Question

Two lenses of power 3D and -5D are placed in contact to form a composite lens. An object is placed at 50cm from this combination. Find the position of the image.

Answer 1

$p1 = 3d \\ p2 = - 5d\\ \\ net \: focal \: length = \frac{1}{p1} + \frac{1}{p2} \\ f = \frac{1}{3} - \frac{1}{5} \\ f = \frac{5 - 3}{15} \\ f = \frac{2}{15} \\ \\ object \: distance(u) = - 50cm = - \frac{1}{2} m \\ focal \: length(f) = \frac{2}{15} m \\ image \: distance(v) = to \: find \\ \\ mirror \: formula - - > \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \\ \\ \frac{15}{2} - 2 = \frac{1}{v} \\ \frac{15- 4}{2} = \frac{1}{v} \\ \frac{1}{v} = \frac{11}{2} \\ v = 0.1818m \\ \\ image \: distance = 18.18cm$