Yikes For you new drivers'

1

• Yikes! For you new drivers.

Disheveled man, from a car accident, talking on
cell phone walking with steering wheel in
hand.)
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EM Waves, Light and Geometric Optics
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EM Waves

• Electromagnetic Waves
• An electromagnetic wave has a frequency f and a
  wavelength ? that are related to the speed of the
  wave by
• 
  vf ?
• Light is the most common example of an
  electromagnetic wave.
• electromagnetic waves include the microwaves you
  use to heat up leftovers for dinner, and the
  radio waves that are broadcast from radio
  stations.
• An electromagnetic wave can be created by
  accelerating charges moving charges back and
  forth will produce oscillating electric and
  magnetic fields, and these travel at the speed of
  light. It would really be more accurate to call
  the speed "the speed of an electromagnetic wave",
  because light is just one example of an
  electromagnetic wave.
• speed of light in vacuum c 3.00 x 108 m/s
• Since all electromagnetic waves travel at the
  speed of light the wave equation becomes
• Cf ?
• C is the ultimate speed limit in the universe.
• Nothing can travel faster than light in a vacuum.

C
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EM Waves

• Electromagnetic Waves
• Properties of electromagnetic waves
• Something interesting about light, and
  electromagnetic waves in general, is that no
  medium is required for the wave to travel
  through. Other waves, such as sound waves, can
  not travel through a vacuum. An electromagnetic
  wave is perfectly happy to do that.
• An electromagnetic wave, although it carries no
  mass, does carry energy.
• The energy carried by an electromagnetic wave is
  proportional to the frequency of the wave.
  Remember tha wavelength and frequency of the wave
  are connected via the speed of light
• Electromagnetic waves are split into different
  categories based on their frequency (or,
  equivalently, on their wavelength).
• Visible light, for example, ranges from violet to
  red. Violet light has a wavelength of 400 nm, and
  a frequency of 7.5 x 1014 Hz. Red light has a
  wavelength of 700 nm, and a frequency of 4.3 x
  1014 Hz. Any electromagnetic wave with a
  frequency (or wavelength) between those extremes
  can be seen by humans.
• Visible light makes up a very small part of the
  full electromagnetic spectrum. Electromagnetic
  waves that are of higher energy than visible
  light (higher frequency, shorter wavelength)
  include ultraviolet light, X-rays, and gamma
  rays. Lower energy waves (lower frequency, longer
  wavelength) include infrared light, microwaves,
  and radio and television waves.

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EM Waves

• Structure of Electromagnetic Waves
• An electromagnetic wave (such as a radio wave)
  propagates outwards from the source (an antenna,
  perhaps) at the speed of light.
• What this means in practice is that the source
  has created oscillating electric and magnetic
  fields, perpendicular to each other, that travel
  away from the source.
• The E and B fields of the EM wave
• Are perpendicular to each other
• are perpendicular to the direction the wave
  travels
• Therefore electromagnetic waves are transverse
  waves.
• The energy of the wave is stored in the electric
  and magnetic fields.

E and B vary sinusoidally with x
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EM Waves
ROY G BIV once said So many waves, so little
time

• Note the overlap between types of waves
• Visible light is a small portion of the spectrum
• Types are distinguished by frequency or wavelength

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EM Waves

• Types of Electromagnetic Waves
• Radio Waves
• Wavelengths of more than 104 m to about 0.1 m
• Used in radio and television communication
  systems
• Microwaves
• Wavelengths from about 0.3 m to 10-4 m
• Well suited for radar systems
• Microwave ovens are an application
• Infrared waves
• Wavelengths of about 10-3 m to 7 x 10-7 m
• Incorrectly called heat waves
• Produced by hot objects and molecules
• Readily absorbed by most materials
• Visible light
• Part of the spectrum detected by the human eye
• The human eye is most sensitive at about 5.5 x
  10-7 m (yellow-green)
• Ultraviolet light
• Covers about 4 x 10-7 m to 6 x 10-10 m
• Sun is an important source of uv light

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EM Waves

• Studying the Universe with Electromagnetic Waves
• These are images of the Crab Nebula
• They are (clockwise from upper left) taken with
• x-rays
• visible light
• radio waves
• infrared waves

