Solve the all parts of given problem:
Problem: The image of a tree on a 35 mm color slide is 1.9 mm high. It is to be projected onto a screen 6 m from the slide, and is to appear 409 mm high.
Part I: What focal length lens (in meters) is needed?
Part II: What is the distance in meters between the lens and the slide?
Part III: What is the magnification of the system?
Please explain each step and equations used.