# The object’s image is at a distance of 20 cm from the diffusing

**The object’s image is at a distance of 20 cm from the diffusing lens with a focal length of 50 cm. What is the distance from the object to the lens?**

To determine at what distance d from the lens an object is located, the image of which is at a distance f from the lens with a focal length F, we use the thin lens formula: 1 / F = 1 / d + 1 / f. We get:

d = F f / (f – F).

It is known from the problem statement that the virtual image of the object is at a distance f = – 20 cm = – 0.2 m from the scattering lens with a focal length F = – 50 cm = – 0.5 m. The minus sign is taken for the F scattering lens and for f of the virtual image. Substitute the values of the quantities into the calculation formula and determine what the distance from the object to the lens is equal to:

d = – 0.5 m (- 0.2 m) / ((- 0.2 m) – (- 0.5 m));

d = 1/3 m ≈ 0.33 m.

Answer: the distance from the object to the lens was ≈ 0.33 m.