Geometrical Optics'

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Geometrical Optics.

• Laws of reflection and refraction.
• Images from by lenses and mirrors.
• Polarization.

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The Ray Model of Light.

• The ray model of light assumes that light travels
  in straight-line paths called light rays.
• For example, a point source of light like the sun
  casts distinct shadows and the beam of a torch
  appears to be a straight line.
• Our whole orientation to the physical world is
  based on this assumption.

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Reflection of Light

• Reflectance is the ratio of the light reflected
  from a surface to the light falling on the
  surface. It is commonly expressed as a
  percentage.
• For example, the reflectance from a smooth silver
  surface is about 95 (with only small amount of
  scattering) whereas black surfaces have
  reflectances of about 5 or less.

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Laws of Reflection

• 1. The angle of incidence, i, is equal to the
  angle of reflection r.
• 2. The incident ray, the reflected ray and the
  normal to the reflecting surface all lie in the
  same plane.

Normal
Incident ray
Reflected ray
i r
Reflecting surface.
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Images formed by plane mirrors.
Object
Image - notice that it is the same distance away
from the mirror
The image is virtual, erect and the same size as
the object.
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The Speed of Light and the Index of Refraction.

• The accepted value for the speed of light, c, in
  vacuum is 2.99792458 x 108 m/s
• This is usually rounded off to 3.00 x 108 m/s.
• The speed of light in other materials (eg glass,
  air..) is less. For example, it is 3/4c in
  water.
• The ratio of the speed of light in a vacuum to
  the speed, v, in a given material is called the
  index of refraction, n, of that material.
  Therefore
• n c/v

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Indices of Refraction
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Index of Refraction.

• Since diamond has a n2.42, the speed of light in
  diamond is
• v c n 3.00 x 108 2.42 1.24 x 108 m/s
• What is the speed of light in salt solution?
• (answer 1.96 x 108 m/s)

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Refraction
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Refraction Snells Law.

• Snells Law

The incident ray, the refracted ray, and the
normal to the boundary at the point of incidence
all lie in the same plane.
When light passes from an optically less dense
medium into an optically more dense medium, the
light ray is bent towards the normal.
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Refraction and the critical angle
Medium 1

• The critical angle is that angle that results
  with the refracted ray making an angle of 90
  with the normal and travels along the boundary
  between the two media.

Critical Angle
Medium 2
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Refraction and apparent depth.
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Refraction and Dispersion
Light entering a prism is refracted towards the
normal, and the emerging ray is refracted away
from the normal, turning the ray through a
considerable angle. Because the refractive index
of a substance varies for the different
wavelengths, a prism can spread out the various
wavelengths of light contained in an incident
beam and form a spectrum.
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How are Rainbows formed?
Only one wavelength from a rain drop makes it
into the eye. But there are many rain drops, in
many different positions and because light will
interact with each rain drop in the same way,
there is steady progression from long wavelengths
(red) near the top of the rainbow to short
wavelengths (blue) near the bottom of the rainbow
with the yellow and green colors in between.
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Formation of images by spherical mirrors.
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Curved Mirrors
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Images formed by lenses
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Real Verses Virtual Images.

• A virtual image is one where the rays of light do
  not actually pass through the image, a piece of
  white paper or film placed a the image would not
  detect the image.
• A real image is one where the light does pass
  through the image and which therefore could
  appear on paper or film placed at the image
  position.

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Converging Diverging Lenses
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Mathematics of Lenses and Mirrors
Positive and Negative numbers Negative ?
Virtual Positive ? Real
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Mathematics of Lenses and Mirrors
Note that this virtual image is formed on the
same side as the object.
Note the positive value for the focal length as
it is a real focus, and the negative value for
the image distance as it is a virtual image.
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Images formed by Concave Lenses
Note that this virtual image is formed on the
same side as the object.
Note the negative value for the focal length for
a diverging lens as it is a virtual focus.
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Images formed by Concave Mirrors.
Image forms here
Note that the mathematical relationship is the
same as for lenses, except that the REAL image is
formed on the same side as the object.
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Chromatic Aberration
ChromaticAberration The non-focusing of light
due to differing wavelengths.
The solution is to introduce another lens. This
combination of lenses is known as an Achromatic
Lens
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Spherical Aberration
Spherical Aberration the non-focusing of light
due to the shape of the mirror.
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The Eye and common defects
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Eyes and Corrective measures.
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Some Optical Instruments.
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Some Optical Instruments.
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Light waves Electromagnetic Model.
Light waves are produced by vibrating electric
charges.
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Polarisation of light.

• If you could view an electromagnetic wave
  traveling towards you, then you would observe the
  vibrations of the wave occurring in more than one
  plane of vibration. This is knowed as unpolarized
  light.
• The process of transforming unpolarized light
  into polarized light is known as polarization.

More information on polarization is available
at http//www.physicsclassroom.com/Class/light/U12
L1e.html
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How does Polarization work?