This is the only other information given, for procedure 2: In procedure 2, suppo

Question

This is the only other information given, for procedure 2:

In procedure 2, suppose the convex lens is placed at the 38.8 cm mark, and an image forms on the screen at the 77.7 cm mark. Find: - the focal length of this lens. 25.9 x cm - the absolute value of the magnification of this lens 2.00 X - the height of the image cm Trial 2: Move the lens anywhere between 40 cm and 44 cm along the scale on the optical bench. Repeat the steps ?n trial 1. Trial 3: Move the lens anywhere between 45 cm and 49 cm along the scale on the optical bench. Repeat the steps in trial 1. Trial 4: Move the lens anywhere between 50 cm and 55 cm along the scale on the optical bench. Repeat the steps in trial 1. NOTE: The magnification changes with object distance, but the focal length should not. If one value for the focal length fis very different from the others: redo that step. 3. Magnification vs. Object Distance: Use the graph on your data sheet to plot absolute magnification vs. object distance. Extend the graph in both directions. NOTE: This is not a straight line. Note what happens to the magnification as the object distance approaches f, the focal distance. 2. Image Distance. Image Size and Focal length Trial 1: Move the lens anywhere between 35 cm and 39 cm along the scale on the optical bench. Record the location of the lens and the screen in the table on your data sheet. Now: . Turn off the covered light and move the screen until the image is exactly focused. Turn the covered light back on, and record the object distance and the image distance in the chart in the table on your data sheet. . Use the object distance and image distance to find the focal length of the lens. Record this value in the chart in the table on your data sheet. . Use the scale on the screen to measure the horizontal length across the image. If the image is too large: Place an index card in front of your screen. With a pen or pencil, mark the ends of the image. Now remove the card. Use a ruler to measure the length of the image. . Record the size of the image in the chart in the table on your data sheet. . Calculate the ratio of the length of the image over the length of the object. This is the absolute value of the magnification M; record this value in the table on your data sheet. Procedure 2: Image in a Convex Lens 1. Set Up: The object is the circular I pattern on the slide, which is 1.9 cm across (from the arrow on one side to the line on the other). The drawing to the right is a blowup of this pattern. a) Put the slide on the front of the light box. Place the light source on the optical bench so the slide is at the 20.0 cm mark on the ruler attached the optical bench. Place the convex lens on a magnetic holder, and place ?t on the optical bench facing the light. NOTE: The object distance is measured from the location of the slide to the location of the lens, not the location of the lens holder! b) Place the screen on a magnetic holder, and place it on the optical bench beyond the lens. The scale on the screen is in centimeters; the small markings are in millimeters (one-tenth of a centimeter). NOTE: The image distance is measured from the location of the lens to the location of the screen, not the location of the screen holder!

Explanation / Answer

image distance is

q = 77.7 cm - 38.8 cm = 38.9 cm

The object distance is

p = 38.8 cm - 20 cm = 18.8 cm

The thin lens equation is

1/ f = 1/ p + 1/ q

= 1/ 18.8 cm - 1/ 38.9 cm

f = 36.38 cm

Magnification of the lens is

M = - q / p = -38.9 cm / 18.8 cm = -2.069

The height of the image is

h_o = ( 2.069 ) ( 1.9 cm ) = 3.93 cm

  

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