Can a single lens save the day for the broken projector?

[Cathmore]

Homework Statement

You have paid big bucks to see The Bourne Legacy at the 3-D IMAX theater in Vancouver. Just before the movie is about to begin, the theater staff tell you that the lens for the projector has just broken! You really want to see the movie and decide that it should be simple to set up a single lens system to project their 90mm film onto a 10 meter tall screen - if you just had a lens!? Fortunately you are there with your great aunt who wears REALLY thick glasses. One of her lenses has an optical power of +3.6 m-1, and the other has a power of +4.2 m-1 (optical power is 1/f). If the screen is 30-m away from the lens, can you save the day and fix the "projector" with one of these lenses?

Your solution should contain:

an explanation of how you decide whether or not you can save the day
a ray diagram of the film-lens-screen system, using at least 3 rays.

Homework Equations

1/f=1/p+1/q
m=hi/ho
m=-q/p

The Attempt at a Solution

I used the information given to find the object distances for both lenses, and from there the magnification, with which I used m=hi/ho to get an image height. One lens ends up making an image of a height about 9.6m, while the other is 11.3m, I figured the smaller image would be more in focus, and would be the one to use. But I run across a problem when I try to draw a ray diagram and realize the image forms at a distance much, much close than 30m. Wouldn't that mean the image would end up being so out of focus as to be unwatchable at 30m?

 

[voko]

Given the image distance, find the object distance. The check what image size you get with this object distance.