What is the focal length of a diverging lens if the image of an object located at a distance of 20 cm is at a distance of 15 cm from it?

To determine what is the focal length F of a diffusing lens, if the object is at a distance d from the lens, the image of which is at a distance f from the lens, we use the thin lens formula: 1 / F = 1 / d + 1 / f. We get:
F = d f / (f + d).
It is known from the problem statement that the object is located at a distance of d = 20 cm = 0.2 m, and the imaginary image of the object is at a distance f = – 15 cm = – 0.15 m. The minus sign is taken for the imaginary image f obtained in a diffusing lens. Substitute the values ​​of the quantities into the calculation formula:
F = 0.2 m (- 0.15 m) / (- 0.15 m + 0.2 m);
F = – 0.6 m.
Answer: the focal length of the diffusing lens is – 0.6 m.