two ways:
• An image is real when
• An image is virtual when
– The reflected light rays
and the incident light
rays actually pass
through the image point.
– The image appears to
be on the same side of
the mirror as the object.
– The image can be
displayed on a screen.
– The incident light rays
do not pass through the
image point.
– The reflected light rays
appear to diverge from
the image point.
– The image cannot be
displayed on a screen.
p
o
q
i
Magnification
• The lateral magnification, M, is defined as
the ratio of the image height to the object
height.
M=
p
h
o
image height
object height
=
h’
h
q
i
h’
Rules for Flat Mirrors
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2.
The image is as far behind the mirror as the object is in
front.
The image is unmagnified, virtual, and upright.
(Upright means the object and image remain in the
same orientation.)
2.
Although, a flat mirror will encounter a right-left reversal
according to the observer.
p
h = h’
h
o
p=q
q
i
h’
Drawing Reflections
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2.
mirror
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location
height
3.
object
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1.
The basic drawing of a
reflection consists of some
essential components:
3.
distance
orientation
4.
and also the drawn in
components
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incident light rays
reflected light rays
image
p
o
5.
Reflect the ray appropriately.
Extend both reflected rays through
the other side of the mirror to obtain
the virtual image location, if
necessary.
5.
i
Reflect the ray appropriately.
Draw another incident light ray from
the top of the object through the
center of curvature until it hits the
mirror.
4.
q


Draw the location of the mirror and
indicate the object distance.
Draw the object with some indication
of its orientation
and height (upright, inverted, etc.).
Draw an incident light ray parallel to
the object distance from the top of
the object to the mirror.
The real image will exist if all rays
intersect on the same side of the
mirror as the object originally was.
Spherical Mirrors
• If the reflecting
surface is concave,
then it is called a
concave mirror.
• If the reflecting
surface is convex,
then it is called a
convex mirror.
Spherical Mirror
Components
• A spherical mirror is a small arc of a spherical shell.
• So with that we identify parts of a spherical mirror based
on it circular nature:
– The center of curvature, C, is the point at which all the
radii of the mirror intersect.
– The radius of curvature, R, is the distance from the mirror
to the center of curvature.
– When the radius of curvature is drawn as a perpendicular
bisector of the mirror, it is called the principle axis.
R
C
Magnification of
Concave Mirror
• Using a little geometry, you will notice that the distance to
the mirror is directly related to the height of the object.
– Using your theorems for similar triangles as well as some
trigonometry, you notice we are concerned with the tangent
ratio of our triangle sides.
M=
image height
object height
=
q
h’
–
=
h
p
q is negative for a virtual image,
and positive for a real image.
Negative sign shows the image is inverted.
p is always positive, that way it
acts as our point of reference.
Mirror Equation
• Using some complex algebra with the similar
triangles will create an equation that can calculate
the image distance by knowing the object distance
and the radius of curvature of the mirror.
1
p
+
1
q
=
2
R
Focal Point
• If we consider our light source to be an infinite distance
away, we observe the following:
– We can treat the light as a series of individual, parallel light
rays
– All of which reflect to intersect at one common point.
• That common point of intersection is called the focal
point, F, of the mirror.
Focal Length
1
p
1
+
q
2
=
• Since p is very large (), then the mirror equation relies
more on the image distance than the object distance.
– So solving for q results in:
• q = R/2
• Because we are attempting to find the focal point, our
image distance is now called the focal length, ƒ.
• And from the above work we see that the focal length will
always be half the radius of curvature.
R
ƒ= 2
R
Revised Mirror Equation
• Recognizing that the focal length is
half the radius of curvature, we can
conclude the following:
• This is the more common and useful form
of the mirror equation.
1
p
+
1
q
=
12
ƒR
R
ƒ= 2
Sign Conventions for Spherical
Mirrors
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p is positive if the object is in front of the mirror. (real object)
p is negative if the object is behind the mirror. (virtual object)
q is positive if the image is in front of the mirror. (real image)
q is negative if the image is behind the mirror. (virtual image)
Both ƒ and R are positive if the center of curvature is in
front of the mirror. (concave mirror)
• Both ƒ and R are negative if the center of curvature is
behind the mirror. (convex mirror)
• If M is positive, the image is upright.
• If M is negative, the image is inverted.
Drawing Ray Diagrams for
Spherical Mirrors
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First draw a ray parallel to the principal axis that will be reflected back
through the focal point.
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The second ray should be drawn through the focal point, and then reflected
parallel to the principal axis.
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Remember that all straight rays that encounter a curved mirror reflect through the
focal point.
