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Lenses
Physics 202Professor Lee
CarknerLecture 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
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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
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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 eye’s near point
The magnification is:m = 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
m = -fob/fey
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Refracting Telescope
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Giant 40 inch Refractor at Yerkes
Observatory,Williams Bay
Wisconsin
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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