PHYS272_Lab8

=Physics for Scientists and Engineers – Lab 8 =

Objective:

 * To observe the relationship between the distances of an object and an image from a thin lens.

Equipment:

 * Optical bench
 * Desk lamp
 * Object slide, image screen and aperture
 * Small round screen
 * Four optical bench carriages with lens and screen holders
 * Converging achromatic lens with focal length of about 13 cm
 * Diverging lens with focal length of about -15 cm
 * FirstScope Telescope assembly with mirror
 * Graphical Analysis software

Physical Principles:
 For the rays shown in figures 1 through 4, light is assumed to be coming from the left, and going toward the right. A converging lens always has two focal points, the primary focal point on the near side of the lens (towards the oncoming light rays) and a secondary focal point on the far side of the lens (away from the oncoming light rays). Light diverging from the primary focal point and approaching a converging lens will exit the lens with the rays parallel. Parallel light rays approaching a converging lens will converge at the secondary focal point. (See figures 1 and 2.) Light coming from very distant objects can be approximated with parallel rays.
 * [[image:https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/fetch.php?w=280&tok=dc6809&media=272.lab7.fig.a.jpg width="280" link="https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/detail.php?id=lab-8&media=272.lab7.fig.a.jpg"]] || [[image:https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/fetch.php?w=280&tok=90526a&media=272.lab7.fig.b.jpg width="280" link="https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/detail.php?id=lab-8&media=272.lab7.fig.b.jpg"]] || [[image:https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/fetch.php?w=280&tok=0a73d9&media=272.lab7.fig.c.jpg width="280" link="https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/detail.php?id=lab-8&media=272.lab7.fig.c.jpg"]] || [[image:https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/fetch.php?w=280&tok=acffae&media=272.lab7.fig.d.jpg width="280" link="https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/detail.php?id=lab-8&media=272.lab7.fig.d.jpg"]] ||

Figures 3 and 4 show the similar points for a diverging lens. Light converging toward the primary focal point and approaching a diverging lens will exit the lens with the rays parallel. Parallel light rays approaching a diverging lens will diverge as if they had come from the secondary focal point. See figures 3 and 4.

The distance from the lens to the focal points is called the focal length. For a converging lens, the focal length is always positive, for a diverging lens it is always negative. Note that if the medium is different on one side of the lens from the other, the relationship between object and image distances will be more complex.

The common equation relating focal length to object, p, and image, q, distances is 1/p + 1/q = 1/f. The object distance p is positive if the object is on the incoming side of the lens (the object is “real”), and negative if the object is on the outgoing side (the object is “virtual”). The image distance q is positive if the image is on the outgoing side of the lens (the image is “real”), and negative if the image is on the incoming side (the image is “virtual”).

The magnification resulting from an image formation is defined to be the ratio of the image height, //h’//, to object height, //h//.

math \displaystyle M=\frac{h'}{h} = -\frac{q}{p} math

1. Determining focal length directly
  //**When using lenses, NEVER touch the lens itself, hold it by the sides only!**//
 * 1) Put a 13 cm converging lens in a lens holder and put the holder rod in an optical bench carriage.
 * 2) Place a white screen into a screen holder with the white surface against the clamping screw, the screen surface is then centered above the rod. Put the screen holder rod into a carraige and place it on the optical bench.
 * 3) Align the lens and screen perpendicular to the optical bench.
 * 4) Use a light source across the room (or out the window), as far away as possible - at least 50 times the focal length, and direct the light from this source through the 13 cm converging lens onto the projection screen.
 * 5) Adjust the position of the screen for sharp focus.
 * 6) Record the position of the lens, x L, and screen, x S , on the optical bench and estimate the focal length as the difference | x S - x L |.

