An optical projector uses four lenses having the same optical axis. The focal lengths of the

lenses are f$\_(1)=-3$cm$,$f$\_(2)=+1\mathrm{.}5$cm$,$f$\_(3)=+6$cm and f$\_(4)=-17\mathrm{.}2$cm$.$ The distance

between the first and second lens is d$\_(12)=1\mathrm{.}25$cm and that between the second and the

third lens is d$\_(23)=15$cm$,$ while the third and fourth lenses are placed at d$\_(34)=1$cm apart.

If the object is $1$ cm away from the first lens. Determine:

a$.$ The position of final image.

b$.$ The total magnification of the final image.

c$.$ The nature of the image.