Mirrors and Lenses

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Chapter 23

• Mirrors and Lenses

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23.1 Flat Mirrors

• Flat mirror (or plane mirror) - reflects light in
  a normal way.
• Object distance (p) - the distance the object is
  from the mirror.
• Image distance (q) - the distance the image is
  from the mirror.
• Images are formed at the point where light rays
  intersect or appear to originate from.
• Figure 23.1 and 23.2

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Images

• Classifications
• Real - a real image is one in which light
  actually intersects or passes through the image
  point.
• Virtual - a virtual image is one in which the
  light does not pass through the image point but
  appears to come (diverge) from that point.

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Flat Mirrors

• The image formed by a flat mirror is virtual.
• Real images can be displayed on a screen (at a
  movie), but virtual images can not.
• The image formed by an object placed in front of
  a flat mirror is as far behind the mirror as the
  object is in front of the mirror.

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Lateral Magnification

• M image height/ object height
• M h/ h
• For a flat mirror, M 1, because h h!

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Summary for Flat Mirrors

• The image is as far behind the mirror as the
  object is in front.
• The image is unmagnified, virtual, and upright
  (the opposite of an upright image is an inverted
  image).

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Rearview Mirrors

• Figure 23.5
• Refracted light is the bright setting, the
  reflected light is the dim setting.

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23.2 Spherical Mirrors

• A spherical mirror has the shape of a segment of
  a sphere.
• Concave mirror (converging mirror) - light
  reflects off of the inner caved in surface.
• Convex mirror (diverging mirror) - light reflects
  off of the outer surface.

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Important terms

• Figure 23.7
• Radius of curvature (R) - distance from the
  center of curvature (C) to the mirror.
• Principal axis - a line drawn from C to the
  mirror.
• O - object
• I - image
• Whenever reflected light passes through an image
  point, the image is real!

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Equations

• Magnification M h/h -q/p
• Mirror equation 1/p 1/q 2/R
• If the object is very far from the mirror (such
  that p approaches infinity), then 1/p 0.
  Therefore, q R/2, thus the image point is
  halfway between the center of curvature of the
  mirror and the center of the mirror.
• In this special case we call the image point the
  focal point, and the distance from the mirror the
  focal length (f). f R/2 1/p 1/q 1/f

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Convex mirrors

• In general, the image formed by a convex mirror
  is upright, virtual, and smaller than the object.

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Ray Diagrams

• We can determine the positions and sizes of
  images formed by mirrors using ray diagrams.
• Rules
• 1. In parallel, out the focal point!
• 2. In the focal point, out parallel!
• 3. Through the center of curvature and back on
  itself!
• Figure 23.12

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Sign conventions for mirrors and example problems

• Table 23.1 (p. 760)
• Ex. 23.2
• Ex. 23.3
• Ex. 23.4

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Uses for spherical mirrors

• Concave mirrors - compact in makeup application
  or a shaving mirror.
• Convex - shopping malls, side view mirrors on a
  car.

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Check this out!
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23.5 Atmospheric refraction

• Visibility of the sun at dusk - figure 23.18.
• Mirage - a mirage is observed when the ground is
  so hot that the air directly above it is warmer
  than the air at higher elevations.
• The layers of air at different heights above the
  earth have different densities and different
  refractive indices.

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23.6 Thin Lenses

• A thin lens consists of a piece of glass or
  plastic, ground so that each of its two
  refracting surfaces is a segment of either a
  sphere or plane.
• Lenses are commonly used to form images by
  refraction in optical instruments, such as
  cameras, telescopes and microscopes.

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Converging and Diverging Lenses

• Figure 23.22
• (a) Converging lenses - thicker in the middle
  than their outer edges.
• (b) Diverging lenses - thinner in the middle
  than their outer edges.
• Figure 23.23

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Thin lens equation

• 1/p 1/ q 1/f
• M -q/p
• Table 23.3 (p. 772)
• Ray diagrams, same as for mirrors except you pass
  through the lens!

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Example problems

• Ex. 23.8
• Ex. 23.9

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Combination of lenses or mirrors

• If two thin lenses (or a lens and a mirror) are
  used to form an image, the image formed by the
  first lens is treated as the object for the
  second lens (mirror).
• The image formed by the second lens (mirror) is
  the final image of the system.
• The overall magnification of a system of lenses
  is the product of the individual magnifications.
• M M1M2

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Lens aberrations

• Defects in shape and form of lenses and mirrors
  can cause imperfections in quality of the images
  produced.
• Spherical aberration - light passing through a
  lens is focused at different points (Fig 23.31
  and 23.30 a).
• Astigmatism - object not on optical axis of lens
  (Fig 23.30 b).
• Coma - light passing through the lens far from
  the optical axis focuses at a different part of
  the focal plane from light passing near the
  center of the lens.

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Chromatic aberration

• The fact that different wavelengths of light
  refracted by a lens focus at different points
  gives rise to chromatic aberration.
• The focal length of red light is greater than
  that of violet light.
• Chromatic aberration can be greatly reduced by
  using a combination of converging and diverging
  lenses made from two different types of glass.

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