Mirrors

1
Mirrors Lenses

• We apply the ray approximation to these very
  important devices

2
Mirrors

• Law of reflection still holds.
• Angle of reflection Angle of incidence
• Object distance p
• Image distance q
• Plane mirrors
• p q.
• Image is upright,
• Image is unmagnified,
• Image is virtual.

3
Real Images Virtual Images

• A real image is formed when the light rays
  actually come from the image point (location.
• A real image can be projected.
• A virtual image is formed when the light rays
  only appear to come from the image point.
• A virtual image can NOT be projected.

4
(Lateral) Magnification

• Suppose the object has a height h,
• and the image has a height h,
• The Lateral Magnification is the ratio of image
  height to object height.

• For a plane mirror, M 1

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6
Problem

• A woman can see an object clearly when its held
  at a distance of 25 cm from her eyes. How far
  should she hold a flat mirror to see her own
  image clearly?
• 12.5 cm

7
Problem

• A man is walking at 1.0 m/s directly toward a
  flat mirror. At what speed is his image
  approaching him?
• 2.0 m/s

8
Rearview Mirror
9
Spherical Mirrors

• We shall specialize to sections of spherical
  mirrors.
• The spherical mirror will have a center of
  curvature C and a radius of curvature R.
• The principal axis connects C with the center of
  the mirror.
• The Law of Reflection still holds.

10
Mirror Equation

• p is the object distance measured along the
  principal axis.
• q is the image distance.
• R is the radius of curvature.
• f is the focal length.

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Rules for Ray diagrams

• p, q, R, f can be positive or negative.
• Concave mirrors
• Both f and R are if the center of curvature is
  in front of the mirror.
• Convex mirrors
• Both f and R are if the center of curvature is
  in back of the mirror.
• If the image is upright, Mgt0.
• If the image is inverted, Mlt0.

12
Rules for Ray diagrams 2

• Learn 3 rays to locate the image.
• Ray drawn parallel to principal axis and is
  reflected through the focal point F.
• Ray drawn through the focal point is reflected
  back parallel to the principal axis.
• Ray drawn through the center of curvature C, is
  reflected back on itself.

• The image above is real and inverted.
• The magnification is negative and M lt 1.

13
Problem

• An 5 cm candle is placed 35 cm in front of a
  concave spherical mirror with a radius of
  curvature of 30 cm. Find the location of the
  image, its height and the magnification of the
  image.
• Is the image real or virtual?

Real
14
Problem

• An 5 cm candle is placed 10 cm in front of a
  concave spherical mirror with a radius of
  curvature of 30 cm. Find the location of the
  image, its height and the magnification of the
  image.
• Is the image real or virtual?

Virtual
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Convex Mirrors

• These have negative f and R.
• The focal point and center of curvature you aim
  is on the back side of the mirror.
• For a single convex mirror, the image will always
  be virtual and smaller.

16
Problem

• An 5 cm candle is placed 10 cm in front of a
  convex spherical mirror with a radius of
  curvature of 30 cm. Find the location of the
  image, its height and the magnification of the
  image.
• Is the image real or virtual?

Virtual
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Caveat

• These rules are an approximation.
• If the rays of light make large angles with the
  principal axis, then the image will not be sharp.
  
• Spherical Aberration.
• Parabolic mirrors do not suffer spherical
  aberration.
• But spherical mirrors are easy to make.

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Problems for concave mirrors

• If the object is infinitely far away, where is
  the image?
• If the image is infinitely far away, where is the
  object?
• Is it possible to have an image with M 1?
• Where should the object be in order to have a
  magnification of 2?