Lab 11 Focal Length of a Convex Lens

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Dec 6, 2023

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1/11 Lab 11: Focal Length of a Convex Lens Objectives The objectives of this lab are to measure the focal length of a converging lens using two different methods. Calculate the focal length and magnification of two converging lenses using the thin- lens and magnification equations. Background Review ‘ Image Formation by Lenses ’ section in Chapter 25 in your textbook and PPT slides. Materials Student Supplied HoL Supplied Digital camera or smartphone 1.5 m measuring tape Two 3” x 5” index cards Pair of safety goggles Lighter or match Ruler Clear roll of tape Lens set: Convex Lens A Convex Lens B

2/11 Two plastic lens holders Plastic screen holder Tea candle 2 Sheets of white paper Table near a window with unobstructed view Textbook or similar object approximately 3 cm thick Procedure You will complete a lab report that includes data tables, photos, graphs (if any) following the instructions given in “How to write a formal lab report”. The lab report should be a single Word document. You will submit the report by using SUBMIT link given in weekly lab modules in MyHCC (Canvas) lab course. Exercise: Determining the Focal Lengths of Convex Lenses In this exercise, you will determine the focal length of two convex lenses using a distant object. You will then determine the focal length of the lenses using a candle. Part 1: Determining the Focal Length with a Distant Object

3/11 Note: This procedure requires a dimly-lit room with an outside-facing window producing an unobstructed view of a distant object. Best results are obtained on a sunny day. 1. Put on your safety goggles. 2. Gather both lenses and lens holders, the screen holder, the measuring tape, and one 3”x 5” card. 3. Place the 3”x 5” card vertically into the screen holder. 4. Place the thick convex lens (now referred to as Lens A) into one lens holder. 5. Locate a large, distant object outside the window approximately 10 or more meters away, such as a tree, telephone pole, or automobile. 6. Place your lens and screen on a table next to a window, keeping them in line with the distant object and placing the lens between the window and screen. See Figure 1.

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4/11 Figure 1. Experimental setup for viewing a distant object outside a window (left) and closeup of image produced on the screen (right). 7. Adjust the position of the lens by moving it back and forth between the window and screen until an image of the distant object focuses on the screen. 8. Measure the distance from the center of the lens to the screen with the measuring tape to the 0.1 cm. Record as the measured focal length in Data Table 1 . Refer to Figure 2.

5/11 Figure 2. Measuring the distance between the lens and screen. 9. Repeat steps 4-8 for the thin convex lens (Lens B). Part 2: Determining the Focal Length with a Candle 10. Gather the lenses in their lens holders, the screen holder with the index card, the candle, a lighter, a book with a height of approximately 3 cm, the measuring tape, and clear tape before you enter a dimly-lit room with a table. Note: Close the blinds of the window if using the same table as in Part 1. 11. Use the clear tape to secure the measuring tape to the table, parallel to a side, with the centimeter scale facing upward. Reference Figure 3 for measuring using the measuring tape.

6/11 Figure 3. Reading the measuring tape. Each centimeter increment is indicated by a long line spanning the width of the measuring tape and is labeled above that line. 12. Place the candle on the book, with the candle wick centered at the 0 cm mark. Record the position in Data Table 2 . 13. Place the screen at the 30.0 cm mark of the measuring tape and record the position to the 0.1 cm in Data Table 2 . See Figure 4.

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7/11 Note: The screen should be placed such that the card acting as the screen, not the edge of the screen holder base, is at the 30.0 cm mark.

8/11 Figure 4. Experimental set-up (top). The candle is centered at the 0.0 cm mark of the measuring tape (bottom left) and the screen is centered at the 30.0 cm mark of the measuring tape (bottom right).

9/11 14. Light the candle using the lighter or a match. Note: Do not leave the burning candle unattended. 15. Place Lens A in its holder between the candle and screen, with the lens closer to the candle than the screen. 16. Adjust the position of the lens by moving it back and forth between the candle and screen until an image of the candle flame focuses on the screen. 17. Record the lens position in Data Table 2 . 18. Observe the image and record its orientation (upright or inverted) and size relative to the candle (larger or smaller) and record in Data Table 2 . 19. Extinguish the candle. 20. Calculate the object distance d o and image distance d i by subtracting the candle position from the lens position and the lens position from the screen position, respectively. Record to the 0.1 cm in Data Table 2 . Refer to Figure 5.

