Two identical thin convex lenses, each of focal length \(f\), are separated by a distance \(d=2.5 f\). An object is placed in front of the first lens at a distance \(d_{\mathrm{a}, 1}=2 f .\) a) Calculate the position of the final image of an object through the system of lenses. b) Calculate the total transverse magnification of the system. c) Draw the ray diagram for this system and show the final image. d) Describe the final image (real or virtual, erect or inverted, larger or smaller) in relation to the initial object.

Based on the calculations, the final image formed by the system of lenses is virtual, inverted, and 2 times larger than the initial object. To draw the ray diagram, follow these steps: 1. Draw the two lenses, labeled Lens 1 and Lens 2, vertically with the distance of 2.5f between them. 2. Place the object at a distance of 2f to the left of Lens 1. 3. Draw the image formed by Lens 1 at a distance of 2f to the right of Lens 1. This image will act as the object for Lens 2. 4. Draw the final image at a distance of f to the left of Lens 2. This final image is virtual, inverted, and 2 times larger than the initial object. 5. Draw at least three principal rays from the object to the final image: a. Ray 1: Parallel to the principal axis from the object, passing through the focal point after refraction through Lens 1, then parallel to the principal axis after refraction through Lens 2. b. Ray 2: Passing through the center of Lens 1 without deviation, then passing through the center of Lens 2 without deviation. c. Ray 3: Passing through the focal point of Lens 1, then parallel to the principal axis after refraction through Lens 1, and finally passing through the focal point of Lens 2. 6. Verify that all three rays intersect at the final image location. The completed ray diagram will show the system of lenses, object, and image locations, as well as the principle rays forming the final image.