14-3: Curved Mirrors

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14-3 Curved Mirrors
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Curved Mirrors

• What are some examples of curved mirrors?

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Concave Spherical Mirrors

• A spherical mirror has the shape of part of a
  spheres surface.
• Concave Spherical Mirror (Converging Mirror) A
  spherical mirror with light reflecting from its
  silvered, concave surface
• Concave mirrors are used whenever a magnified
  image of an object is needed

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Terms you need to know
Term Definition Symbol(s)
Center of Curvature The center of the spherical shell of which the mirror is a small part C
Radius of Curvature The distance from the mirrors surface to the center of curvature R
Height of object The height of the object h ho
Height of image The height of the image h, hi
Object distance The distance between the object and the mirror p do
Image distance The distance between the image and the mirror q di
Focal Length Focal length is equal to half the radius of curvature f
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Concave Spherical Mirrors (p.531)
A spherical mirror is represented as a shell of a
sphere
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Concave Mirror (p.531)
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The Mirror Equation

• To use the mirror equation, you must use the
  correct signs.
• Object and image distances are positive if they
  form on the front side of the mirror
• Object and image distances are negative if they
  form on the back side of the mirror

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Sample Problem (p.536 2)

• A concave shaving mirror has a focal length of 33
  cm. Calculate the image position of a cologne
  bottle placed in front of the mirror at a
  distance of 93 cm.

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Solve the problem

• p .93 m
• f .33 m
• q?

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Magnification Equation
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Sample Problem (p.536 2)

• A concave shaving mirror has a focal length of 33
  cm. Calculate the magnification of the image. Is
  the image real or virtual? Is the image inverted
  or upright?

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Sign Conventions for Magnification
Orientation of image with respect to object Sign of M Type of image
Upright Virtual
Inverted - Real
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Find the magnification
The magnification is negative, therefore the
image is real and inverted.
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Ray Diagrams

• A ray diagram is a drawing that uses geometry to
  locate an image formed by a mirror.
• There are different rules for drawing ray
  diagrams depending on the type of mirror you have.

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How to draw a ray diagram (p. 533-534)

• For spherical mirrors, there are three different
  reference rays.
• The intersection of any two rays locates the image

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Rules for drawing reference rays (p. 534)
Ray Line drawn from object to mirror Line drawn from mirror to image after reflection
1 Parallel to principal axis Through focal point F
2 Through focal point F Parallel to principal axis
3 Through center of curvature (C) Back along itself through C
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How to draw a ray diagram
Ray 1
Ray 2
The intersection Of any 2 rays gives the image
location
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Objects inside the focal point
f
C
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Sample Problem (p.536 2)

• A concave shaving mirror has a focal length of 33
  cm. Calculate the image position of a cologne
  bottle placed in front of the mirror at a
  distance of 93 cm. Draw a ray diagram to confirm
  your results.

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Draw the diagram
The image is inverted and about half the height
of the object.
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Convex Mirrors

• Convex mirrors take objects in a large field of
  view and produce a small image
• Side-view mirrors on cars are convex mirrors.
  Thats why they say objects are closer than they
  appear

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Convex Spherical Mirrors (p. 537)

• A convex spherical mirror (diverging mirror) is
  silvered so that light is reflected from the
  spheres outer, convex surface
• The image distance is always negative!
• The image is always a virtual image!
• The focal length is negative !

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Ray diagrams for convex mirrors

• The focal point and center of curvature are
  behind the mirrors surface
• A virtual, upright image is formed behind the
  mirror
• The magnification is always less than 1

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Drawing the reference rays

• Ray 1 is drawn parallel to the principal axis
  beginning at the top of the object. It reflects
  from the mirror along a line that intersects the
  focal point

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Ray 2

• Ray 2 starts from the top of the object and goes
  as though its going to intersect the focal point
  but it reflects parallel to the principal axis

Ray 1
Ray 2
f
C
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Ray 3

• Ray 3 starts at the top of the object and goes as
  though its going to intersect the center of
  curvature

Ray 1
Ray 3
Ray 2
f
C
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Convex Spherical Image Formation

• The image forms at the intersection of any two of
  the three rays behind the mirror.

Ray 1
Ray 3
Ray 2
f
C
The rays do not intersect in front of the mirror!!
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Sign conventions for mirrors (p. 538)
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Sample Problem (p. 540 6)

• A candle is 49 cm in front of a convex spherical
  mirror that has a focal length of 35 cm. What are
  the image distance and magnification? Is the
  image virtual or real? Is the image inverted or
  upright? Draw a ray diagram to confirm your
  results.

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Solving the problem

• Remember that for convex mirrors, the focal
  length and image distance are always negative.

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The Magnification of the Image

• Since the magnification is positive, the image is
  upright and virtual

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Ray diagram for the Image
C
f
Remember that you only need to draw two of the
three rays to find the image.