Wave Theory

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Wave Theory part 2
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Electromagnetic Spectrum

• An electromagnetic spectrum is a map of the
  total range of waves. All are forms of LIGHT!

Usually, high frequency (low ?) is on the
right. Low frequency (high ?) is on the left.
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• Notice the wide range of waves. We only perceive
  visible light, a tiny fraction of the whole
  spectrum...

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Speed of Light

• In a vacuum, all electromagnetic waves have a
  velocity of 300,000,000 m/s! (3x108m/s)

Thats 186,000 miles per second!
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• There are a number of wave phenomenon that are
  characteristic of all Waves
• 1 Reflection
• 2 Refraction
• 3 Diffraction
• 4 Interference
• 5 Resonance
• They all involve the movement of energy in to
  form of waves sometimes from 1 material to
  another!

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Moving from one medium to another Once a wave
(incident wave) has reached a change in media,
part of the energy is transferred to the medium
that is immediately next to it (transmitted wave)
and part is reflected backward (reflected
wave).The energy transferred depends on the
difference between the mediums. If there is a
significant difference, almost all the energy
will be reflected.  
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• If the mediums are similar, most of the energy
  will be transferred. However, the reflected waves
  will be inverted if the medium that comes next is
  more dense or it won't be inverted if the medium
  is less dense.
• Ex
• sound moving from air to water
• light moving into a piece of glass
• earthquake waves moving from solid rock to molten
  rock

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1 Reflection of Waves If we draw a line
perpendicular to a surface, this line is the
normal of the surface. When a ray of light hits
the surface of an object, part of the light is
reflected. If the ray of light is at an angle
with the surface, then the angle between the
incident ray and the normal incident anglewill
be the same angle between the normal and the
reflected ray reflected angle. This is called
the law of reflection.
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Normal Line
Incident Ray
Reflected Ray
Incident Angle
Reflected Angle
Boundary / Mirror
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http//library.advanced.org/10796/ch10/ch10.htm
Most surfaces are not completely flat. When
millions of rays of light hit the rough surface
of an object, they are reflected in all
directions. This is how we can see illuminated
objects.  
http//micro.magnet.fsu.edu/primer/java/reflection
/reflectionangles/index.html
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White Light

• White light is not a distinct color. Instead,
  white light is the combination of all the other
  colors.

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Newtons Prism Work

• Before Newton, it was thought that the prism
  added color to the light
• Newton tested this idea by breaking the light
  into the spectrum, then again dividing a single
  color of the spectrum with another prism to test
  if it would again add color to the light.
• Once he discovered it did not, he reached the
  conclusion that the original white light had
  contained all of the colors that were seen coming
  from the prism.

http//micro.magnet.fsu.edu/primer/java/scienceopt
icsu/newton/index.html
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Selective Reflection

• When we perceive an object to be a particular
  color, we actually are receiving only one
  particular color of light in our eyes.

Ex A banana looks yellow because it reflects
only yellow light. It absorbs all the other
colors.
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Black

• When an object appears black, it means that all
  colors ( frequencies) of light are being absorbed
  by that object. None are being reflected.

Often, black objects are hotter because they are
absorbing more light/energy.
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• If a rose were illuminated with a red light, you
  would see the red rose, but the stem and leaves
  would look nearly black. Since they are green,
  that means they reflect only green light ( absorb
  red).

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2 Refraction of Waves

• When a wave travels from one medium to a second
  medium, The original wave is redirected at a
  different wavelength at a different angle (bend)
  from the normal to the surface.
• The index of refraction determines the amount of
  change in wavelength and angle. (bending the wave)

http//micro.magnet.fsu.edu/primer/java/scienceopt
icsu/refraction/index.html
http//www.physics.uoguelph.ca/applets/Intro_physi
cs/refraction/LightRefract.html
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Refraction of Water Waves
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Refraction of Light Beam

• Refraction -- bending of light wave path as light
  passes from one material to another material.

• Refraction occurs at the boundary and is caused
  by a change in the speed of the light wave upon
  crossing the boundary.
• Direction of bending depends upon whether light
  wave speeds up or slows down at the boundary.

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Transmission Across a Boundary

• Light wave speed changes
• Light wavelength changes - frequency does not
  change

• Only time a wave can be transmitted across a
  boundary, change its speed, and still not refract
  is when wave approaches boundary in a direction
  which is perpendicular to it.

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Ray Diagrams
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Optical Density

• Optical density -- tendency of the atoms of a
  material to hold on to absorbed energy from a
  photon in the form of vibrating electrons before
  reemitting it as a new photon
• The more optically dense a material is, the
  slower a wave will move through the material.

