Here we derive the thin lens equation, starting from the two equations of the previous slide that we obtained by considering two sets of similar triangles: eq.(1): i/f = (hi + ho)/ ho , and eq. (2): hi /ho = i/o. We can solve eq.(2) for hi : hi = i*ho /o. Now we plug this expression for hi into eq. (1), and we obtain: i/f = 1/ ho *(i* ho /o + ho). Cancelling ho yields: i/f = i/o + 1. Finally, dividing both sides by i gives the thin lens equation: 1/f = 1/o + 1/i .