ch13 convex lenses

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					                                                             Name _______________________

                                                          Partner _______________________

                                Activity: Convex Lenses

Purpose: To investigate the optical properties of convex lenses.

Materials
  convex lens                  meter stick supports            pins
  lens support                 index cards                     cardboard
  two meter sticks             light source on support         drawing paper

Introduction
The behavior of convex lenses is very similar to that of concave mirrors. Both convex
lenses and concave mirrors are converging optical devices. Incident light rays that
are parallel to the principal axis are directed toward a single point, called focal
point, as they pass through the lens.
Recall that real images formed by mirrors appear in front of the mirror. Because
lenses transmit light rather than reflecting it, real images formed by lenses are on
the opposite side of the lens from the object. Virtual images are formed on the same
side of the lens as the object.
The images formed by a lenses are governed by the same equations as those of curved
mirrors:
                                       1 1   1
                                          
                                       f do di
                                        h   d
                                     m i  i
                                       ho   do
Sign conventions for lenses are similar to those of mirrors:
1.    The object height and object distance will always be assumed positive.
2.    The focal length is positive for convex lenses and negative for concave lenses.
3.    The image distance is positive when the image is real and negative when it is
      virtual.
4.    The image height is positive when the image is erect and negative when it is
      inverted.
In this investigation, you will measure f, do, di, ho and hi. You will verify that the
lens equations do indeed describe the behavior of convex lenses.


Procedure
                     Part A. Determining the focal point of the lens.
1. For reference, write the number of your convex lens in the data table. It appears
   on the envelope holding the lens. Be sure to return the lens to the same envelope
   when you are finished.
2. Hold the lens facing an opening in the shade of an otherwise darkened room.
3. Hold a card behind the lens. Move the card until the image from outside the window
   is in sharp focus. Measure the distance from the card to the lens in cm. This is
   the focal length of the lens. Record it in the data table.
                     Part B. Measuring images produced by the lens.
1. Set up an optical bench using one meter stick, the meter stick supports, and the
   light source. The arrow drawn on the light bulb should be pointed toward the
   “zero” end of the optical bench.
2. Use a lens support to secure the lens at the “zero” end of the optical bench,
   centered on the edge of the meter stick.
3. Place the “zero” end of a second meter stick directly in line with the “zero” end
   of the optical bench. This meter stick will be used to measure the image distance.
4. Plug in the light and position it at a distance of 4 focal lengths from the lens.
   Measure the height of the object (the arrow on the light bulb) using an index card
   held up to the front of the bulb.
5. Hold an index card vertically and slide it along the image meter stick until the
   image is in sharp focus. Record the image distance. Also, mark the top and bottom
   of the image on the index card and measure its height. Record these values in the
   data table.
6. Repeat the above procedure for object distances equal to 3, 2, 1.5, 1.25 and 1
   focal lengths.
7. To measure the image distances for object distances of 1/2 and 1/4 focal lengths,
   use the “line of sight” method. With the lens still in the lens support, prop the
   lens between two books so that the lens is oriented vertically, and one-half of
   the lens is visible above the books. Put a piece of cardboard over each book, and
   a piece of paper over each piece of cardboard. Bridge the gap between the two
   pieces of paper with tape, to keep the papers in the same position relative to
   each other.
8. Place a pin one-half focal length away from the lens. From the opposite side of
   the lens, sight the pin, first from the right and then from the left, placing two
   pins on each side in line with the image of the object pin.
9. Remove the lens. Put the two pieces of paper down over a third piece of paper
   centered between them and use tape to secure all three pieces. Mark the position
   previously occupied by the center of the lens with a straight line. Extend lines
   along each line of sight until both lines cross, adding additional pieces of paper
   if required.
10. Repeat steps 7 to 9 for an object pin placed one-quarter focal length from the
    lens.
11. Measure the object and images distances and record them in the data table. You
    will not be able to measure the image height. You may share results with your lab
    partner. Each person should analyze one of the constructions and attach it to
    his/her lab.
Analysis
Be sure that the signs of the values entered in your data table are consistent with
the sign conventions presented in the introduction.

1. Perform the calculations needed to complete the data table. Percent differences
   are computed as follows:


                    1 1 1                                   hi di
                                                            
                    di do f                                 ho do
             %dif =         x100                     %dif =       x100
                        1                                     di
                        f                                     do
                  hi              di
   Note that if      is positive,    will always be negative, and vice-versa. Since
                  ho              do
   the magnitudes of these two ratios are to be compared, the two values are to be
   added, not subtracted, in the second equation above.

                     1       1
2. Make a graph of      vs.    . Find the slope and the y-intercept. Record these
                     di     do
   values neatly on the graph paper.

Questions
Questions 1 - 3 relate to a simple camera that uses one convex lens.

1. What is the value of do when a picture of a landscape is taken?

   (a) do>2f   (b) do=2f   (c) f<do<2f    (d) do is slightly larger than f   (e) do<f

   Will the image be inverted or erect? Larger or smaller than the object?


2. What is the value of do when a photographer makes a life-size picture of a postage
   stamp?

   (a) do>2f   (b) do=2f   (c) f<do<2f    (d) do is slightly larger than f   (e) do<f

3. What is the value of do when a photographer makes an enlarged picture of grains of
   sand?

   (a) do>2f   (b) do=2f   (c) f<do<2f    (d) do is slightly larger than f   (e) do<f

   Will the image be inverted or erect?

4. When a convex lens is used as a magnifying glass, what is the value of do?

   (a) do>2f   (b) do=2f   (c) f<do<2f    (d) do is slightly larger than f   (e) do<f

5. When a convex lens is used in a slide projector, what is the value of do?

   (a) do>2f   (b) do=2f   (c) f<do<2f    (d) do is slightly larger than f   (e) do<f

6. In general, relative to f, what values of do give images that can be focused on a
   screen (real images)?



7. In general, relative to f, what values of do give images that you observe by
   looking through the lens at them (virtual images)?



8. In a fixed focus camera, the film is positioned so that the distance between the
   film and the lens (di) is equal to the focal length f. In more elaborate cameras,
   the distance between the lens and film may be changed.

   Why is it not possible to take close up pictures with a camera with a fixed focus?
CONVEX LENS DATA TABLE

mirror number = _________            focal length (f) = ________________ cm       1/f = ________________ cm-1

                                  1/do
                                  +                                                   real or   erect or    larger
do      di      1/do     1/di                      ho    hi                                                 or
                (cm-1)   (cm-1)   1/di     %diff                              %diff   virtual   inverted
(cm)    (cm)                      (cm-1)
                                                   (cm   (cm    hi/h   di/d                                 smaller
                                                   )     )      o      o
4f



3f



2f



1.5f



1.25f



1f*



1/2f
                                                   x     x      x      x      x
1/4f
                                                   x     x      x      x      x

*Fill in if image exists; otherwise, write “no image.”

				
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