I 4 Lab 14: Ray tracing & image formation Differentiate between Real and Virtual images. Understand how image formation occurs using concave and convex lenses. Understand how image formation occurs using concave and convex mirrors. Draw the geometrically accurate trajectory of light through convex and concave lenses in various arrangements. Draw the geometrically accurate trajectory of light reflected by convex and con- cave mirrors. Apply the correct mathematical model to arrangements of mirrors and/ or lenses. Calculate the size (height) and location (focal point) of images produced by ware ious arrangements of mirrors and lenses. 14. 1 principal rays Click this Geometric optics simulation link, then the \"Play" icony and select "lenses,\" check the "principal\" box, and select the arrow image in the dropdown box at the top left. Principal rays are the rays which are used to derive the mathematical relations, due to their easily observable geometric properties. In table 141 observe how the trajectory of each ray is aected by the lens. Categorize each Refracted ray as either unchanged, parallel to axis, or intersecting image focus. Incident Ray trajectory Refracted Ray Trajectory Ray 1: parallel to axis Ray 2:1ntersecting object focus Ray 3: Ray Incident on center of lens Table 14.1: Analysis of principal Rays CHAPTER 14. LAB 14: RAY TRACING 5 IMAGE FORMATION nt 141 Use basic geometry and trigonometry to answer all questions. All answers should be written in terms of the following miables: focal point, F; object height, he; image height, h,; object distance, 0; and image distance i. 1. Find 2 expressions for the slope of Ray 1 after refraction. 2. Find 2 expressions for the slope of Ray 2 prior to the lens, 3. Find an expression for the slope of Ray 3. 4. Provide an argument showing the following right triangles are similar: Triangle 1: Si : he,52 : o and hypotenuse given by Ray 3 on the left of the lens. and Triangle 2: S] = hush = i and hypotenuse given by Ray 3 on the right of the lens. . Use the similarity to show: [2, = ha - :. Note that these principal rays will bchavc the same regardless of the typc of lens or mirror, and can be drawn if the Focal points, and center of curvature of the lens or mirror are known. The Convergence of the principal rays allows us to draw diagrams of objects and their images: Ray 1 always begins parallel to the axis and intersects the focal point. Ray 2 always intersects the focal point prior to lens or mirror and results in a ray parallel to the axis. Ray 3 always is incident upon the center of the lens, and is unchanged. Similar geometric reasoning to that used to answer questions in 141 can be used to de- rive expressions for magnication, and the thin lens equation, which hold for mirrors and Concave lenses so long as we are careful about the sign of he foci and position of the images. 14.2 Lenses I Checkpoint 142 Fill out the following table, 142 for the Concave lens and draw each case. 14.3. MIRRORS Upright or Image Size: Image type: inverted magnied or reduced 2; Real or Virtual Object position (left), mm) Image position, 1(cm) 3F 2F Table 142: Concave Lens Checkpa t 143 Fill out the following table, 143 for the Convex lens and draw each case. Upright or Image Size: Image type; Object position (left), inverted magnied or reduced {:1 Real or Virtual own) Image position, 1(cm) 3F 2F Table 14.3: Convex Lens Checkpo' 1 14-4 1. . What is responsible for image formation? 2. What are the properties which distinguish real vs. virtual images? 3. . Play with each of the sliders, and make a statement for each relating how the variables affect the image and focal point 14.3 Mirrors Click the mirror simulation at bottom of the screen, then repeat the experiment from above with Concave and Convex mirrors. Again, check the principal box, and select the arr Checkpo t 145 Fill out the following table, 144 for the Concave mirror and draw each case. Page 4 of 4 CHAPTER 14. LAB 14: RAY TRACING & IMAGE FORMATION Object position (left), Upright or Image Size Image type: o(cm) Image position, i(cm) inverted magnified or reduced hi Real or Virtual 3F 2F IF F Table 14.4: Concave Mirror Checkpoint 14-6 Fill out the following table, 14.3 for the Convex mirror and draw each case. Object position (left), Image position, i(cm) Upright or Image Size: Image type: o(cm) inverted magnified or reduced hi Real or Virtual 3F 2F IF Table 14.5: Convex Mirror Checkpoint 14-7 What are the similarities and differences between the characteristics of the images formed by the mirrors and the lenses you have studied? License This Lab is licensed under CC BY-SA 4.0; a derivative from, Original work "Bulding Models to Describe Our World" by Martin et. al. The Lab uses the Geometric optics simulation, from PhET Interactive Simulations at Uni- versity of Colorado Boulder, under CC BY-SA 4.0, as well. The lab remixed content from a Phet contribution, which is shared under a not declared license and was originally authored, remixed, and/or curated by Jose Salvador