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             F            F
        f                      f

Converging                    Diverging
   Lens                         Lens
  Find the focal length of a converging lens by
            holding it up to a window.
(See how far away from the lens you need to hold
a piece of paper to focus the image on the paper.)

     Web Link: Spherical mirrors and lenses
                  Ray Tracing for Lenses
             Light passes through a lens
      There is a focal point on both sides of a lens

Converging Lens:

Ray #1:
Parallel to the axis
Refracts through F

Ray #2:
Through F
Refracts parallel to axis

Ray #3:
Through Center of
lens undeflected
Example: Camera
Example: Slide Projector
  Glass      Web Link:
             Ray tracing
        Results: Ray Tracing for Converging Lenses
           (in each case, draw in the 3 rays for practice)

Object distance > 2f: Image is smaller, and inverted, real

                  2F           F              F

Object between f and 2f: Image is larger, inverted, real

             2F        F              F

Object between f and mirror: Image is larger, upright, virtual

                2F         F              F
   Summary of images in a Converging Lens

OBJECT                               IMAGE
   Location      Size   Attitude         Location               Type

beyond 2F'    smaller   inverted between 2F and F        real

at 2F'        same size inverted at 2F                   real
between 2F'
and F'        larger    inverted beyond 2F               real

at F'                                no clear image
                                   same side as object
inside F'     larger    upright    (behind lens)         virtual
                Now, for Diverging lenses……
           Web Link: Spherical mirrors and lenses

For a Diverging Lens:
Ray #1: Parallel to the axis on the left
Refracts as if it came from F on the left
Ray #2: Heads toward F on the right
Refracts parallel to the axis on the right

Ray #3: Through the center of the lens undeflected

Example: Glasses to correct nearsightedness
      Results: Ray Tracing for Diverging Lenses
               (draw in the 3 rays for practice)

           No matter where the object is:
Image is always smaller, upright, virtual, same side of lens

                  F                                 F

                 Web Link: Ray tracing

                      Web Link:
               Ray Tracing Summary for
                  Mirrors and Lenses
      These equations also work on lenses:

      1 1 1                            di
                                m 
      do di f                          do
     The Thin Lens             The Magnification
       Equation                    Equation

  But the variables are defined slightly differently
                 now because……….

  For a mirror, a real     For a lens, a real image
image was on the same      is on the opposite side
   side as the object            as the object
           Sign conventions for Lenses

    Focal length (f)            Object distance (do)
    + converging
                                + object on the left
     - diverging

Image distance (di)              Magnification (m)
+ image on the right (real)      + upright
- image on the left (virtual)    - inverted




  If the image of the book is 5.0 cm below
  the lens, find the focal length of the lens.

  A camera with a focal length of 50 mm takes a
  photograph of a 100 m tall building from 350 m
     away. How tall is the image on the film?
                  The Human Eye

                          Web Links: Eye lens,
                          Vision and Eyesight

    Near Point –
Closest distance the
 eye can focus on          Far Point –
(about 25 cm when      Farthest distance
   we are young)       the eye can focus
                       on (should be  )
    Someone who is Nearsighted cannot
     focus on far away objects. (Their
         far point is not at infinity.)

Nearsightedness can be corrected
     with diverging lenses

   Here’s how it works

 Without my contact lenses, I need to stand 35 cm or
 less from the TV in order to see it in focus. Find the
   focal length of the contact lenses that correct my
   Someone who is Farsighted cannot
      focus on objects too near.

Farsightedness can be corrected with
         converging lenses

     Here’s how it works

       The man has a near point of 48 cm. His
      reading glasses are 2.0 cm from his eyes,
         and with them on, he can read the
      newspaper as close as 25 cm to his eyes.
         Find the focal length of his glasses
                 Lens Aberrations

1) Spherical Aberration

         Can you think of two ways that this
           problem could be eliminated?
2) Chromatic Aberration

How to correct this problem?


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