Fall2023 Thin Lenses Lab Online (New Simulator)-1

1 Thin Lenses Lab Online Introduction The purpose of this activity is to determine the relationship between object distance and image distance for a thin convex lens. A thin lens is one whose thickness is negligible in comparison to the image and object distance. A convex lens is thicker in the center than at the edges and can also be called a positive lens or converging lens. A concave lens is thinner at the center than at the edges and can also be called a negative lens or a diverging lens. Use a light source, optics bench, lens, and viewing screen to measure object distance, image distance and size. The technological pieces of equipment pictured here make use of lenses. Theory When a light source, like a light bulb shine, it radiates light in all directions. A lens will alter the direction of those rays of light which strike it, resulting in either a real or virtual image to be formed. If the rays of light go from the source through the lens to form a single point in space, it will form a real image. However, a virtual image is formed if the projections from the rays of light form on the same side as the source. These can be seen in Figure 1 and Figure 2. These distances and focal lengths are related by The Thin Lens Equation : ? ? + ? ? = ? 𝒇 Where ? is the distance from the object to the center of the lens, ? is the distance from the location the image forms to the center of the lens, and 𝑓 is the focal length (also called focus length) of the lens. There is a focal length on both sides of the lens. Fig. 1: Real Image Formation p q h h’ f O I F p q h h f O I F p q h h f O I F Fig. 2: Virtual Image Formation

2 Object distances, image distances and focal lengths can be positive or negative. There is also a Magnification Equation to help predict how large or small the image will be compared to the size of the original object. This equation is: 𝐌 𝐞𝐱𝐩 = ± 𝒉 ′ 𝒉 = − ? ? The various rays in the diagrams are given names. For a converging lens the following figure lists the names of the three rays in the diagram. Fig. 3: Ray Naming The Parallel Ray starts at the top of the object height, runs parallel to the lens’s main axis, and then at the center of the lens where it crosses the lens’s minor axis it changes direction, and intersects with the focal length on the back side of the lens. The Chief Ray starts at the top of the object height and goes through the center of the lens where the lens’s main and minor axis intersect. The Focal Ray starts at the top of the object height and intersects the focal length on the front side of the lens till it reaches the minor axis of the lens, then it runs parallel with the main axis of the lens.

4 2. Next, you will need to set the value of the focal length. You will do this by placing the cursor on the “Focus” on the left side of the lens. Then left click and hold while moving the point (blue circle). You will move the Focus (left or right) to change the focal length. For Part 1, set the focal length to 2.00 cm. (Again, 2 is displayed for f, but record 2.00 cm). 3. Now you want to start recording the data by changing the object distance. When setting the object distance, try to get the actual value as close to the nominal value listed in Table 1 as possible (±0.05). First, try to set the object distance to 2.75 cm. The 2.75 cm value is the nominal value. Below, the actual value recorded in Table 1 will be 2.74 cm (which is within ±0.05). When changing the object distance, the object height my also change. Before recording any data, make sure the image height is still as close to 2.00 cm as possible. You should be able to keep the object height within ±0.03 cm. As seen below in the example, the height is 2.01 cm which is within ±0.03 range. Once the object distance and height are set, record the image distance, and Experimental Magnification. Here, di = 7.44 cm and M = -2.72. focal length object distance

5 4. Next, change the object distance to 3.00 cm (±0.05 cm). Make sure the object height is still close to 2.00 cm (±0.03 cm) and then record the data for that trial. 5. Repeat the process for the rest of the values in Table 1. Procedure: Part 2 1. Next, you will need to set the value of the focal length. You will do this by again placing the cursor on the “Focus” on the left side of the lens. Then left click and hold while moving the point (blue circle). You will move the Focus (left or right) to change the focal length. For Part 2, set the focal length to 4.50 cm (±0.05 cm). (Here, 4.5 is displayed for f, but record 4.50 cm). Next, set the height of the object. Again place the cursor on the blue circle at the top of the object arrow. Then, while clicking on and holding the left mouse button, move the cursor up or down to change the height of the object. For Part 2, set the height of the object to 1.00 cm. Again, watch the number of decimal places you use in recording your data. object distance

