Chapter 36 Refractive Surfaces and Lenses

1
Chapter 36 Refractive Surfaces and Lenses
PHYS 2326-32
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Concepts to Know

• Spherical Refracting Surfaces
• Thin Lenses

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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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Differences From Mirror

• Light goes through
• There are effects from the index of refraction
• Sign Conventions must change

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Plane Surface Boundary
p
q

• For a plane mirror
• pq and M 1
• What about for a fish tank?

h
?
Object
?
Image
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Plane Refraction

• Unlike the mirror
• viewing into another
• index of refraction
• medium is affected
• even by a flat plane

q
n1.30
n1.00
Object
p
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Refraction

• Fig. 36.17 shows a spherical boundary between two
  media of different indices of refraction
• Using Snells law and the small angle
  approximation one can achieve eqn 36.8

?2
?1
n2
n1
?1
d
a
?
ß
I
C
O
R
p
q
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Refracting Surface

• Eqn 36.8 provides the result of the geometric
  derivation from Fig. 36.17
• Notice that the image distance depends upon the
  object distance, Radius of curvature and the
  index of refraction for each media
• Note too, that if R becomes infinite we have a
  flat plane surface and (n2-n1)/R becomes 0 so
• q -(n2/n1)p eqn 36.9

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Lenses

• Lenses have 2 surfaces, not just one
• A lens may have a concave, convex, or plane
  surface referred to as plano when being
  described
• A lens is converging or diverging
• Converging lens types include biconvex,
  concave-convex, and plano-convex
• Diverging lens types include biconcave,
  convex-concave, and plano-concave

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Refracting Surface Sign Conventions
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Lens

• Eqn 36.10 starts with eqn 36.8 and assumes n1
  1.00 and n2 n for surface 1
• Eqn 36.11 is for surface 2 and differs because
  the light is going from inside the material out
  to the air, n1 n and n2 1.00 for surface 2
• The image formed by surface 1 becomes the object
  for surface 2

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Thin Lens Equation

• Note that p2 -q1 t and p2 will be positive
  by the sign convention because q1 has a negative
  value
• if t is very small, p2 -q1 (for both real or
  virtual image)

R1
R2
n1
I
O
t
C1
p
q1
p2
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Thin Lenses

• Eqn 36.11 becomes Eqn 36.15, The Lens Makers
  Equation

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Lens Makers Equation

• Can be used to determine R1 and R2 for a lens
  given a desired focal length and an index of
  refraction
• If given the index of refraction and radii of
  curvature (R1 and R2), one can find the focal
  length
• If assume n is the ratio of the index of
  refraction between the lens and what it is
  immersed in other than air the eqn can be used

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Image Magnification

• M h/h -q/p which is the same as for
  mirrors.
• When M is positive, image is upright and on the
  same side of the lens as the objec
• When M is negative, the image is inverted and on
  the opposite side of the lens

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Thin Lens Equation

• Eqn 36.15, the lens makers equation can be used
  with 36.14 to create 36.16, a thin lens equation
  exactly like that of mirrors.
• Note that focal points are the same distance on
  both sides of the lens
• Also, a converging lens is thicker in the middle
  while a diverging lens is thinner in the middle

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Table 36.3
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Ray Tracing for Converging Lens

• Ray 1 parallel to principal axis refracted
  through focal point on back side of lens
• Ray 2 draw through lens center continues straight
  line
• Ray 3 through focal point on front side or as if
  coming from focal point (if inside f) and
  emerging parallel to principal axis

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Ray Tracing for Diverging Lens

• Ray 1 drawn parallel to principal axis, emerges
  away from the focal point on the front side
• Ray 2 drawn through lens center in straight line
• Ray 3 drawn towards backside focal point emerges
  parallel

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Example Problem 1

• A thin double concave lens has a radius of 10cm
  on both sides and made from glass with an index
  of refraction 1.5. A light bulb 2cm tall is
  located 50cm in front of the lens along the
  principal axis. a) What is the focal length of
  the lens? Converging or diverging? b) Where is
  the bulb image? c) What is the image height?
  Enlarged or reduced? Erect or inverted?

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• Equations
• 1/f (n-1)(1/R1 1/R2)
• 1/p 1/q 1/f
• M -q/p h/h
• a) f? 1/f (1.5-1)(1/(-10) 1/(10))-0.5(2/10)
• f -10cm (diverging)
• b) 1/50cm 1/q 1/(-10), q -12.5cm
• on front side and it is virtual
• c) m -12.5/50 0.5cm reduced, erect

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Problem 36.33

• 36.33 An object located at 20cm to left of a
  diverging lens with focal length f -32.0cm.
  Determine a) the location and b) the
  magnification of the image. c) Construct a ray
  diagram

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• The problem provides p object distance and f
  focal length
• Can use thin lens eqn to solve for q image
  distance
• Can then use magnification definition to
  determine the magnification
• Ray tracing for a diverging lens

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Ray Tracing for Diverging Lens

• Ray 1 drawn parallel to principal axis, emerges
  away from the focal point on the front side
• Ray 2 drawn through lens center in straight line
• Ray 3 drawn towards backside focal point emerges
  parallel