Lenses

1
Lenses

• Physics 202
• Professor Lee Carkner
• Lecture 23

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Refraction

• Lenses can be used for the same purposes
• Lenses have focal lengths and real and virtual
  images, but their properties also depend on the
  index of refraction
• Unlike a mirror, you look through a lens
• It has two sides we have to account for

3
Lenses

• Light incident on a lens is refracted twice, once
  when entering and once when leaving
• Our thin lenses are composed of two refracting
  surfaces placed back to back
• If the two surfaces are the same, the lens is
  symmetric

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Lenses and Mirrors

• Mirrors produce virtual images on the opposite
  side from the object
• i is negative in both cases
• Mirrors produce real images on the same side as
  the object
• i is positive in both cases
• If a mirror curves towards the object, f and r
  are positive (real focus)
• Real is positive, virtual is negative

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Converging Lens

• Rays initially parallel to the central axis are
  focused to the focal point after refraction
• The focal point is on the opposite side from the
  incoming rays
• Converging lenses produce images larger than the
  object
• m -i/p

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Diverging Lens

• Rays initially parallel to the central axis
  diverge after refraction, but can be traced back
  to a virtual focus
• f is virtual and negative
• Diverging lenses produce images smaller than the
  object

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Lens Equations

• A thin lens follows the same equation as a
  mirror, namely
• 1/f 1/p 1/i
• 1/f (n-1) (1/r1 -1/r2)
• Where r1 and r2 are the radii of curvature of
  each side of the lens (r1 is the side nearest the
  object)
• For symmetric lenses r1 and r2 have opposite sign

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Converging Lenses and Images

• Objects in front of the focal point (nearer to
  the lens) produce virtual images on the same side
  as the object
• Image is virtual so i is negative
• Objects behind the focal point (further from the
  lens) produce real images on the opposite side of
  the lens
• Image is real so i is positive

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Diverging Lenses and Images

• For either lens the location of images is the
  reverse of that for mirrors
• Real images have positive i, virtual images have
  negative i

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1)
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2)
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Two Lenses

• To find the final image we find the image
  produced by the first lens and use that as the
  object for the second lens
• M m1m2
• We can approximate several common optical
  instruments as being composed of a simple
  arrangement of thin lenses
• In reality the lenses are not thin and may be
  arranged in a complex fashion

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DualLenses
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Near Point

• How can you make an object look bigger
• Increases angular size
• The largest clear (unlensed) image of an object
  is obtained when it is at the near point (about
  25 cm)
• A converging lens will increase the angular
  diameter of an object
• mq q/q

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Magnifying Lens

• If the object is inside the near point you can
  view it through a lens which will produce a
  virtual image outside of the near point
• The magnification is
• mq 25 cm /f
• This is the size of the object seen through the
  lens compared to its size at the near point

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Magnifying Glass
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Compound Microscope

• The objective creates a real image focused at the
  focal point of the eyepiece
• The magnification of the objective is m -i/p
• i is very close to the distance between the
  lenses, s
• The total magnification is the product of the
  magnification of each
• M (-s/fob)(25 cm/fey)
• where s is the distance between the focal point
  of the lenses (the tube length) and f is the
  focal length

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Microscope
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Refracting Telescope

• The rays coming in from infinity are refracted by
  the objective to create a real image at the
  common focal point
• The total angular magnification of the telescope
  depends on the ratio of the eyepieces
• mq -fob/fey

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Refracting Telescope
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Newtonian Telescope
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Telescopes

• The magnification of the telescope can be altered
  by changing eyepieces
• Short focal length means more magnification
• Limited by blurring effects of atmosphere
• The largest practical refracting telescope has an
  objective with a diameter of about 1m
• The objective becomes so large it is hard to
  build and support

23
Next Time

• Read 35.1-35.5
• Homework Ch 34, P 69, 71, 72, 80, Ch 35, P 1,
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