Problem $3$: Two converging lenses, one with a focal length of $22\mathrm{.}0$ cm and the other with a focal length of $10\mathrm{.}0$ cm $,$ are placed $25\mathrm{.}0$ cm apart with an object placed $50\mathrm{.}0$ cm in front of the converging lens. Determine $($a$)$ the position and $($b$)$ the magnification of the final image formed. $($c$)$ Show by ray tracing that the image is virtual or real and determine the image distance and magnification.

You must draw the ray diagram to scale to receive full credit; you may also use drawing$/$drafting software to draw the diagram. $[20$pts$]$