Lab 10-Thin Lenses_online_updated

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Apr 3, 2024

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PHYS 2: Spring 2023 Fall 2021 1 Lab 10 Thin Lenses You will need to run (1) a simulation and (2) do an experiment in this lab. Answer the following questions as you work through the lab . Write your answers in blue . (Note that we may miss your response if it does not stand out) Re-load the file in a PDF format in Canvas before the due date. Objectives: By the end of the lab you should be able to 1. Do ray tracing to locate an image formed by a thin converging and diverging lens. 2. Experimentally locate image of an object formed by a thin converging lens at various distances. 3. Extract the focal length of a magnifying glass from object and image distance graph. Overview: I n this lab, you will (i) do ray tracing in a simulation to form an image and characterize it, (ii) measure the focal length of a thin lens and (iii) measure the magnification of an image. You will use a converging lens (sometimes called a bi-convex lens) for the experiments. A lens is called a converging lens when rays parallel to the principal axis actually converge to a point (rather than “appear” to converge) . Converging lenses have a positive focal length, ? . Ray Tracing: This part of the lab is a simulation. You will trace three rays to form an image and characterize it. See below. Measurement of the focal length: You will use the thin lens equation, 1 ? = 1 ? + 1 ? to calculate the focal length ? from the object distance ? and the image distance ? . All the distances are measured from the center of the thin lens. Measurement of the Magnification: You will use two equations to measure the magnification, 𝑀 . They are: 𝑀 = ℎ 𝑖 ℎ ? = − ? ? Here ℎ 𝑖 is the image height and ℎ ? is the object height.

PHYS 2: Spring 2023 Fall 2021 2 We will use the following sign convention: An image is upright ℎ 𝑖 is positive inverted ℎ 𝑖 is negative Image measurement from the lens Image and source are at opposite side of the lens Real and inverted image, ? is positive Image and source are on the same side of the lens Virtual and upright image ? is negative Learning Objectives: At the end of this lab, you should be able to 1. Trace three light rays incident from a source to a lens and form an image at the point the refracted rays (appear to) converge. 2. Calculate and measure the focal length ? of a thin lens from object that is far away (“infinity”) 3. Calculate the focal length ? of a thin lens from various object and resulting image distances. 4. Calculate the magnification of an image by (i) measuring it directly and using 𝑀 = ℎ 𝑖 ℎ 0 ; and (ii) from the object distance ? and image distance ? using 𝑀 = − ? ? . Materials needed: For the experimental part you will need: (1) Lens: A magnifying glass (I got mine for $5 from Amazon). (2) A source: photo from your cellphone or a night light (turned on) or any bright object. (3) A screen: a white piece of paper. (4) A distance measuring device: a ruler that has centimeter marks. (5) Other: scotch tape, some boxes, or books to prop up and hold your source, lens and screen.

PHYS 2: Spring 2023 Fall 2021 3 1. Simulation of Geometric Optics: Open Geometric Optics https://www.physicsclassroom.com/Physics-Interactives/Refraction-and- Lenses/Optics-Bench/Optics-Bench-Refraction-Interactive Click on the top left icon to make the simulation full screen. Take a few minutes to be familiar with the simulation by moving the lens, the object, etc. You can turn a ray “ON” or “OFF. Reload the page. Select the Converging Lens and make sure that the focal length of the lens, ? = 20 ?? 1a. Turn Ray 1 ON only . Describe the ray below. [2 points] Ray 1 goes straight horizontally then it hits the lens and refracts downwards 1b. Turn Ray 2 ON only. Describe the ray below. [2 points] Ray 2 goes downward at roughly a 45 degree angle and when it hits the lens the ray hits the lens it levels of and goes horizontal 1c. Turn Ray 3 ON only: Describe the ray below. [2 points] Ray 3 goes downward at an angle between ray 2 and ray 1 and does not change its course when it hits the lens Table 1: Turn all three rays ON and fill in the table below. Keep the focal length to ? = 20 ?? [10 points] Object distance, ? (??) Image distance, ? (??) Object height ℎ 𝑖 (??) Image height ℎ 𝑂 (??) Magnification 𝑀 = ℎ 𝑖 ℎ 𝑂 Magnification 𝑀 = − ? ? 80 cm 26.9 10 -3.3 -3.03 -.336 60 cm 30 10 -5 -2 -.5 40 cm ( 2? ) 40 10 -10 -1 -1 30 cm 60 10 -20 -.5 -2 20 cm ( ? ) inf 10 -inf 0 -inf 15 cm 60 10 40 .25 -4 10 cm 20 10 20 .5 -2

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PHYS 2: Spring 2023 Fall 2021 4 1d. Diverging lens: Reload the page. Select “Diverging Lens” in the simulation. Slide the object and observe the image. Pay attention to the (i) size of the image compared to the size of the object, (ii) the image is inverted or upright at any distance. Write your observation below. [4 points] Every focal length you move the object the image gets smaller for example 1 focal length away its ½ the size of the actual object at 2F its 1/3 and at 3F it ¼ and so on so forth. The image is always upright at any distance. 1f. Conclusion for part 1: Characterize the image. Circle the correct answer [2x6 = 12 points] A) The image is upright when the object distance is more than / less than the focal length of a converging lens. B) The image is real when the object distance is more than / less than the focal length for a converging lens. C) A real image is formed in the same side / opposite side as the source. D) The real image height is smaller than the object height when the object distance is less than ? / between ? & 2? / greater than 2? . E) The height of the virtual image formed by a converging lens is larger than / smaller than the height of object. F) The height of the virtual image formed by a diverging lens is larger than / smaller than the height of object. 2. Measuring the Focal Length of a Magnifying Glass: Experimental set up : Gather the material listed in page 1. Tape a white paper on the vertical side of a box. This paper will be the screen where you will project the images from the lens of a magnifying glass (MG). This experiment is best done in a room that is semi dark. The source (cell phone) should be bright, and the screen should in a darker place. A good light condition is a small lamp in the room or using a hallway light. 2a. Image formed by an object at a large distance. Select a light in your room that is far from the lens. A “l on g distance” is more than one bed length approximately. Turn the light ON. Focus the image of the light on the paper (see the diagram below) and measure the distance, ? 0 . Write down the image distance. ? 0 51 cm This image distance is an approximate focal length of the lens: ? 0 = ? 0 = 51 cm [2 points]

