Chapter 36 Mirrors and Image Formation

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Chapter 36 Mirrors and Image Formation
PHYS 2326-31
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Concepts to Know

• Mirrors
• Plane, Concave, Convex
• Sign Conventions
• Object Distance
• Image Distance
• Focal Length
• Magnification

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Concepts to Know

• Enlarged, Reduced
• Erect, Inverted
• Real, Virtual
• Reversed (Perverted)
• Converging, Diverging
• Aberration
• Principle Rays

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Definitions

• Plane surface one that is flat
• Concave surface, one that is curved inward at the
  center
• Convex surface, one that is curved outward

Eye
Plane
Concave
Convex
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Objects Images

• Image from a Plane Mirror
• p object to surface, q surface to image
• h object height, h image height
• Magnification M 1 for flat mirror

p
q
h
h
?
Object
?
Image
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Images

• Virtual Image - no light reaches image
• Real Image - light rays reach image
• Erect or Upright Image directions unchanged
  (object up is same direction as image up)
• Inverted Image directions opposite (object up
  is image down)
• Reversed Image left seems right

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Spherical Mirrors

• Parameters of a spherical mirror
• Principal axis line through C and V where V is
  the center of the mirror
• C Center of Curvature center of sphere or
  circle (2 dimensions)
• R Radius of Curvature
• F Focal point
• Radius lines are always
• normal to surface
• of circles and spheres

V
R
C
principal axis
F
Concave
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• Given an object to the left of C, by the law of
  reflection, ? ?, light rays will converge at a
  point between V and C for rays with small angles
  to the principal axis
• For larger angles the rays will intersect at
  different points creating spherical aberration
  See Fig. 36.8

V
C
principal axis
O
I
Concave
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Image Concave Mirror

• Rays through C are normal to surface ?0
• Draw rays to V (intersection of surface and
  principal axis) ? ? and through C, ?0
• Tan ? h/p -h/q, since M h/h, -q/p
• Note -h inverted
• Image is
• smaller
• inverted
• real
• outside point F

Concave
p
R
h
V
?
a
a
h
C
?
F
q
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• since tan a -h/(R-q) h/(p-R)
• h/h -(R-q)/(p-R) eqn 36.3
• 1/p 1/q 2/R eqn 36.4 MIRROR EQN
• For a very distant object where p-gt infinity, 1/p
  0 so 1/q 2/R
• This case it is called the focal point F, where F
  2/R eqn 36.5
• hence 1/p 1/q 1/f, eqn 36.6, the mirror
  equation
• The focal point is where rays parallel to the
  axis pass through

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Spherical Convex Mirror

• Often called a diverging mirror
• Concepts presented are valid for this type of
  mirror as well if adhere to the following
  procedure
• R, F q negative
• p, h h positive

R
C
V
principal axis
F
p
q
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Procedure

• Front side of mirror where light waves
  originate and move towards the mirror
• Back side is the other side

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Mirror Sign ConventionsTable 36.1
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Ray Trace Example 1

• Object outside focal point
• Image inverted and smaller
• Rays drawn through C, and parallel to principal
  axis and through F

V
C
F
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Ray Trace Example 2

• Object is inside the focal point F
• Image is virtual, upright and magnified

V
C
F
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Ray Trace Example 3

• Convex mirror
• Image is virtual, reduced and upright

R
C
V
F
p
q
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Ray Tracing

• Principal axis goes through C, center of
  curvature so is perpendicular to the surface at
  V. Bottom of object.
• Ray 1 top of object parallel to principal axis
  goes through Focal point or reflects away from
  focal point for convex mirror
• Ray 2 top of object through focal point
  reflects parallel to axis where it intersects
  mirror
• Ray 3 top of object through Center of curvature,
  reflects back on self

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Example Problem 1

• Given object of height 1 cm located 30cm in front
  of a concave mirror of focal length 10 cm, what
  is a) radius of curvature? b) Location of image?
  c) Real/virtual image? d) Magnification? e)
  Enlarged? f) Image height? g) upright/inverted?

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V
C

• h 1cm, p 30cm, f10cm
• f R/2, 1/p 1/q 1/f
• M -h/h, M -q/p
• R 2f 20cm
• q 1/(1/f 1/p) 15cm
• Real
• M -q/p -15/30 -0.5
• Reduced
• M-h/h , -0.5 -0.5cm/1cm
• Inverted

F
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