A slide projector produces a 500 times enlarged image of a slide on a screen 10m away. If the screen is moved 2m closer, by what distance should the slide be moved towards or away from the lens so that the image remains focused on the screen? What is the magnification in this case? Assume that the projector consists of a single convex lens for magnification.
We have 1/f = (1/v) - (1/u)
Where f is the focal length of the lens, u the x coordinate of the object and v is the x coordinate of the image.
In the first case, v = 10m and the magnification M = v/u = ...
Answer with detailed mathematical steps.