Physics 114

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Lecture 11Geometric optics

• Physics 114

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Principles of geometric optics
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Concepts

• Ray model of light
• Image formation
• Reflection
• Refraction
• Dispersion
• Total internal reflection

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EM waves

• c speed of light (m/s)
• f frequency (Hz1/s)
• l wavelength (m)

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Ray model of light

• Light is an EM wave ?diffraction (go around
  obstacles)
• This happens on microscopic scale
• In everyday life we use straight line
  approximation for light propagation Ray model
  of light ? geometric optics
• We infer positions of objects assuming light
  travels in straight lines.

Geometry is important, Bring ruler and
pencil, make good pictures!!!
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Reflection

• We see objects because
• They emit light (Sun, light bulb)
• They reflect light (Moon, table)
• angle of incidence angle of reflection
• qiqr

Rough surface Polished surface.
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Formation of image

• Eye assumes light propagates in straight lines ?
  image (rays of light crossing) is formed behind
  the mirror
• do distance to object
• di distance to image
• For plane mirror
• do di

If light actually goes through the place where
image is formed ? real image
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Speed of light in medium

• Speed of light in vacuum
• c3.0x108m/s
• Speed of light in media
• vltc
• Index of refraction
• nc/v gt1.0

From table 33-1 Vacuum n1.00 Air
n1.0003 Water n1.33 Diamond n2.42
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Refraction

• The front is slowing down

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Refraction, Snells law
Bend toward normal Bend away from normal
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Image formation

• Eye still assumes light propagates in straight
  lines ? optical illusions
• Image is shifted
• Pool appears shallower

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What if n depends on l?

• If n depends on l ? angle of refraction depends
  on l
• n(red)ltn(green)

• A-red, B-green
• B- red, A-green

A
B
Dispersion This is why rainbow occurs
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Total internal reflection
For qgtqc - total internal reflection no light
come out all light is reflected Fiber
optics Necessary condition from thick to thin
media
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Spherical mirrors

• Convex mirror bulges out diverges light
• Concave mirror caves in converges light

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Focus

• Parallel beam of light (e.g. from a very distant
  object) is converged in 1 point focal point F
• Distance from the mirror to F is called focal
  distance, or focus
• f r/2

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Ray tracing

• 3 Easy rays
• Parallel ? through focus
• Through focus ? parallel (reversible rays)
• Through the center of curvature C ? itself

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Magnification

• h0 object height
• h0gt0 - always
• hi image height
• higt0 upright image
• hilt0 inverted image
• mhi/h0 - magnification

mgt1 image larger than object mlt1 image
smaller than object
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Mirror equation

• d0 distance to object
• d0gt0 - always
• di distance to image
• digt0 real image
• dilt0 virtual image

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Convex mirror

• Virtual focus parallel beam focuses behind the
  mirror
• flt0
• Same rules for ray tracing.

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Sign convention for mirrors

• higt0?dilt0 upright image is always virtual
• hilt0?digt0 inverted image is always real

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Images in curved mirrors

• Concave mirror
• d0gtr (real, inverted), smaller
• rgtd0gtf (real, inverted), larger
• d0ltf (virtual, upright), larger

• Convex mirror
• Image is always
• (virtual, upright), smaller.