A concave mirror will go through the focal point and then hit the mirror.
A convex mirror will hit the mirror while on line to the focal point, but the reflection
that needs to be accounted for will be parallel to the principal axis.
The third and final ray is drawn through the center of curvature and reflected
back upon itself.
o
o
i
C
i
F
F
C
Image of a Convex
Mirror
• Notice the image for a convex mirror will always be:
– Virtual
(-q)
– Upright
(+M)
– Smaller than the object
(M<1 so h’ < h)
o
i
F
C
Color
• The color of an object is dependent on the
reflecting and absorbing properties of the
material.
– The color we see is the reflected light from
the material.
• So if all the light is reflected off the surface, then
the color we see is the color that was transmitted
to the material.
• Some light may be absorbed in the form of heat
and some transmitted through the material.
– Remember, every time a wave hits a boundary,
some of the wave is reflected and most is
transmitted.
Primary Colors v Additive Colors of Light
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Elementary colors are those
colors that are split from the
rainbow.
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Red, orange, yellow, green,
blue, indigo & violet.
Three of those colors cannot
be formed from any other
two.
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– Red, Yellow, & Blue
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They are called primary
colors.
Since white light can be split
into elementary colors, it is safe
to assume that elementary
colors can be mixed to form
other colors.
Due to the interference and
intensity properties of light,
yellow and green behave
differently than pigments.
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Yellow can actually be created
from red and green.
However, green cannot be
formed from anything else.
So the primary additive colors
of light are:
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Red, Green, & Blue
Polarization
•
Because of the electromagnetic nature of light, a light source can be
thought of as a round point sending off cylindrical beams of light
rays.
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This takes into account the wave nature of the electric field created
by light rays.
And it takes into account the perpendicular magnetic field wave that
accompanies light rays.
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And since the original light source can be oriented or vibrating in any
direction, we assume that light can travel as a cylindrical beam.
A wave is said to be polarized if its electrical field vibrates in the
same direction at all times through a particular point.
Polarization by Selective Absorption
• The most common technique for polarizing light is to
use a material that is a good electrical conductor that
can alter the electric field plane of the unpolarized light.
– This will allow waves whose field vectors vibrate in a
plane parallel to the desired direction to pass through
while absorbing those waves that travel perpendicular.
• This can be done by placing sheets of aligned, longchain hydrocarbons to become the electron transfer
molecules that will alter the electric field.
– In 1932, E. H. Land discovered this process for material
which he called polaroid.
• The material is dipped in iodine to create a better conducting
chain of hydrocarbons.
Polarization Notation
• We commonly refer to the direction
perpendicular to the molecular chains as
the transmission axis.
• Remember, the molecular chains are
responsible for supplying “free” electrons that
will alter the electric field.
– In an ideal polarizer, light with an electric
field parallel to the transmission axis will
pass through.
• So light with an electric field perpendicular to the
transmission axis will be absorbed.
Intensity of Light Transmitted by a Polarizer
• To adjust the intensity of polarized light we can
send it through two polarizing sheets varying
transmission axes.
– The first sheet is called the polarizer.
• Its main responsibility is to align all incident light rays
along parallel electric fields.
– The second sheet is called the analyzer.
• This sheet intercepts the now polarized light beam
with a new transmission axis that is set at an angle of
 to the axis of the polarizer.
• This is how polarized sunglasses work.
– They eliminate glare by absorbing the unwanted
incident light rays and only allow the desire angle of
light rays to pass through!
• Example: Fishing glasses
How Malus’s Law Works
Polarization by Reflection
• Recall that an incident light beam on any boundary will
partially reflect some of its beam.
– The reflected ray can become partially polarized,
completely polarized, or stay unpolarized.
• The evidence for this is since the wave is reflected we are
altering the electric field(s) that bounce off the surface.
• An angle of incidence between 0o and 90o will become
polarized to some extent.
– An angle of incidence at 0o or 90o leaves the reflected
light unpolarized.
• That is because none of the light transfers into the medium
nor is reflected, it is a straight uninterrupted beam of light.
Polarization by Scattering
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A third form of polarization often observed in our atmosphere comes from
the reflection and absorption of light by a system of particles.
This is called polarization by scattering.
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The electrons in the medium can absorb and reradiate the light as it
attempts to pass through the medium.
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The electrons are sent into vibration as light energy begins to excite the atom.
When the electron changes state, it will reradiate the light energy and alter its
electrical field.
So much of the light that we receive from the sun is partially polarized by
our atmosphere.
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And some of the sun’s light we never see because it is polarized to a very
low intensity.