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If the new medium is more dense, the light bends
because it slows down. How much do you ask?
This decrease in speed is given by the formula
v c / n where v - is the new speed of light
and n is
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Index of Refraction

• Index of Refraction is a measure of optical
  density
• Represented by n
• The higher n is, the more optically dense the
  material and the slower light travels in the
  material

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Indices of Refraction
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Refraction of light   When a ray of light passes
from one medium to another, it bends. Depending
of the new medium the light will travel faster or
slower. If the light travels faster in the second
medium, then this medium is called the rarer
medium (or less dense)
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Refraction of light  On the other hand, the
medium in which the light travels slower, in this
case the first one, is called the denser medium.
When a ray of light enters a denser medium, it is
bent towards the normal. When a ray of light
enters a rarer medium, it is bent away from the
normal.  
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http//micro.magnet.fsu.edu/primer/java/scienceopt
icsu/refraction/index.html
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Law of Refraction Snells Law

• There is a formula to predict how much a wave
  will bend as it travels into a new medium
• n1sinq1 n2sinq2

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http//theory.uwinnipeg.ca/physics/light/node5.htm
l
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n1 sin ?1 n2 sin ?2 (1.00) (0.643)
(x) (0.53) X 1.21
Angle of Incidence
?1 40?
AIR - n1 1.00
? - n2
Angle of Refraction
?2 32?
New Angle of Incidence
New Angle of Refraction
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At the boundary of 2 media Some of the light
wave is always reflected. However, when a ray of
light goes from a denser medium to a rarer
medium, all the light will be reflected if the
angle of incidence is greater than the critical
angle. The critical angle is the angle of
incidence for which the refracted ray is at 90
degrees with the normal.  
http//micro.magnet.fsu.edu/primer/java/refraction
/criticalangle/index.html
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http//micro.magnet.fsu.edu/primer/java/diffractio
n/basicdiffraction/index.html
3 Diffraction When a wave travels through a
small hole in a barrier, it bends around the
edges. This is called diffraction.

• The bending of a wave around an obstacle

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4 InterferenceofWaves
The Addition of waves can add (Constructive) or
subtract(Destructive). Standing waves are a
result of waves combining in phase
http//micro.magnet.fsu.edu/primer/java/interferen
ce/doubleslit/index.html
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Collision of waves When two waves traveling in
opposite directions through the same medium
collide, the amplitude of the resulting wave will
be the sum of the two initial waves. Remember
the energy of the 2 waves is influencing the
motion of the media - the energy pulls on the
media.The resulting phenomenon is called
interference and there are two types
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Collision of waves  Constructive interference is
when the amplitudes of the initial waves are in
the same direction. The resulting wave will be
larger than the original waves. The highest point
of a constructive interference is called an
antinode.  
Constructive!
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Destructive interference is when the amplitudes
of the initial waves are opposite. The amplitude
of the resulting wave will be zero. The point in
the middle of a destructive interference is
called a node and it never moves (in light - it
would be a dark spot)
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When waves add and subtract
The Principle of Superposition
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Interference of waves
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Summary

• Waves are a pulses of energy through a medium
• Waves properties Speed, amplitude, wavelength,
  and frequency
• Waves change through mediums by
• Reflection
• Refraction
• Diffraction
• Interference

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ORIGIN OF LIGHT  Where does light come from? How
is it produced? The least complex answer is that
light comes from the atom itself - the motion of
the electrons around the nucleus. When an
electron drops an energy level - a packet of
light (photon) is produced. This is the
phenomenon that you studied in the online
activity.
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VISIBLE LIGHT  Of all the electromagnetic waves,
visible light is the only portion of
electromagnetic waves that can be detected by the
human eye. It is a very small section of the
spectrum and visible wavelengths run from 7.5
x 10-7 m (red) to 3.5 x 10 -7 m (purple).
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Luminous and illuminated bodies  Light is
produced by a luminous body. A light bulb is a
luminous body that emits light in almost every
direction. Light travels in straight lines at
299,792,458 m/sec in a vacuum. OR 3.0 X 108 m/s
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Luminous and illuminated bodies When light hits
an object OR another medium, it is reflected or
refracted . An illuminated body reflects light.
When a ray of light reaches our eyes, the
receptors in our eyes will produce a different
color sensation depending on the wavelength of
the light wave.  
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COLORS Red, green and blue are known as
primary colors, because when they are added
together white light is formed. By mixing primary
colors in pairs we obtain secondary colors. Blue
and red produce magenta, and blue and green
produce cyan.  
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Why the Sky is Blue

• Our sky, atmosphere, is made up of various
  particles ( mostly N2 and O2 ) that vibrate at
  various frequencies.
• When hit by light of various frequencies, some
  react, some dont.

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• The violet/blue light is reflected/scattered the
  most, so we see those colors.
• Our eye cones arent as sensitive to violet, so
  we see a predominantly blue sky.

