Final answer:
Using the thin-lens equation and ray tracing, one can find the image distance and magnification for an object placed farther than the focal length from a converging lens. Given object distance and focal length, the image distance and magnification are calculable through formulas and can be verified with a scaled ray tracing diagram.
Step-by-step explanation:
Understanding the Thin-Lens Equation and Ray Tracing
When an object is placed farther away from a converging lens than its focal length, one can use the thin-lens equation to find the image distance and magnification. Given that the object distance (do) is 0.75 m and the focal length (f) is 0.50 m, we can determine the image distance (di) and magnification (m) using these values.
The thin-lens equation is given by 1/f = 1/do + 1/di, and magnification is calculated as m = -di/do. When the object is placed at a distance greater than the focal length of the lens, we expect to find a real and inverted image on the opposite side of the lens.
For the ray tracing method, a scale drawing helps us to visually pinpoint where the rays coming from the object will converge on the other side, providing an approximate value for di. The magnification can also be visually estimated, showing whether the image is enlarged or reduced compared to the object.
After these calculations and approximations, we can verify the values obtained through the equations with the results of the ray tracing, ensuring consistency in our solution.