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Optics

• EM Wave Polarization
• polarized light is a form of polarized EM wave.
• light in which there's a preferred direction for
  the electric and magnetic field vectors in the
  wave.
• unpolarized light
• there is no preferred direction the waves come
  in with electric and magnetic field vectors in
  random directions.
• Most light sources emit unpolarized light
• How can light be polarized?
• Reflection-Light reflecting off a surface will
  tend to be polarized, with the direction of
  polarization (the way the electric field vectors
  point) being parallel to the plane of the
  interface.
• selectively absorbing light with electric field
  vectors pointing in a particular direction.
• Certain materials, known as dichroic materials,
  do this, absorbing light polarized one way
• Liquid crystal displays, such as those in digital
  watches and calculators, also exploit the
  properties of polarized light.
• Sunglasses can be polarized (with lenses that
  only allow vertically polarized light to pass
  through)

Liquid crystalline material is sandwiched between
two glass plates that have seven electrodes,
which can be individually charged, attached to
them. Light passing through Polarizer 1 is
polarized in the vertical direction and, when no
current is applied to the electrodes, the liquid
crystalline phase induces a 90 degree twist of
the light and it can pass through Polarizer 2,
which is polarized horizontally. This light can
then form one of the seven segments on the
display.
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Optics

• The Nature of Light
• Before the beginning of the nineteenth century,
  light was considered to be a stream of particles
• The particles were either emitted by the object
  being viewed or emanated from the eyes of the
  viewer
• Newton was the chief architect of the particle
  theory of light
• He believed the particles left the object and
  stimulated the sense of sight upon entering the
  eyes
• Christian Huygens argued that light might be some
  sort of a wave motion
• Thomas Young (1801) provided the first clear
  demonstration of the wave nature of light
• He showed that light rays interfere with each
  other
• Such behavior could not be explained by particles
• During the nineteenth century, other developments
  led to the general acceptance of the wave theory
  of light
• Maxwell asserted that light was a form of
  high-frequency electromagnetic wave
• Hertz confirmed Maxwells predictions
• Some experiments could not be explained by the
  wave nature of light
• The photoelectric effect was a major phenomenon
  not explained by waves
• When light strikes a metal surface, electrons are
  sometimes ejected from the surface
• The kinetic energy of the ejected electron is
  independent of the frequency of the light
• Einstein (in 1905) proposed an explanation of the
  photoelectric effect that used the idea of
  quantization
• The quantization model assumes that the energy of
  a light wave is present in particles called
  photons
• In view of these developments, light must be
  regarded as having a dual nature

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Optics

• Light Rays
• Geometric optics involves the study of the
  propagation of light
• The ray approximation is used to represent beams
  of light
• It uses the assumption that light travels in a
  straight-line path in a uniform medium and
  changes its direction
• when it meets the surface of a different medium
• or if the optical properties of the medium are
  nonuniform
• A ray of light is a line drawn perpendicular to
  the wave front and points in the direction of
  velocity of the wave

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Optics

• Reflection of Light
• A ray of light, the incident ray, travels in a
  medium
• When it encounters a boundary with a second
  medium, part of the incident ray is reflected
  back into the first medium
• This means it is directed backward into the first
  medium
• Specular reflection is reflection from a smooth
  surface
• The reflected rays are parallel to each other

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Optics

• The Law of Reflection
• The normal is a line perpendicular to the surface
• It is at the point where the incident ray strikes
  the surface
• The incident ray makes an angle of ?1 with the
  normal
• The reflected ray makes an angle of ?1 with the
  normal
• The angle of reflection is equal to the angle of
  incidence
• This relationship is called the Law of Reflection
• ?r ?i
• The incident ray, the reflected ray and the
  normal are all in the same plane

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Optics

• Formation of Images by a Plane Mirror
• The object distance is the distance from the
  object to the mirror or lens
• Denoted by do
• The image distance is the distance from the image
  to the mirror or lens
• Denoted by di
• Images
• always located by extending diverging rays back
  to a point at which they intersect
• Images are located either at a point from which
  the rays of light actually diverge or at a point
  from which they appear to diverge
• A real image is formed when light rays pass
  through and diverge from the image point
• Real images can be displayed on screens
• A virtual image is formed when light rays do not
  pass through the image point but only appear to
  diverge from that point
• Virtual images cannot be displayed on screens
• Plane (Flat) Mirrors
• Simplest possible mirror
• Light rays leave the source and are reflected
  from the mirror
• /do//di/
• The image is virtual (always)

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Optics

• Spherical Mirrors
• A spherical mirror has the shape of a section of
  a sphere
• The mirror focuses incoming parallel rays to a
  point
• A concave spherical mirror has the silvered
  surface of the mirror on the inner, or concave,
  side of the curve
• A convex spherical mirror has the silvered
  surface of the mirror on the outer, or convex,
  side of the curve
• The mirror has a radius of curvature of R
• Its center of curvature is the point C
• The distance between the image point (focal
  point) F and the middle of the mirror is the
  focal length f

