Find the focal length of a plano-convex lens if the object is at a distance of 40 cm from the lens, and the image is at a distance of 20 cm.

It is known from the condition that the object is at a distance of 40 cm from the lens, and the image is at a distance of 20 cm.
To put it briefly:
d = 40 cm = 0.4 m;
f = 20 cm = 0.2 m.
Need to find:
F -?
To solve the problem, we apply the thin lens formula:
1 / F = 1 / d + 1 / f.
where F is the focal length, m;
d is the distance from the optical center of the lens to the object, m;
f is the distance from the optical center of the lens to the image of the object, m.
Let us express the focal length from the formula:
1 / F = (d + f) / d * f;
F = d * f / (d + f).
It remains to substitute the values ​​into the formula and perform calculations:
F = (0.4 * 0.2) / (0.4 + 0.2) = 0.08 / 0.6 = 0.1 (3) = 0.13 m.