A converging lens has one focal length $f$, and once an object stands in front of it, two distances matter: $d_o$ (dee-oh, lens to object) and $d_i$ (dee-eye, lens to image). The thin lens equation ties all three: $\dfrac{1}{f} = \dfrac{1}{d_o} + \dfrac{1}{d_i}$ (read aloud: one over f equals one over d-o plus one over d-i). It is this chapter's first full ladder: pick the formula, rearrange it, place the givens, then compute.

The one rule of reciprocal land: never add the plain distances. Flip each number, add the flips, and flip the total back at the very end. The values in this lesson are chosen to be kind — $\tfrac{1}{30} + \tfrac{1}{15} = \tfrac{1}{30} + \tfrac{2}{30} = \tfrac{3}{30} = \tfrac{1}{10}$, focal length 10 cm, no calculator harmed. When the unknown moves, the equation rearranges by SUBTRACTING a reciprocal from $\tfrac{1}{f}$ — same land, same rule.