2. Real Object Converging Lens Setup
 Place the printed candle object in a clamp and move the carriage close to the 0 cm position on the optical bench. This is the object and the object position will be measured from the object to the lens. Do not change this position during the experiment. Mount the lens and the prism image screen in carriages on the optical bench. Set the light bulb source so that the light passes through the candle objects and through the lens. The light is then projected onto the flat screen (see figure above).
 * [[image:https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/fetch.php?w=400&tok=1274a5&media=lensa.jpg width="400" link="https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/detail.php?id=lab-8&media=lensa.jpg"]] || [[image:https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/fetch.php?w=400&tok=cfe579&media=lens2.jpg width="400" link="https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/detail.php?id=lab-8&media=lens2.jpg"]] ||

Using the same lens as in the first experiment (13 cm focal length small achromatic lens) record a series of object and image distances in a table. Let the object distances (lens positions) be about 0.80, 0.50, 0.30, 0.20 and 0.18 meters. For each one of these object distances move the screen position until a sharp focus is observed. Record this position of the screen as the image position.

Plot a graph of 1/q vs. 1/p and title it “Real Object, Converging Lens.” Both p and q are positive numbers. The y intercept is the power of the lens which is the reciprocal of the focal length. The slope of the line should be -1. Calculate the focal length and compare with what you obtained in part 1. Are the images upright or inverted? For what object distances are the images larger than the object? For what distances are they smaller than the object? Draw a to scale ray diagram for the p = 0.50 m setup.

Determining conjugate points: Place the observing screen at xi = 72 cm so that the sum of the object and image distances is 72 cm. Move the lens and find two lens positions so that the image is a distance of 72 cm from the object. Record these lens positions. Whenever p + q is larger than 4 f there are two lens positions that will form an image on the screen. Why is this true?

3. Virtual Object Diverging Lens
 Put the screen at 80.5 cm and place the 13 cm focal length converging lens near the 50 cm mark. The object slide should still be at the 0 cm mark. Move the lens to focus as sharp an image as possible on the screen. Clamp down the 13 cm lens and do not move it for the rest of this part of the lab. By leaving the lens at the same position, the virtual object remains above the 80 cm mark.
 * [[image:https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/fetch.php?w=500&tok=7ff04c&media=raydiagdivvirt.jpg width="436" height="242" link="https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/detail.php?id=lab-8&media=raydiagdivvirt.jpg"]] || [[image:https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/fetch.php?w=500&tok=cadefd&media=optics-setup-part-iii.jpg width="381" height="259" link="https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/detail.php?id=lab-8&media=optics-setup-part-iii.jpg"]] ||
 * ~ Sample ray diagram for a diverging lens with a virtual object ||~ Diverging Lens Setup ||

Next, place the diverging lens in a holder at the 70 cm position. Move the screen to the point of sharpest focus and record the position of both the diverging lens and the screen. Repeat for diverging lens positons of 71 cm, 72 cm, 73 cm, 74 cm, 75 cm and 76 cm.

Plot a graph of 1/q vs. 1/p and title it accordingly. Now p is negative while q is positive. The y-intercept is the power of the lens and the slope of the line should be -1. Calculate the focal length and compare with the expected value. Construct a graphical solution for the situation where the diverging lens was at 70 cm by tracing the three rays. Compare the predicted image distance with the observed one.

4. Mirror
<span style="color: #333333; display: block; font-family: Arial,sans-serif; font-size: 14px;"> Replace the object slide at the 0 cm mark with the telescope. Make sure to align the back of the telescope (where the mirror is) with the 0 cm mark. Note: the distance from the front of the telescope to the mirror is 25.8 cm. Remove the lenses and screen and put the object slide 1.2m from the mirror. Place the small round screen in a holder between the mirror and object slide with the flat side facing the mirror. Move the screen until the image is in focus and record the object and image distances. Repeat measurements for object distances of 110 cm, 90 cm and 70 cm.
 * [[image:https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/fetch.php?w=200&tok=ce56f7&media=lens4.jpg width="200" link="https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/detail.php?id=lab-8&media=lens4.jpg"]] || [[image:https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/fetch.php?w=500&tok=d99b92&media=142.lab10.fig.5.jpg width="500" link="https://www.andrews.edu/phys/wiki/PhysLab/lib/exe/detail.php?id=lab-8&media=142.lab10.fig.5.jpg"]] ||

Plot 1/q vs 1/p and compare the value for the focal length from your graph with the mirror expected focal length of 30 cm.