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Chapter 23
LIGO mirror
LIGO mirror
Credit LIGO Laboratory, Caltech
Credit LIGO Laboratory, Caltech

• Mirrors and Lenses

James Webb Space Telescope
Credit NASA
http//www.ubergizmo.com/15/archives/2010/ 09/diy_
macro_lens_for_your_nexus_one.html
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Images and Mirrors

• Definitions
• object distance p - distance from the object to
  the mirror, lens
• image distance q - distance from the image to the
  mirror, lens
• lateral magnification M - ratio of the image
  height to the object height
• Images are formed at the point where
• The rays of light actually intersect (real
  image)
• The rays of light appear to originate (virtual
  image)
• To find where an image is formed, it is always
  necessary to follow at least two rays of light as
  they reflect from the mirror

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Types of Images for Mirrors and Lenses
Real Image

• A real image is one in which light actually
  passes through the image point
• Real images can be displayed on screens
• A virtual image is one in which the light does
  not pass through the image point
• The light appears to diverge from that point
• Virtual images cannot be displayed on screens
• When you look in a flat mirror, you see a virtual
  image

Virtual Image
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Magnification

• The lateral magnification is defined as
• Magnification doesnt always mean enlargement
• The image can be smaller than the object
  (sometimes called de-magnification)

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Flat Mirrors

• One ray starts at P, follows path PQ and reflects
  back on itself
• A second ray follows path PR and reflects
  according to the Law of Reflection
• Both rays appear to come from a single point
  behind the mirror
• The image is as far behind the mirror as the
  object is in front
• p q
• The image is unmagnified
• The image height is the same as the object height
• h h and M 1

• The image
• is virtual
• is upright
• has the same orientation
• as the object
• There is an apparent
• left-right reversal in the image

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Concave Spherical Mirrors

• A spherical mirror has the shape of a segment of
  a sphere
• concave spherical mirror - mirror surface on the
  inner (concave) side of the curve
• The mirror has a radius of curvature of R
• center of curvature is the point C
• Point V is the center of the spherical segment
• A line drawn from C to V is called the principle
  axis of the mirror

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Concave Mirror, Image

• A point source of light placed at O
• Rays drawn from O after reflecting from the
  mirror, rays converge at point I
• Point I is called the image point
• Light actually passes through the point so the
  image is real

• Geometry can be used to determine the
  magnification of the image
• h is negative when the image is inverted with
  respect to the object

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Image Formed by a Concave Mirror

• Relationship between image and object distances
• mirror equation
• If an object is very far away, then p? and 1/p
  0
• Incoming rays are essentially parallel
• In this special case, the image point is called
  the focal point

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Focal Point and Focal Length, cont

• The distance from the mirror to the focal point
  is called the focal length
• The focal length is ½ the radius of curvature
• The focal point is dependent solely on the
  curvature of the mirror, not by the location of
  the object
• f R / 2
• The mirror equation can be expressed as

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Problem 23.47, p 787

• An object placed 10.0 cm from a concave spherical
  mirror produces a real image 8.00 cm away from
  the mirror. If the object is moved to a new
  position 20.0 cm from the mirror, what is the
  position of the image? Is the final image real or
  virtual?

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Convex Mirrors

• Rays from any point on the object diverge after
  reflection as though they were coming from a
  point behind the mirror
• Image is virtual - lies behind the mirror at the
  point where the reflected rays appear to
  originate
• In general, the image formed by a convex mirror
  is upright, virtual, and smaller than the object

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Sign Conventions for Mirrors
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Ray Diagram for Concave Mirror, p gt R

• The object is outside the center of curvature of
  the mirror
• The image is real
• The image is inverted
• The image is smaller than the object

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Ray Diagram for a Concave Mirror, p lt f

• The object is between the mirror and the focal
  point
• The image is virtual
• The image is upright
• The image is larger than the object

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Ray Diagram for a Convex Mirror

• The object is in front of a convex mirror
• The image is virtual
• The image is upright
• The image is smaller than the object

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Images Formed by Refraction

• Rays originate from the object point, O, and pass
  through the image point, I
• When n2 gt n1,
• Real images are formed on the side opposite from
  the object

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Flat Refracting Surface

• The image formed by a flat refracting surface is
  on the same side of the surface as the object
• The image is virtual
• The image forms between the object and the
  surface
• The rays bend away from the normal since n1 gt n2

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Atmospheric Refraction and Mirages

• A mirage can be observed when the air above the
  ground is warmer than the air at higher
  elevations
• The rays in path B are directed toward the ground
  and then bent by refraction
• Related to total internal reflection n is
  smaller near the ground
• The observer sees both an upright and an inverted
  image

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Answer to 23.47