You place an object $19\mathrm{.}6$ cm in front of a diverging lens which has a focal length with a magnitude of $13\mathrm{.}0$ cm $.$ Determine how far in front of the lens the object should be placed in order to produce a new image that is $4\mathrm{.}15$ times smaller than the original image.

Can you write the thin lens equation that gives a relationship between the focal length of a lens, the object distance, and the image distance?

Can you write the thin lens equation that gives a relationship between the object distance, image distance, and magnification? cm