Image Formation 1:

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Chapter 36

• Image Formation 1
• Flat mirror
• Spherical mirrors

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Notation for Mirrors and Lenses

• Object that emits light.
• Image that forms in our brain.
• Magnification The ration of the size of the
  image to the size of the object.

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Notation for Mirrors and Lenses

• The object distance is the distance from the
  object to the mirror or lens
• Denoted by p
• The image distance is the distance from the image
  to the mirror or lens
• Denoted by q
• The (lateral) magnification of the mirror or lens
  is the ratio of the image height to the object
  height
• Denoted by M,

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Types of Images

• A real image is formed when light rays pass
  through and diverge from the image point
• Real images can be displayed on screens
• A virtual image is formed when light rays do not
  pass through the image point but only appear to
  diverge from that point
• Virtual images cannot be displayed on screens

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Images Formed by Flat Mirrors

• Simplest possible mirror
• Light rays leave the source and are reflected
  from the mirror
• Point I is called the image of the object at
  point O
• The image is virtual

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Find Images Formed by Flat Mirrors

• One ray starts at point P, travels to Q and
  reflects back on itself
• Another ray follows the path PR and reflects
  according to the law of reflection
• The triangles PQR and PQR are congruent
• One can prove that

and
PLAY ACTIVE FIGURE
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Reversals in a Flat Mirror

• A flat mirror produces an image that has an
  apparent left-right reversal
• For example, if you raise your right hand the
  image you see raises its left hand
• The reversal is not actually a left-right
  reversal
• The reversal is actually a front-back reversal
• It is caused by the light rays going forward
  toward the mirror and then reflecting back from
  it

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Properties of the Image Formed by a Flat Mirror
Summary

• 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
• The image is upright
• It has the same orientation as the object
• There is a front-back reversal in the image

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Example

• What is the minimum length of a flat mirror so
  that you can see yourself full height in the
  mirror?
• What is the minimum length of a flat mirror so
  that you can see Johns full height in the
  mirror?

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Another example

• Determine the image distances of the first and
  second order images with respect to their own
  mirror.

3 m
1 m
A
B
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Spherical Mirrors

• A spherical mirror has the shape of a section of
  a sphere
• A concave spherical mirror has the silvered
  surface of the mirror on the inner, or concave,
  side of the curve
• A convex spherical mirror has the silvered
  surface of the mirror on the outer, or convex,
  side of the curve

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Concave Mirror, Notation

• The mirror has a radius of curvature of R
• Its 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 principal
  axis of the mirror

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Paraxial Rays

• We use only rays that close to the principal axis
• Such rays are called paraxial rays
• This is the case when the mirror radius is very
  large compare to the size of the mirror

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Focal Length

• When paraxial rays are parallel with the
  principal axis, they reflect on the mirror and
  meet at one point on the principal axis.
• This point (the image of these parallel rays) is
  called the focal point
• The distance from the mirror to the focal point
  is called the focal length
• It can be proved that the focal length is ½ the
  radius of curvature

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Focal Length
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Focal Point

• The colored beams are traveling parallel to the
  principal axis
• The mirror reflects all three beams to the focal
  point
• The focal point is where all the beams intersect
• It is the white point

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Find the image

• Method 1 the ray diagram

Ray 3 begins as an incident ray that passes
through the center of curvature, strikes the
mirror perpendicularly, and reflects back, moving
along the same line as the incident ray.
Ray 1 starts as an incident ray that is parallel
to the principal axis. It reflects off the mirror
and passes through the focal point after it
reflects.
Ray 2 starts as an incident ray that passes
through the focal point and then reflects
parallel to the principal axis.
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The ray diagram
Ray 3 begins as an incident ray that passes
through the center of curvature, strikes the
mirror perpendicularly, and reflects back, moving
along the same line as the incident ray.
Ray 2 starts as an incident ray that passes
through the focal point and then reflects
parallel to the principal axis.
Ray 1 starts as an incident ray that is parallel
to the principal axis. It reflects off the mirror
and passes through the focal point after it
reflects.
Image up-side-down, smaller, real
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The five object locations and their images
PLAY ACTIVE FIGURE
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Convex Mirrors

• A convex mirror is sometimes called a diverging
  mirror
• The light reflects from the outer, convex side
• The rays from any point on the object diverge
  after reflection as though they were coming from
  some point behind the mirror
• The image is virtual because the reflected rays
  only appear to originate at the image point

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Find the image

• Method 1 the ray diagram

Ray 1. Ray 1 is incident parallel to the
principal axis. If we extend the reflected
component of this ray backward through the
mirror, the virtual ray will pass through the
focal point.
Ray 2. Instead of passing through the focal
point, the incident part of ray 2 is directed
toward it. Before it can reach the focal point
behind the mirror, it reflects parallel to the
principal axis. Its virtual extension behind the
mirror is also parallel to the axis.
Ray 3. The incident component of Ray 3 is
directed toward the center of curvature on the
far side of the mirror and reflects back along
the same line. The virtual extension of the
reflected ray passes through the center of
curvature.
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Only one case for a diverging mirror
Image always upright, smaller, virtual
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Notes on Images

• With a concave mirror, the image may be either
  real or virtual
• When the object is outside the focal point, the
  image is real
• When the object is at the focal point, the image
  is infinitely far away
• When the object is between the mirror and the
  focal point, the image is virtual
• With a convex mirror, the image is always virtual
  and upright
• As the object distance decreases, the virtual
  image increases in size