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
• It has two sides we have to account for

3
Lenses

• We will consider only thin lenses, i.e. thickness
  much smaller than i, p or f
• If the two surfaces are the same, the lens is
  symmetric

4
Lenses and Mirrors

• Mirrors produce virtual images on the opposite
  side from the object
• Mirrors produce real images on the same side as
  the object
• 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 and Diverging
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Converging Lens

• A lens consisting of two convex lenses back to
  back is called a converging lens
• 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

• A lens consisting of two concave lenses back to
  back is called a diverging lens
• f is virtual and negative
• Diverging lenses produce images smaller than the
  object

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Converging and Diverging
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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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Three Types of Images
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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
• Objects behind the focal point (further from the
  lens) produce real images on the opposite side of
  the lens

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Diverging Lenses and Images

• No matter where the object is, a diverging lens
  produces an upright, virtual image on the same
  side as the object
• Virtual images form on the same side as the
  object, real images form on the opposite side

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Three Types of Images
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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
• For a two lens system the magnification is
• M m1m2
• 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

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Magnifying Lens

• You can use a magnifying lens to overcome the
  limitation of your eyes 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

• A simple compound microscope consists of an
  objective and eyepiece
• The eyepiece acts as a magnifying glass
• The magnification of the objective is m -i/p
• p is very close to the focal length of the
  objective, fob
• 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

• In a telescope the two lenses are placed so that
  the two inner focal points are in the same place
• The eyepiece then magnifies the real image
• mq -fob/fey

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Refracting Telescope
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Giant 40 inch Refractor at Yerkes
Observatory,Williams BayWisconsin
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Newtonian Telescope
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Telescopes

• The magnification of the telescope can be altered
  by changing eyepieces
• Magnification is not the most important property
  of a telescope
• The true purpose of the objective lens is to
  gather more light than your eye can and focus it
  so that it can be viewed
• The objective becomes so large it is hard to
  build and support