PHYS 2: Spring 2023 Fall 2021 5 2b. Images formed by an object at various finite distances. Set up a cellphone with your favorite photo (or any source of light) vertically on a table or desk or a wall. (I used my kitchen table). You can use a masking tape as a guide (optional) to ensure that the source, the lens, and the screen lie on a straight line. See Fig. 2A below get an idea about the experimental set up. Prop up the lens and the source so that you can see a nice image on the screen. Make sure that the magnifying glass is (i) not tilted and (ii) the face of the lens is parallel to the face of the cellphone. The image will be formed in a strange location otherwise and you won’t be able to find it easily. To locate the image: Bring a white paper very close to the lens and then start to move it back slowly. You will see a bright fuzzy light at first. As you keep on moving the sheet backwards you will see that an image is forming. Place your screen here and adjust the screen distance until you see a sharp image. Tip: Select a photo that is less “busy”. It is easier to identify the features of the image . Fig. 2A Fig. 2B Fig 2C 2c. Measure the object and the image distances in the following order: (1) Set the distance between the source and the lens ( ? ) at the approximate distance listed in Table 2, column two. Measure the distance with a ruler in centimeter. Record the data in Table 2. (2) Locate the image on the screen by moving the screen along the line of the lens and the source. Adjust the screen so that the image is sharp. Measure the distance between the lens and the screen ( ? ) in centimeter. Record that distance in Table 2. Repeat Step 1 and 2 for several readings. Paste a picture of your experimental setup, image in the space below. [ 3 Points]

PHYS 2: Spring 2023 Fall 2021 6 2d. Data Table and collecting data: Everyone will have a magnifying glass with a different focal length ? . The second column in Table 2, presents object distance in multiples of ? 0 . You need to write the actual measured value of the object distance in column three. Your object distance should be close to the suggested value. It does not have to be exact. Your measurement may have some error since you will “eyeball” the center of the lens. It is okay to have a small error. You are collecting several data points. You can extract a reasonably good result from the best fit line of your plot. Write “No image” if you cannot form an image. Table 2: Collecting data for measuring the focal length of the magnifying glass [15 points] Object distance in terms of ? 0 Object distance ? (cm) Image distance ? ( cm) 1 ? (??) −1 1 ? (??) −1 1 4 ? 0 No image No image No image No image 2 3 ? 0 No image No image No image No image 3 2.5 ? 0 40 128 4 2.3 ? 0 42 117 5 2 ? 0 102 6 1.8 ? 0 92 7 1.6 ? 0 82 8 1.5 ? 0 76.5 9 1.4 ? 0 71.4 10 1.3 ? 0 11 1.2 ? 0 12 1.1 ? 0 13 ? 0 14 0.9 ? 0 15 0.5 ? 0

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PHYS 2: Spring 2023 Fall 2021 7 2e. Plot Graphs and Calculate the focal length of the Magnifying glass lens from the data collected. Graph 1: Plot the image distance ? ( ? -axis) as a function of the object distance ? ( ? – axis). You can use the graph paper and plot it by hand. You can also use the “Scatter Plot” in Excel (Don’t join the points). Paste your graph below. Plot ? 𝒗𝒔. ? [5 points] Graph 2: Plot the 1/ ? ( ? -axis) as a function of 1/ ? ( ? - axis). You can use the graph paper and plot it by hand. You can also use the “Scatter Plot” in Excel. Draw a Best Fit Line *(see below for Excel plotting instruction). Paste your graph below. **The following YouTube video gives you step by step instruction on Scatter Plot and drawing Best fit line in Excel https://www.youtube.com/watch?v=xPllgp12uY4 (3:30 min)

PHYS 2: Spring 2023 Fall 2021 8 Plot of 𝟏/ ? 𝒗𝒔.𝟏/? [5 points] Calculation of the focal length from the 𝟏/? 𝒗𝒔. 𝟏/? plot: [2 x 5 = 10 points] Compare the equation of a straight line, ? = ? + ?? , with the thin lens equation, 1 ? = 1 ? − 1 ? , The slope of the graph, ? = −1 ; Your graph slope is ___________ The ? -intercept ? = 1/? ; Your graph ? -intercept is = __________ cm -1 . Therefore, the focal length ? ?𝑙?𝑡 = 1 𝑦−𝑖?𝑡??𝑐??𝑡 = _________ cm Calculation of % difference from the measured value, % 𝐷𝑖???????? = ⌊ ? 0 −? ?𝑙?𝑡 ? 0 ⌋ × 100 = ___________ 2f. Concluding observation: [2 x 4 = 8 points] 1. The image I projected on the screen was inverted. This type of image is real / virtual. 2. The real image magnification is high, i.e. 𝑀 > 1 when the object distance is between ________ and ___________ (fill in the blanks with multiples of ? . 3. There was no image when the object distance was: _________ (write in terms of ? ). 4. When I use my magnifying glass to read, I can see an upright image. This is because this type of image is …… (write below) …….

Lab 10-Thin Lenses_online_updated

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