The image of the object is located at a distance of 36 cm from the diffusing lens

The image of the object is located at a distance of 36 cm from the diffusing lens, which has a focal length of 12 cm, at what distance from the lens is the object.

Let’s use the thin lens formula, for this we denote the imaginary image – f, and the imaginary focus – F.
Let’s compose the formula:
1 / (- F) = 1 / d + 1 / (- f);
Let’s transform the formula:
1 / d = 1 / f – 1 / F = (f – F) / f * F;
Let’s transform the formula one more time:
d = (F * f) / (f – F);
Let’s substitute the values into the formula:
d = (36 * 12) / (36 – 12);
Let’s count:
d = 432/24;
d = 18 cm;
d = 0.18 m.
Answer: d = 0.18 m.