7 Analysis of Thin Lenses Lab Online Name_Juan Sarabia_____________________________________________ Course/Section_Phy-1971______________________________________ Instructor__Christopher Dunn__________________________________________ Table 1: 𝒇 = ?. ??_____________ cm Object Height = _2.00________ cm (13 points) Trial Object Distance p or do (cm) Actual Image Distance q or di (cm) Actual Image Height hi (cm) Actual 1/q Actual 1/p Experimental Magnification M experimental Theoretical Magnification M theoretical # Nominal Actual 1 2.75 2.76 7.27 -5.30 0.14 0.36 -2.63 -2.64 2 3.00 3.00 6.00 -4.00 0.17 0.33 -2.00 -2.00 3 3.50 3.50 4.67 -2.65 0.21 0.29 -1.33 -1.33 4 4.00 4.00 4.00 -2.00 0.25 0.25 -1.00 -1.00 5 4.50 4.50 3.60 -1.61 0.28 0.22 -0.80 -0.80 6 5.00 5.00 3.33 -1.33 0.30 0.20 -0.67 -0.67 7 5.50 5.49 3.14 -1.15 0.32 0.18 -0.57 -0.57 8 6.00 6.00 3.00 -1.00 0.33 0.17 -0.50 -0.50 9 6.50 6.49 2.89 -0.88 0.35 0.15 -0.45 -0.44 10 7.00 7.00 2.80 -0.80 0.36 0.14 -0.40 -0.40 11 8.00 8.00 2.67 -0.67 0.37 0.13 -0.33 -0.33 12 9.00 9.00 2.57 -0.57 0.39 0.11 -0.29 -0.29 13 10.00 10.00 2.50 -0.50 0.40 0.10 -0.25 -0.25 14 12.00 12.00 2.40 -0.40 0.42 0.08 -0.20 -0.20 Complete Table 1 by calculating the Theoretical Magnifications for each of the object distances. Show work for one of these calculations. (2 points) Mexp=-q/p=-7.27/2.75=-2.64

8 1. Using Excel, or some other graphing program, or by hand, make a graph of Image Distance vs. Object Distance (q vs. p), then answer the following questions about this graph. (10 points) 2. What value does the image distance approach as the object distance becomes larger? (5 points) The image distance would be approaching the focal point value of 1 I/f 3. What value does the object distance approach as the image distance becomes larger? (5 points) It approaches the focal length of I/f 4. How does the value of the answers to questions 2 and 3 relate to the lens?

10 Table 2: 𝒇 = ?. ??___________ cm Object Height = _1.00________ cm (8 points) Trial Object Distance p or do (cm) Actual Image Distance q or di Actual Image Height hi (cm) Actual 1/q Actual 1/p Experimental Magnification M experimental Theoretical Magnification M theoretical # Nominal Actual 1 3.25 3.25 -11.66 3.59 -0.08 0.31 3.59 2 3.00 3.00 -9.01 3.00 -0.11 0.33 3.00 3 2.75 2.74 -6.98 2.55 -0.14 0.36 2.55 4 2.50 2.50 -5.65 2.26 -0.18 0.40 2.26 5 2.25 2.25 -4.50 2.00 -0.22 0.44 2.00 6 2.00 2.00 -3.60 1.80 -0.28 0.50 1.30 7 1.75 1.74 -2.83 1.63 -0.35 0.57 1.63 8 1.50 1.51 -2.26 1.50 -0.44 0.66 1.50 9 1.25 1.25 -1.73 1.39 -0.58 0.80 1.38 10 1.00 1.00 -1.29 1.29 -0.78 1.00 1.29 11 0.75 0.76 -0.92 1.21 -1.09 1.32 1.23 12 0.50 0.49 -0.54 1.12 -1.85 2.04 1.08 Complete Table 1 by calculating the Theoretical Magnifications for each of the object distances. Show work for one of these calculations. (2 points)

11 1. Using Excel, or some other graphing program, make a graph of Magnification vs. Image Distance (M vs. q). Add the trendline and display the equation on the chart. (5 points) Mexp=-q/p= -(-11.66)/3.25=3.59

13 The image that is produced when the object is placed in between the focal point and the lens is called a virtual image. The image will have a magnification that is greater than 0, therefore it would be upright. The image will also be larger than the object because it would be magnified also it would be on the same side as the object.