VII. Optics

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VII. Optics

• Originally Properties and Use of Light.
• Now Much More General.

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VII1 Introduction into Geometrical Optics
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Main Topics

• Introduction into Optics.
• Margins of Geometrical Optics.
• Fundamentals of Geometrical Optics.
• Ideal Optical System.
• Fermats Principle.
• Reflection and Reflection Optics.

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Introduction into Optics I

• Since thousands of years ago people have tried to
  find an answer to a simple question What is
  light?
• The first important discoveries were done some
  three thousand years ago and recently our
  knowledge almost doubles every year. Yet the deep
  insights change slowly and the question immutably
  remains.

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Introduction into Optics II

• For a long time it was believed that light is a
  flow of some microscopic particles. So called,
  corpuscular theory, based on this idea had been
  supported e.g. by Isaac Newton ( 1642-1727) who
  managed to complete the human knowledge in
  several fields e.g. mechanics and gravitation. In
  spite of his great authority, experiments
  revealed clearly wave properties of light.

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Introduction into Optics III

• They were ingeniously summarized by James Clerk
  Maxwell (1831-1879). So now we know that visible
  light are in fact electromagnetic waves with
  wavelengths of 400 700 nm.
• Surprisingly the particle wave problem
  remains unsolved since experiments exist, which
  support both ideas.

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Introduction into Optics IV

• Energy of light (EMW) is transferred and also
  absorption and emission are accomplished by some
  minimal quanta photons. (They are bosons, there
  is no limit on number of photons in the same
  state).
• However motion of light through a lens, hole a
  set of slits is governed by wave characteristics.

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Introduction into Optics V

• It was found that this dualism of waves and
  particles is an intrinsic property of the
  microscopic world and the acceptance of the idea
  that microscopic entities can be particles and
  waves at the same time is a basic idea on which
  the quantum theory, the best, yet not easy to
  understand, description of the microscopic world,
  we recently have, is build.

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Introduction into Optics VI

• Due to this dualism also the scope of optics
  widened. It deals with not only the behavior and
  use of visible light but generally all
  electromagnetic and other waves but also for
  instance with focusing particles such as
  electrons or neutrons.

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Margins of Geometrical Optics I

• Although, optics is an extremely wide and complex
  scientific field, for many practical and
  industrial purposes its 1st approximation the
  geometrical optics can be used. The effects it
  deals with can be treated by pure geometry. It
  inherits some properties of waves, such as
  straight propagation, independence and
  reciprocity but it stops to be valid if other
  wave properties e.g. interference start to
  matter.

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Margins of Geometrical Optics II

• Typically wave properties start to matter when
  the size of optical elements are comparable to
  the wavelength. This is the case in radio- and
  microwave techniques but also limits the
  resolution of optical instruments.
• Particle properties are detectable for EMW of
  high energies but also for visible light.

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Margins of Geometrical Optics III

• Geometrical optics can be used when the
  wavelength can be considered (close to) zero and
  the energy of the electromagnetic waves is small
  (or materials are used where e.g. fotoeffect is
  negligible).
• These conditions are usually met when dealing
  with visible light at high intensities.

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Fundamentals of Geometrical Optics I

• First important assumption is that light travels
  in the form of rays. Those are lines drawn in
  space, which correspond to the flow of radiant
  energy. In isotropic and homogeneous materials
  rays are straight lines perpendicular to the
  wavefronts of the waves.
• Lines can be treated by pure geometry.

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Fundamentals of Geometrical Optics II

• Rays can relatively easily be traced through an
  optical system and wavefronts and other qualities
  of imaging can be reconstructed.
• Rays follow a principle of reciprocity, if a ray
  can pass through an optical system in one
  direction, it can pass also in the opposite one.
  This is one result of the Fermats principle.

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Fermats Principle I

• Fermats principle is a convenient basis for
  describing the very simple but also very
  complicated optical phenomena. It states
• A light if going from point S to point P must
  traverse an optical path length which is
  stationary with respect of variations of that
  path.

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Fermats Principle II

• It is a heritage of wave properties which says
  that rays neighboring the real ray are (almost)
  in-phase with it.
• Usually, the meaning is that from all the
  possible rays that can travel between two points,
  the real ray is the one, which makes its path in
  the shortest time.

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An Ideal Optical System I

• By an optical system we are trying to focus all
  rays emanating from some point S in the object
  space into some point P in the image space.
• If this is reached the optical system is
  stigmatic for these two points.
• By ideal optical system would every 3-dim region
  in one space be stigmatically imaged in the other
  region.
• The regions are interchangeable due to
  reciprocity.

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An Ideal Optical System II

• Properties of a real optical system should be as
  close as possible to that of the ideal one.
• Moreover the rays in the system should be easily
  traceable and due to simple parametrization an
  simple equation should be available which would
  relate the positions of the object and the image.
• Optical systems are based on the effects of
  reflection and refraction.

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Reflection I

• Lets use the Fermats principle to find the law
  of reflection at a top of a flat surface
• Point S is a source of many rays which spread out
  radially. Since the observation point P is in the
  same space, the ray which comes first from S to P
  will be the shortest one. We can find it using a
  trick when we reflect the point S behind the
  mirror.

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Reflection II

• From simple geometry it follows that the angle of
  incidence is equal the angle of reflection. In
  optics we measure these angles from the normal to
  the reflecting surface.
• This is valid for any element of the surface.
• If a surface of a reasonable size is smooth the
  reflection is specular and from P we can see the
  image of S or it is diffuse (paper, Moon)

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Reflection Optics I

• Using reflection is one possibility to build
  optical elements, in this case various kinds of
  mirrors, to produce image of an object. The image
  can be either real, if the rays really path
  through it or virtual if eye, only sees the rays
  coming from the direction of the image.
• R. O. is important for X-rays and neutrons.

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Reflection Optics II

• Every optical element has a principal axis, which
  is roughly its axis of its symmetry.
• If an ideal mirror is stroked by rays coming
  parallel with the principal axis the rays either
  focus in the focal point in the case of concave
  mirrors or they seem to come from a virtual focal
  point behind the mirror, if it is convex.
• Optical properties of ideal mirror are described
  by one parameter only, the focal length f, the
  distance of the focal point from the mirrors
  center.

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Reflection Optics III

• The surface of an ideal mirror should be
  parabolic.
• Recently, it is in principle possible to make a
  parabolic mirror but in usual applications much
  cheaper spherical mirrors are used but they
  suffer from spherical aberration and can be
  successfully used only for paraxial rays those
  very close to the principal axis.

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Reflection Optics IV

• The distance of the object do, the image di and
  the focal length f obey the mirror equation
• 1/do 1/di 1/f
• It can be derived from similar triangles.
• The treatment of convex mirrors is similar but
  their focal length is negative.

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Reflection Optics V

• We can also define the lateral magnification m
  hi/h0 - di/do
• Recently, special optical systems are being
  widely developed for instance for X-rays,
  neutrons or fiber optics, which use total
  reflection which appears at very low angles of
  incidence on simple or multi-layer surfaces.

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Homework

• Chapter 33 16, 18, 36, 37
• Chapter 34 4, 5, 17, 18

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Things to read and learn

• Chapters 33 and 34.
• Try to understand all the details of the scalar
  and vector product of two vectors!
• Try to understand the physical background and
  ideas. Physics is not just inserting numbers into
  formulas!

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Maxwells Equations I

• .