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LIGHT ORIGIN REVIEW QUIZ 1. WHERE DOES LIGHT COME
FROM? - EXPLAIN THE MECHANISM. 2. WHY DO WE SEE
COLORS? - HOW IS IT WE SEE COLORS? 3. WHAT ARE
THE COLORS OF THE VISIBLE SPECTRUM? 4. NAME AT
LEAST 4 OTHER FORMS OF ELECTROMAGNETIC RADIATION.
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LIGHT WAVES VISUAL DEVICE CRITERIA 1. MUST USE
AT LEAST 1 REGULAR SIZE PIECE OF
CONSTRUCTION PAPER 2. AESTICHALLY PLEASING 3. USE
MIND-MAP DESIGN OR FLOW CHART DESIGN 4. MUST
INCLUDE THE FOLLOWING ITEMS - ORIGIN
OF LIGHT - BOHR ATOM - EMISSION ABSOPTION
SPECTRA ORIGINS - TRANSFER OF ENERGY - TYPE OF
WAVE MOTION - ELECTROMAGNETIC SPECTRUM
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Apparent Depth

• Light exits into medium (air) of lower
  index of refraction,  and turns left.

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Spear-Fishing

• Spear-fishing is made more difficult by the
  bending of light.
• To spear the fish in the figure, one must aim at
  a spot in front of the apparent location of the
  fish.

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Delayed Sunset

• The sun actually falls below below the horizon
• It "sets", a few seconds before we see it set.

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Green Flash
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Broken Pencil
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Water on the Road Mirage
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Palm Tree Mirage
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• Sometimes an object may have a very different
  appearance depending on the wavelength of light
  you are using to observe it. Ex visible light
  and infrared picture of the constellation Orion

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The Human Eye

• Our eyes are remarkable organs designed to detect
  visible light. The design of a camera is very
  similar to our eye.

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• Light passes through the clear cornea of your
  eye. The cornea bends light so that you have a
  wide field of view.
• Then light goes through the pupil, which is the
  variable black opening in the iris ( colored
  part) of your eye.
• The lens focuses the light onto the sensitive
  retina of your eye.

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Color Vision

• There are two types of vision receptors in the
  eye Rods and Cones
• Color vision is possible because of the Cones.
• Animals without color vision have only Rods.

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• In general, females have better color vision than
  males.
• In fact, a high of males have some degree of
  color blindness.
• This doesnt mean that they see the world in BW,
  but instead their color vision isnt as vivid.

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• You should see a 25 in the dot pattern. The
  following tests will be more difficult if you are
  color blind

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• Normal color vision 45
• Red/Green color blindness no pattern

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• Normal color vision 6
• Red/Green color blindness no pattern

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Optical Illusions

• Here are some illusions to illustrate how our
  eye/brain makes judgements. The light our eyes
  receive may be objective, but we often interpret
  this data subjectively. Our vision perception is
  not always very scientific.

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• What do you see?

A dalmation?
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• What do you see?

A mans face, or the word liar written in cursive.
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• Do you see the spiral?

Actually they are concentric circles.
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• The square inscribed in the circle is NOT kinked.
  

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• How many black dots do you see?

None
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• Two faces?
• Wine goblet?

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• What do you see??

Scene with tree, or baby?
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Selective Transmission

• Not all objects reflect light (opaque), some let
  light pass through them ( transparent). In this
  case, if a transparent object looks blue, this
  means that all colors except blue are being
  absorbed.

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Mixing Colored Light

• The sun is a pretty good source of white light.
  Below is a curve showing the relative proportions
  of the visible light it produces

R O Y G B I V
Infra-red
ultraviolet
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• The colors of white light are often simplified
  into three components Red, Green, Blue

These are often called the additive primary colors
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• When the three additive primary colors of light
  are mixed, the following results are obtained

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• If a golf ball were illuminated with RBG lamps,
  could you explain the following result?

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Pigments

• If you have ever used play-dough, youve noticed
  that if you mix R,B,G colors of clay, you dont
  get white as a result!

This is an example of mixing pigments, not light.
Different results are obvious here.
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• In a lump of clay, you see the light that is
  reflected (leftover), after the rest has been
  absorbed.
• For this reason, in painting and printing,
  magenta, cyan, and yellow are called the
  subtractive primary colors.
• They are often referred to loosely as red,
  yellow, and blue.

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• In a color ink jet printer, you often have a
  color cartidge with cyan, magneta, and yellow
  colors. (CMY)
• These small dots are used to create any image
  needed. An additional black cartridge is often
  included.

