Answer to Question #251909 in Optics for Josh

Question

How far apart are an object and an image formed by a 75.0cm focal length converging lens if the image is 2.5x larger than the object and is real.

Answer 1

$m = \frac{v}{u} = 2.5 \\ \frac{1}{u} + \frac{1}{v} = \frac{1}{f}$

Multiplying by v on both sides and replacing $\frac{v}{u}$ by m

$m + 1 = \frac{v}{f} \\ 3.5 = \frac{v}{75} \\ v = 262.25 \; cm \\ u = \frac{v}{m} = \frac{262.25}{2.5} =105 \; cm \\ u +v = 105 +262.25= 367.25 \; cm$