36.3 Images Formed by Refraction - PowerPoint PPT Presentation

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36.3 Images Formed by Refraction

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Images by Refraction, 3 ... Real images are formed by refraction in the back of the surface ... Images from lenses. Light passing through a lens experiences ... – PowerPoint PPT presentation

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Title: 36.3 Images Formed by Refraction


1
36.3 Images Formed by Refraction
2
Images Formed by Refraction
  • Consider two transparent media having indices of
    refraction n1 and n2
  • The boundary between the two media is a spherical
    surface of radius R
  • Rays originate from the object at point O in the
    medium with n n1

3
Images by Refraction, 2
  • We will consider the paraxial rays leaving O
  • All such rays are refracted at the spherical
    surface and focus at the image point, I
  • The relationship between object and image
    distances can be given by
  • (36.8)

4
Images by Refraction, 3
  • The side of the surface in which the light rays
    originate is defined as the front side
  • The other side is called the back side
  • Real images are formed by refraction in the back
    of the surface
  • Because of this, the refraction sign conventions
    for q and R are opposite the reflection sign
    conventions

5
Sign Conventions for Refracting Surfaces
6
Flat Refracting Surfaces
  • If a refracting surface is flat, then R ??,
    therefore
  • q ?(n2 / n1)p (36.9)
  • The image formed by a flat refracting surface is
    on the same side of the surface as the object
  • For n1 n2 a virtual image is formed between the
    object and the surface
  • For n1 of the object

7
Active Figure 36.20
(SLIDESHOW MODE ONLY)
8
Example 36.5 Gaze Into the Crystal Ball
  • A set of coins is embedded in a spherical plastic
    paper weight of radius 3.0 cm, with n 1.50. One
    coin is located 2.0 cm from the edge of the
    sphere. Find the position of the image of the
    coin.
  • Here n1 n2 so a virtual image is formed inside
    the paperweight.
  • R is negative

9
36.4 Thin Lenses
  • Lenses are commonly used to form images by
    refraction
  • Lenses are used in optical instruments
  • Cameras, telescopes, microscopes
  • Images from lenses
  • Light passing through a lens experiences
    refraction at two surfaces
  • The image formed by one refracting surface serves
    as the object for the second surface

10
Image Formed by a Lens
  • The lens has an index of refraction n and two
    spherical surfaces with radii of R1 and R2
  • R1 is the radius of curvature of the lens surface
    that the light of the object reaches first
  • R2 is the radius of curvature of the other
    surface
  • The object is placed at point O at a distance of
    p1 in front of the first surface

11
Image From Surface 1
  • There is an image formed by surface 1
  • Since the lens is surrounded by the air, n1 1
    and n2 n ?
  • Equation (36.8) becomes
  • (36.10)
  • If the image due to surface 1 is virtual, q1 is
    negative, and it is positive if the image is real

12
Image From Surface 2
  • For surface 2, n1 n and n2 1
  • The light rays approaching surface 2 are in the
    lens and are refracted into air
  • Use p2 for the object distance for surface 2 and
    q2 for the image distance, so equation (36.8)
    becomes
  • (36.11)
  • From the virtual image at surface 1 p2 q1
    t
  • q1 is negative and t is the thickness of the lens
  • From the real image at surface 1 p2 q1
    t
  • q1 is positive

13
Image Formed by a Thin Lens
  • A thin lens is one whose thickness t is small
    compared to the radii of curvature
  • For a thin lens, the thickness, t, of the lens
    can be neglected
  • In this case, p2 q1 for either type of image
  • Hence equation (36.11) becomes
  • (36.12)

14
Image Formed by a Thin Lens, 2
  • Adding equations (36.10) and (36.12) we obtain
  • (36.13)
  • Then the subscripts on p1 and q2 can be omitted
    as in the figure and rewrite equation (36.13) as
  • (36.14)

15
Lens Makers Equation
  • The focal length f of a thin lens is the image
    distance q that corresponds to an infinite object
    distance
  • This is the same as for a mirror
  • Making p ? ? and q ? f, so equation (36.14) will
    become the lens makers equation
  • (36.15)
  • Given n and f the lens maker can determine the
    values of R1 and R2
  • Given R1, R2 and n lens maker can calculate the
    value of f

16
Thin Lens Equation
  • Using equation (36.15) we can write equation
    (36.14) in a for identical to equation (36.6) for
    mirrors.
  • The relationship among the focal length, the
    object distance and the image distance is the
    same as for a mirror
  • (36.16)

17
Notes on Focal Length and Focal Point of a Thin
Lens
  • Because light can travel in either direction
    through a lens, each lens has two focal points
  • One focal point is for light passing in one
    direction through the lens
  • The other is for light traveling in the opposite
    direction
  • However, there is only one focal length
  • Each focal point is located at the same distance
    from the lens

18
Focal Length of a Converging Lens
  • The parallel rays pass through the lens and
    converge at the focal point
  • The parallel rays can come from the left or right
    of the lens

