Derivation of the Thin Lens Equation (continued)

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 .

 

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