Part 1: Qualitative Analysis of a Thin Lens

• • This Lab is best done in the dark.  You will need a desk lamp, flashlight, or other portable source of light that you can turn off and on as you perform the experiment.  You will also need a flat, smooth surface at least one meter long upon which to set up your “optical bench”.  This can be a desk top, tile floor, or any smooth surface that will afford one meter’s worth of unimpeded space.
  • Now that you have a portable source of light and an area to set up your optical bench, watch the “Setting Up and Optical Bench Video” available on Blackboard.  Set up your “optical bench” as instructed in the video.
  • Make sure your screen is back to the 90 cm mark on the tape measure.  Move the lens to the 15 cm mark on the tape measure.  You are now ready to begin.
  • Make sure to turn your desk lamps off when you are focusing!
  • Slide the image screen towards the lens until you see a “focused” image of the arrows.
  • Qualitatively describe the image, including its orientation (relative to the object).
  • Play with the set-up.  Change the \(i\)’s and \(o\)’s and observe what you need to do to re-focus the image. Are there lens and object locations where it is impossible to get a focused image?  Think about why that may be.
  • For the following, move the lens to the 17 cm mark on the tape measure and move the image screen to get a focused image. Do you think the ratio of \(i\) to \(o\) should be equal to the ratio of the image height, \(h_{i}\), to the object height, \(h_{o}\)?  (The object height, \(h_{o}\) of your arrows is 3.2 cm. Note that the object consists of two arrows, one in front of the other.  The 3.2 cm height is the length of the arrow in front, measured from the tail of the arrow to its tip.  When measuring \(h_{i}\), make sure you measure the same arrow of the image from tail to tip).  Verify your answer by measuring and recording without uncertainty \(h_{i}\)  , \(i\), and \(o\).  Calculate the two ratios.  Are the two ratios approximately equal?

Part 2: Measurement of the Focal Length of a Thin Lens

• • The goal is to measure the focal length, \(f\) (without uncertainty), of the lens by plotting \(1/i\) versus \(1/o\).
  • Make a table (or tables) of \(o\) (\(o\) is the distance from the object to the lens), \(\delta o\), \(o\) +/- \(\delta o\), \(s\) (\(s\) is the distance from the object to the image screen), \(\delta s\), \(s\) +/- \(\delta(s)\), \(i\) (\(i\) is the distance from the lens to the image screen, it is calculated by subtracting \(o\) from \(s\)), \(\delta i\), \(i\) +/- \(\delta i\), \(1/o\), \(\delta(1/o)\), \(1/o\) +/- \(\delta(1/o)\), \(1/i\), \(\delta(1/i)\) and \(1/i\) +/- \(\delta(1/i)\).  Recall that small delta, \(\delta\), refers to the uncertainty of the measurement. The uncertainties in \(o\) and \(s\) are your best estimates.  You will need to use the error propagation rules when calculating \(\delta i\), \(\delta(1/o)\), and \(\delta(1/i)\), You may need to refer to the Error Propagation Rules sheet on Blackboard.  For a full explanation as to how the propagation rules are derived, refer to the uncertainty reference material in the Lab Manual.
  • We will measure four \(o\) and \(i\) values together with their uncertainties.  Start with your image screen at the 90 cm mark on your tape measure and the lens at the 10 cm mark.  Slide the lens slowly towards the image screen until you have a crisp, focused image.  Record \(o\), \(s\), and \(i\) (to obtain \(i\) you will have to subtract \(o\) from \(s\)) and their uncertainties (see above).  Now move the lens to the 15 cm mark.  This time slide the image screen towards the lens until you have a focused image.  Record \(o\) (15 cm), \(s\) and \(i\) and their uncertainties (see above).  Repeat this procedure for \(o\) equal to 17 cm and \(o\) equal to 20 cm.
  • Plot \(1/i\) vs. \(1/o\) with error bars using EXCEL. Have Excel provide the equation of your line by adding a Trendline. Have Excel display the equation of the line to two decimal places for both the slope and y-intercept.  If you do not have access to EXCEL, you may plot by hand and draw a best fit line to calculate the slope by hand.  Pull off the y-intercept value from where your best fit line intersects the y axis (Do not calculate this value)  Note that you are not calculating the uncertainty in the slope nor y-intercept, therefore do not draw worst fit lines!
  • Use straight line analysis (correlate the equation of your line and the lens equation) to answer the following:
    What is the value of the slope of your best fit line?  What should it be based on the correlation between the equation of your line and the lens equation?
    Determine \(f\) without uncertainty and compare it with the expected value of 10.0 cm. If your value is not reasonably close to the actual value (say within 15%), try to determine what you did incorrectly.