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Optics

• Spherical Mirror Images and The Mirror Equation
• In order to accurately describe an image formed
  by a concave or convex mirror we can use the
  mirror equation and magnification equation below

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Optics

• Ray Diagrams
• A ray diagram can be used to determine the
  position and size of an image
• They are graphical constructions which reveal the
  nature of the image
• They can also be used to check the parameters
  calculated from the mirror and magnification
  equations
• To draw a ray diagram, you need to know
• The position of the object
• The locations of the focal point and the center
  of curvature
• Three rays are drawn
• They all start from the same position on the
  object
• The intersection of any two of the rays at a
  point locates the image
• The third ray serves as a check of the
  construction
• Ray Diagram for a concave mirror
• Ray 1 is drawn from the top of the object
  parallel to the principal axis and is reflected
  through the focal point, F
• Ray 2 is drawn from the top of the object through
  the focal point and is reflected parallel to the
  principal axis
• Ray 3 is drawn through the center of curvature,
  C, and is reflected back on itself

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Optics

• Refraction of Light
• Index of Refraction
• Light travels slower in a transparent material
  than it does in a vacuum
• Photons are absorbed, reemitted and scattered by
  matter, therefore slowing the light down
• This process causes the light ray to deviate or
  refract from its incident direction
• This is called refraction
• This refraction is constant for various materials
  and is defined as the index of refraction and is
  always less than 1
• As light travels from one medium to another, its
  frequency does not change
• Both the wave speed and the wavelength do change
• The wavefronts do not pile up, nor are created or
  destroyed at the boundary, so must stay the
  same
• The frequency stays the same as the wave travels
  from one medium to the other
• v ?
• 1 2 but v1 ¹ v2 so ?1 ¹ ?2

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Optics

• Refraction of Light
• Snells Law
• When light travels from one material to another,
  the angle of refraction and angle of incidence
  are related by
• n1 sin ?1 n2 sin ?2
• ?1 is the angle of incidence
• ?2 is the angle of refraction
• The experimental discovery of this relationship
  is usually credited to Willebrord Snell and is
  therefore known as Snells law of refraction
• Example 1 page 775
• For a given material, the index of refraction
  varies with
• the wavelength of the light passing through the
  material
• This dependence of n on ? is called dispersion
• Snells law indicates light of different
  wavelengths is
• bent at different angles when incident on a
  refracting material
• Prisms
• Since all the colors have different angles of
  deviation
• white light will spread out into a spectrum
• Violet deviates the most

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Optics

• Refraction of Light
• Total Internal Reflection
• When light crosses an interface into a medium
  with a higher index of refraction, the light
  bends towards the normal. Conversely, light
  traveling across an interface from higher n to
  lower n will bend away from the normal. This has
  an interesting implication at some angle, known
  as the critical angle, light traveling from a
  medium with higher n to a medium with lower n
  will be refracted at 90 in other words,
  refracted along the interface. If the light hits
  the interface at any angle larger than this
  critical angle, it will not pass through to the
  second medium at all. Instead, all of it will be
  reflected back into the first medium, a process
  known as total internal reflection.
• The critical angle can be found from Snell's law,
  putting in an angle of 90 for the angle of the
  refracted ray. This gives
• For any angle of incidence larger than the
  critical angle, Snell's law will not be able to
  be solved for the angle of refraction, because it
  will show that the refracted angle has a sine
  larger than 1, which is not possible. In that
  case all the light is totally reflected off the
  interface, obeying the law of reflection.
• Optical fibers are based entirely on the
  principle of total internal reflection. An
  optical fiber is a flexible strand of glass. A
  fiber optic cable is usually made up of many of
  these strands, each carrying a signal made up of
  pulses of laser light. The light travels along
  the optical fiber, reflecting off the walls of
  the fiber. With a straight or smoothly bending
  fiber, the light will hit the wall at an angle
  higher than the critical angle and will all be
  reflected back into the fiber. Even though the
  light undergoes a large number of reflections
  when traveling along a fiber, no light is lost to
  refraction

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Optics

• Refraction of Light
• Applications of Refraction
• Lenses
• Lenses are commonly used to form images by
  refraction
• Lenses are used in optical instruments
• Cameras, Telescopes, Microscopes
• Light passing through a lens experiences
  refraction at two surfaces
• The image formed by one refracting surface serves
  as the object for the second surface

Converging lens
Diverging lens
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Optics

• Lens Images and The Thin Lens Equation
• In order to accurately describe an image formed
  by a converging or diverging lens we can use the
  lens equation and magnification equation below