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Review Questions
87
Review Questions

• Keeping the previous concepts in mind, try the
  following question

Since magenta is equivalent to blue and red, its
just like combining RBG to get white!
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• So, each of the following is also true because in
  each case you are adding the equivalent of RGB
  together to get white

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Complimentary Colors

• When two colors are added together to produce
  white, they are called complimentary colors.
• The previous two slides contain examples of
  complimentary colors.
• Magenta Green
• Yellow Blue
• Cyan Red

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Subtracting Colors?

• With the previous color rules in mind, you can
  also subtract colors

White is equivalent to RGB combined. When you
subtract the R, you are left with G and B. As
learned previously, these two combine to make
cyan!
91

• Using all the information you now have, try the
  following question

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Why are Sunsets Red

• Q If the sky is blue here on Earth, why do we
  see sunsets as orange/red?

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• A In the previous description, we said the
  atmosphere scatters or reflects the blue light
  the most. This leaves the red light to continue
  through the atmosphere.

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When the sun is low on the horizon, the light is
passing through a lot of the atmosphere. The
blue is scattered (subtracted), and orange/red
light is leftover.
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• The blueness of the sky, or the redness of a
  sunset depends on many factors like humidity and
  air pollution.
• In 1883, Mt. Krakatoa erupted. The addition of
  many small particles produced more spectacular
  sunsets/rises around the world.

96
Why is the Ocean Green/Blue?

• Again, the answer has to do with absorbtion and
  transmission.
• Water resonates or vibrates at infrared and red
  frequencies. This means it absorbs the red
  light. If the red light is taken away, the
  remaining green blue light ( cyan ), remains!

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• Once again, the exact color of the water depends
  on many factors.

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Review Question

• Q Why does the blood of an injured deep sea
  diver look greenish-black when photographed with
  natural light, but red when a flash is used?

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Deep in the water, most of the red light has
already been absorbed. Thus, with no red light
reflecting off the normally red blood, it looks
black. With a flashbulb, there is a new source
of red light to be reflected!
100

• Can you say the color of each word without
  reading the actual word?
• For example, for the first word you would say
  green since the letters are green.

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http//library.advanced.org/10796/ch10/ch10.htm
THE ELECTROMAGNETIC SPECTRUM
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http//library.advanced.org/10796/ch10/ch10.htm
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CONVERGING (CONVEX) LENS - GENERAL IMAGE FORMATION
DIVERGING (CONCAVE) LENS - GENERAL IMAGE FORMATION
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CONVERGING LENSES
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CONVERGING LENSES
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The diagrams above shows that in each case, the
image is located behind the lens a virtual
image an upright image reduced in size (i.e.,
smaller than the object)
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LENS EQUATION
Sample Problem 1 A 4.0-cm tall light bulb is
placed a distance of 45.7 cm from a double convex
lens having a focal length of 15.2 cm. Determine
the image distance and the image size.
108
Sample Problem 1 A 4.0-cm tall light bulb is
placed a distance of 45.7 cm from a double convex
lens having a focal length of 15.2 cm. Determine
the image distance and the image size. ho 4.0
cm do 45.7 cm f 15.2 cm 1/f
1/do 1/di 1/(15.2 cm) 1/(45.7 cm) 1/di
0.0658 cm-1 0.0219 cm-1 1/di 0.0439 cm-1
1/di di 22.8 cm
109
Sample Problem 1 A 4.0-cm tall light bulb is
placed a distance of 45.7 cm from a double convex
lens having a focal length of 15.2 cm. Determine
the image distance and the image size. ho 4.0
cm do 45.7 cm f 15.2 cm hi/ho
- di/do hi /(4.0 cm) - (22.8 cm)/(45.7
cm) hi - (4.0 cm) (22.8 cm)/(45.7 cm) hi
-1.99 cm
110
Sample Problem 2 A 4.0-cm tall light bulb is
placed a distance of 8.3 cm from a double convex
lens having a focal length of 15.2 cm. (NOTE
this is the same object and the same lens, only
this time the object is placed closer to the
lens.) Determine the image distance and the image
size ho 4.0 cm do 8.3 cm f 15.2 cm 1/f
1/do 1/di 1/(15.2 cm) 1/(8.3 cm) 1/di
0.0658 cm-1 0.120 cm-1 1/di -0.0547 cm-1
1/di di -18.3 cm
111
Sample Problem 2 A 4.0-cm tall light bulb is
placed a distance of 8.3 cm from a double convex
lens having a focal length of 15.2 cm. (NOTE
this is the same object and the same lens, only
this time the object is placed closer to the
lens.) Determine the image distance and the image
size ho 4.0 cm do 8.3 cm f 15.2 cm
hi/ho - di/do hi /(4.0 cm) - (-18.2
cm)/(8.3 cm) hi - (4.0 cm) (-18.2 cm)/(8.3
cm) hi 8.8 cm http//www.glenbrook.k12.il.us/g
bssci/phys/Class/refrn/u14l5f.html