For each part of this question address it in two ways: by drawing and interpreting appropriate geometrical diagrams and by appealing to the lens equation and the expression for lateral magnification and demonstrating your result mathematically. If your two approaches do not agree, explain which one is correct and why the other is wrong.

Suppose you are using a camera and wish to have a larger image of a distant object than you are obtaining with the lens currently in use. Would  you change to a lens with a longer or a shorter focal length? Explain your reasoning. (Hint: Note that the object distance is essentially fixed.)

Suppose you are using a slide projector and wish to obtain a larger image on the screen. You cannot achieve this by moving the screen farther from the projector because you are already using the entire length of the room. Would you change to a lens with a longer or a shorter focal length than the one you are using? Explain your reasoning. (Hint: Note that the image distance is essentially fixed.)