Mirrors

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Mirrors Lenses

• Chapter 23

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Chapter 23 Learning Goals

• Understand image formation by plane or spherical
  mirrors
• Understand image formation by converging or
  diverging lenses

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Understand Image Formation by Plane or Spherical
Mirrors

• Relate the focal point of a spherical mirror to
  its center of curvature
• Locate the image of a real object and determine
  if the image is
• Real or virtual
• Upright or inverted
• Enlarged or Reduced

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Flat Mirrors

• Use a picture to define the following
• image and object ( I O)
• image object distance ( q p )
• image object height ( h h )
• real image
• virtual image

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Flat Mirrors
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Lateral Magnification

• M image height h
• object height h

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Summary of Flat Mirrors

• The image is as far behind the mirror as the
  object is in front of the mirror
• The image is unmagnified, virtual, upright

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Spherical Mirrors

• Two types of spherical mirrors
• Concave Mirror
• Convex Mirror

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Spherical Mirrors

• Use a picture to define the following for a
  concave mirror and convex mirror
• principal axis
• center of curvature ( C )
• radius of curvature ( R )
• image point and object ( I O)
• image object distance ( q p )
• image object height ( h h )

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Focal Length Shown by Parallel Rays
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Spherical Mirrors

• When the object is very far from the mirror
• The image point is halfway between the center of
  curvature and the center of the mirror
• The image point will be called the focal point
• The image distance will be called the focal
  length

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Spherical Mirrors
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Ray Diagram for Concave Mirror, p gt R
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Ray Diagram for a Concave Mirror, p lt f
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Ray Diagram for a Convex Mirror
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Spherical Mirrors

• Magnification Equation
• M image height h - q
• object height h p

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Spherical Mirrors

• Mirror Equation
• 1 1 2
• p q R
• Mirror Equation in terms of focal length
• 1 1 1
• p q f

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Ray Diagrams (Mirrors)

• Front, or real, side
• R is positive
• p q positive
• incident light
• ?-------------
• reflected light

• Back, or virtual, side
• p q negative
• R is negative
• No light

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Sign Convention for Mirrors
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Ray Diagrams

• Steps for Drawing ray diagrams
• Ray 1 is parallel to the principal axis is
  reflected through the focal point, F
• Ray 2 is drawn through the focal point,
  reflected parallel to the principal axis.
• Ray 3 is drawn through the center of curvature,
  C, and is reflected back on itself.

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Ray Diagrams

• The intersection of any two of these rays at a
  point locates the image

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Summary of Thin Lenses
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Spherical Abberation

• Rays are generally assumed to make small angles
  with the mirror
• When the rays make large angles, they may
  converge to points other than the image point
• This results in a blurred image

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Understand image formation by converging or
diverging lenses

• Know what factors affect the focal length of
  lenses
• Determine by ray tracing
• Location of the image of a real object
• Upright or inverted image
• Real or virtual image
• Use the thin lens equation to solve problems
• Analyze simple situations in which the image
  formed by one lens is the object for another lens

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Thin Lens Shapes

• These are examples of converging lenses
• They have positive focal lengths
• They are thickest in the middle

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More Thin Lens Shapes

• These are examples of diverging lenses
• They have negative focal lengths
• They are thickest at the edges

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Thin Lenses

• Converging Lenses
• biconvex
• convex-concave
• plano-convex

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Thin Lenses
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Thin Lenses

• Diverging Lenses
• biconcave
• convex-concave
• plano-convex

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Thin Lenses
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Ray Diagrams (Lenses)

• Front side
• p positive
• q negative
• --------------?
• incident light

• Back side
• p negative
• q positive
• -------------?
• refracted light

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Sign Convention for Lenses

• f is () for a converging lens
• f is (-) for a diverging lens
• R1 R2 are () if the center of curvature is in
  back of the lens (converging)
• R1 R2 are (-) if the center of curvature is in
  front of the lens (diverging)

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Ray Diagrams (Lenses)

• Steps for Drawing ray diagrams
• Ray 1 is parallel to the principal axis is
  refracted through one of the focal points
• Ray 2 is drawn through the center of the lens and
  continues straight through.
• Ray 3 is drawn through the other focal point,
  emerges from the lens parallel to the principal
  axis

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Thin Lenses

• Thin Lens Equation
• 1 1 2
• p q R
• Thin Lens Equation in terms of focal length
• 1 1 1
• p q f

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Thin Lenses

• Magnification Equation
• M image height h - q
• object height h p

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Ray Diagrams for Lenses

• Converging Lenses
• Object behind the focal point
• Object in front of the focal point
• Diverging Lenses
• Object behind the focal point
• Object in front of focal point

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Combination of Thin Lenses

• The image formed by the first lens is treated as
  the object for the second lens

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Chapter 23 Resources

• http//www.physicsclassroom.com/Class/refrn/U14L5e
  b.html