A point source S and its image S1 are located on opposite sides of the lens with a focal length

A point source S and its image S1 are located on opposite sides of the lens with a focal length F on its main optical axis. The distance from them to the lens is the same. Calculate the distance L between source S and its image S1.

Let’s use the equation for a thin lens:
1 / F = 1 / d + 1 / f,
where
F is the focal length of the lens,
d is the distance from the object to the lens,
f is the distance from the object image to the lens;
To find:
L = f + d;
According to the condition of the problem
f = d;
Then
1 / F = 1 / (2 * d);
d = F / 2 and
f = F / 2;
We get
L = F.