Lenses

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Lenses

• We use the refractive capability of the air-glass
  interface to bend light
• Lenses control the amount of bending to achieve
  different results
• Lenses can be either converging or diverging if
  they are either concave or convex

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Lenses
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Lenses
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Lens Definitions
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Image Formation
Light from every part of the vase strikes every
part of the wall. The result is that no clear
image is seen.
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Image Formation
The pinhole blocks most of the light so that only
light from one place on the vase can hit one
place on the wall.
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Image Formation
The lens insures that light from one place on the
vase only strikes one place on the wall. But it
allows for much more light than the pinhole.
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Magnifying Glass
Note that flower is inside the focal point of the
lens
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Converging Lens

• When the object is outside the focal point, the
  image appears on the other side of the lens and
  is inverted

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Ray Tracing
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Lens Defects

• Distortions caused by lenses are called
  aberrations
• There are several kinds of aberrations
• Correct aberrations by using multiple lenses,
  often of different kinds of glass
• The two most common kinds are spherical and
  chromatic

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Spherical Aberration
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Chromatic Aberration
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Wave-Particle Duality

• This is a shocking topic and a difficult
  discussion because it shocks your common sense
• Recall that Young demonstrated the wave nature of
  light with the two-slit interference pattern that
  relied on refraction of light at the edges of the
  slit

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Wave Particle Duality

• In 1862, Maxwell published his famous equations
  describing electric and magnetic fields and
  showed that EM waves must exist as field induced
  electric and magnetic fields
• Thus, he demonstrated mathematically how the EM
  waves worked.
• In 1887, Heinrich Hertz created radio waves with
  Maxwells wave properties

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Wave Particle Duality

• So, what is the problem?
• A phenomenon called the photoelectric effect had
  puzzled physicists for a long time
• Basically, for some metals, if you shine light on
  the metal, it will emit electrons
• These electrons are called photoelectrons

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Photoelectric Effect

• Problem is as follows
• Light is an EM wave
• The changing electric field shakes electrons in a
  metal
• If you shine the light for a long time,or have a
  bright enough light, an electron should
  eventually get enough energy to break free and
  become a photoelectron
• NOT WHAT IS OBSERVED!!!

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Photoelectric Effect

• If the light is of high enough frequency, then
  photoelectrons appear immediately
• The number of electrons that appear depends on
  the intensity of the light
• So we have a frequency dependence that we cant
  explain by shaking electrons with the electric
  field

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Photoelectric Effect

• What to do?
• Einstein said consider light as a stream of
  particles
• This is something that Newton had proposed long
  before, but Youngs experiment made people
  discard the idea
• Einsteins light particles are called photons

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Photoelectric Effect

• So how do we relate properties of the photon to
  the wavelength or frequency of the light wave
• Einstein proposed the energy carried by the
  photon is proportional to the frequency of the
  light

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Photoelectric Effect

• This effect requires that photons be completely
  absorbed and all the energy of the photon be
  given to the electron
• Then the electron would have enough energy to
  escape the metal
• Red light photons had to little energy for the
  electrons to escape

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Photoelectric Effect

• Blue or violet light photons have higher energy
  since their frequencies are higher
• Thus producing photoelectrons requires a
  frequency high enough so that the photons have
  enough energy to allow the photoelectrons to
  escape the metal
• Dim light would mean fewer photons and thus fewer
  photoelectrons

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Photoelectric Effect

• Now we have a dilemma
• The double slit experiment shows that light is a
  wave
• The Photoelectric Effect shows that light is a
  particle
• Which is it????
• Answer BOTH!!!

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Wave-Particle Duality

• In order to explain these two experiments we need
  to invoke the duality of light
• Light is both a wave and a particle at the same
  time!!!
• Defies our common sense, but we must trust the
  results of experiments, so it must be true
• Later we will see that all material particles
  have wave properties