Question

An object is placed 12cm from a converging lens. An image of the object is formed 12cm from the second focus on the other side of the lens. Calculate the focal length.

Answer 1

Answer on Question 37991, Physics, Optics We will use thin lens formula to solve this problem. As you know

$\frac{1}{d_{o}}+\frac{1}{d_{i}}=\frac{1}{f}$

where $d_{o}$ is object distance, $d_{i}$ is image distance and $f$ is focus length. we are given that $d_{i}=f+l$, $l=12$ cm and $d_{o}=12$ cm. So we can find

$\frac{1}{d_{o}}+\frac{1}{f+l}=\frac{1}{f}$

$(f+l+d_{o})f=d_{o}(f+l)$

$f^{2}+lf-d_{o}l=0$

$f^{2}+12f-144=0$

From where we find that physical solution is $f\approx 7.4$ cm.