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10/11 Figure 5. Determining the object and image distances. 21. Calculate the magnification using the following equation: 𝑀 = − 𝑑𝑖 𝑑𝑜 22. Record the magnification to the 0.1 in Data Table 2 . 23. Calculate the focal length using the thin-lens equation: 1 ? = 1 𝑑 𝑜 + 1 𝑑 𝑖 𝑂𝑅 ? = 𝑑 𝑜 𝑑 𝑖 𝑑 𝑜 + 𝑑 𝑖

11/11 24. Record the calculated focal length to the 0.1 cm in Data Table 2 . 25. Repeat steps 16-24, with the lens placed closer to the screen than the candle. 26. Calculate the average focal length using the equation: ?𝑎𝑣? = ?𝑡𝑟𝑖𝑎𝑙1 + ?𝑡𝑟𝑖𝑎𝑙1 2 27. Record the average focal length to the 0.1 cm in Data Table 2 . 28. Repeat steps 12-27 for Lens B, centering the screen at the 110.0 cm mark instead of the 30.0 cm mark. Record all values in Data Table 3 . Part 3: Observing Changes in an Imaged Formed by a Convex Lens 29. Place the candle on the box at the 0.0 cm mark and the screen at the 50.0 cm mark. 30. Light the candle. 31. Place Lens A between the candle and the screen, then focus an image of the candle flame on the screen.

12/11 32. Predict what will happen to the image if one half of the lens is covered. Record your prediction in Panel 1 . 33. Test your prediction by holding the second 3”x5” card (or another sheet of folder paper) next to Lens A such that it covers one half of the lens. Record your observations in Panel 2 . 34. Extinguish the candle. Cleanup: • Return the HOL materials to the lab kit. Data and Analysis Data Tables Data Table 1: Focal Length of Lenses Using a Distant Object Lens Measured Focal Length (cm) A 17.42 B 7.81 Data Table 2: Focal Length of Lens A Using a Candle Trial 1 Trail 2 Candle Position (cm) 0 0

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13/11 Screen Position (cm) 30 30 Lens Position (cm) 6.8 25.5 d o (cm) -6.8 -25.5 d i (cm) 23.2 4.5 Upright or Inverted inverted inverted Larger or Smaller larger smaller Calculated Magnification -3.4 -0.18 Calculated Focal Length (cm) 5.26 3.82 Average Focal Length (cm) 4.54 Data Table 3: Focal Length of Lens B Using a Candle Trial 1 Trail 2 Candle Position (cm) 0 0 Screen Position (cm) 110 110 Lens Position (cm) 5 95

14/11 d o (cm) -5 -95 d i (cm) 95 5 Upright or Inverted Inverted Upright Larger or Smaller Larger Smaller Calculated Magnification -15.5 -0.05 Calculated Focal Length (cm) -7.75 -0.05 Average Focal Length (cm) 6.25 Panel 1: Prediction for Image Appearance Our prediction of the image appearance was that the image will remain largely the same.

15/11 Panel 2: Observation of Image Discussion: 1) Why is it beneficial to perform these exercises in a dimly-lit room? It would ultimately allow for better visual of the image on the screen. The image would be more visible. 2) Is magnification a constant property of a lens? Reference Data Tables 2 and 3 and the definition of magnification to explain your answer. It really depends on magnification as well as distance. It is not a constant property of a lens, which is shown in the data tables 2 and 3. 3) What factors contribute to error in this exercise? Describe experimental factors that could be modified, and unalterable properties of materials used. The image tends to fade in a very slow manner.

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16/11 The most challenging part was positioning the lens, and that is where most of the errors occurred and even errors in the measurements itself. 4) Did your prediction in Panel 1 match the results you described in Panel 2? Explain the physical phenomenon that produced what you described in Panel 2 and any discrepancies with your prediction. It did not match the results because the image faded away because there was a decrease in light visibility. Conclusion: We had many errors in this lab, but it was from the challenges and positioning of the lens and measurement inaccuracies. Things that may have affected the results might have been the lens magnification on distance, and human error. All of these affected the outcome of this experiment. References: Physics College Textbook, 2023. Dr. W Lab Template.

Lab 11 Focal Length of a Convex Lens

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