19
Focal Length of a Diverging Lens
  • The parallel rays diverge after passing through
    the diverging lens
  • The focal point is the point where the rays
    appear to have originated

20
Determining Signs for Thin Lenses
  • The front side of the thin lens is the side of
    the incident light
  • The back side of the lens is where the light is
    refracted into
  • This is also valid for a refracting surface

21
Sign Conventions for Thin Lenses
22
Magnification of Images Through a Thin Lens
  • The lateral magnification of the image is
  • When M is positive, the image is upright and on
    the same side of the lens as the object
  • When M is negative, the image is inverted and on
    the side of the lens opposite the object

23
Thin Lens Shapes
  • These are examples of converging lenses
  • They have positive focal lengths
  • They are thickest in the middle

24
More Thin Lens Shapes
  • These are examples of diverging lenses
  • They have negative focal lengths
  • They are thickest at the edges

25
Ray Diagrams for Thin Lenses Converging
  • Ray diagrams are convenient for locating the
    images formed by thin lenses or systems of lenses
  • For a converging lens, the following three rays
    are drawn
  • Ray 1 is drawn parallel to the principal axis and
    then passes through the focal point on the back
    side of the lens
  • Ray 2 is drawn through the center of the lens and
    continues in a straight line
  • Ray 3 is drawn through the focal point on the
    front of the lens (or as if coming from the focal
    point if p
    parallel to the principal axis

26
Ray Diagram for Converging Lens, p f
  • The image is real
  • The image is inverted
  • The image is on the back side of the lens

27
Ray Diagram for Converging Lens, p
  • The image is virtual
  • The image is upright
  • The image is larger than the object
  • The image is on the front side of the lens

  • 28
    Ray Diagrams for Thin Lenses Diverging
    • For a diverging lens, the following three rays
      are drawn
    • Ray 1 is drawn parallel to the principal axis and
      emerges directed away from the focal point on the
      front side of the lens
    • Ray 2 is drawn through the center of the lens and
      continues in a straight line
    • Ray 3 is drawn in the direction toward the focal
      point on the back side of the lens and emerges
      from the lens parallel to the principal axis

    29
    Ray Diagram for Diverging Lens
    • The image is virtual
    • The image is upright
    • The image is smaller
    • The image is on the front side of the lens

    30
    Active Figure 36.28
    (SLIDESHOW MODE ONLY)
    31
    Image Summary
    • For a converging lens, when the object distance
      is greater than the focal length
    • (p )
    • The image is real and inverted
    • For a converging lens, when the object is between
      the focal point and the lens, (p
    • The image is virtual and upright
    • For a diverging lens, the image is always virtual
      and upright
    • This is regardless of where the object is placed

    32
    Fresnal Lens
    • Refraction occurs only at the surfaces of the
      lens
    • A Fresnal lens is designed to take advantage of
      this fact
    • It produces a powerful lens without great
      thickness

    33
    Fresnal Lens, cont.
    • Only the surface curvature is important in the
      refracting qualities of the lens
    • The material in the middle of the Fresnal lens is
      removed
    • Because the edges of the curved segments cause
      some distortion, Fresnal lenses are usually used
      only in situations where image quality is less
      important than reduction of weight

    34
    Two Thin Lenses (Combination)
    • If two thin lenses are used to form an image
    • The image formed by the first lens is located as
      if the second lens were not present
    • Then a ray diagram is drawn for the second lens
    • The image of the first lens is treated as the
      object of the second lens
    • The image formed by the second lens is the final
      image of the system

    35
    Two Thin Lenses, 2
    • If the image formed by the first lens lies on the
      back side of the second lens, then the image is
      treated as a virtual object for the second lens
    • p will be negative
    • The same procedure can be extended to a system of
      three or more lenses
    • The overall magnification is the product of the
      magnification of the separate lenses

    36
    Two Thin Lenses, 3
    • Consider a case of two lenses in contact with
      each other
    • The lenses have focal lengths of 1 and 2
    • If p1 p is the object distance for the
      combination, equation (36.16) becomes
    • Since the lenses are in contact, p2 q1

    37
    Two Thin Lenses, final
    • For the second lens q2 q ,
    • Adding the two previous equations for the
      combination of the two lenses
    • (36.17)
    • Two thin lenses in contact with each other are
      equivalent to a single thin lens having a focal
      length given by the above equation

    38
    Example 36.6 Where is the Final Image?
    39
    Example 36.6 Where is the Final Image? , 2
    • The location of the image formed by lens 1
    • The image of lens 1 becomes object for lens 2,
      with p2 20cm 15cm 5cm ?
    • Then, the total magnification will be

    40
    Material for the Midterm
    • Examples to Read!!!
    • Example 36.11 (page 1149)
    • Examples in Class!!!
    • Example 36.9 (page 1146)
    • Example 36.10 (page 1147)
    • Homework to be solved in Class!!!
    • Question 9
    • Problems 21, 28
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