Lens' question. There's no object. What am I supposed to do

This is the scheme: http://www.flickr.com/photos/76342179@N0…
The question says that, after passing the diverging lens, the parallel rays form a circle of 20cm diameter on the wall. And asks what's the lens' focal distance.

There's no object. What am I supposed to do??

I get that the focal point is at - 10 cm. ie 10 cm to the left of your lens.
The definition of the focal point is that point which parallel rays meet ( converging) or that point that the rays appear to have come from ( diverging)

As the circle has a diameter of 20 cm then it is 10 cm from the axis.
Draw the line backwards from this point to the point on the lens that the light hit ( 2.5 cm from the axis)
Extend this line further to the left until it reaches the axis.

This is the focal point.

By similar triangles you should see that 7.5 / 30 = 2.5 / x
so x is 10 cm to the left of the lens.

Note that the circle on the wall is not necessarily an image. Nothing in the question implies that this is the case.

The parallel rays are 5 cm apart, but your spot on the wall (the image) is 20 cm. That means the magnification is a factor of 4.

Magnification of a lens is given by image distance (v) over object distance (u). There's a minus in there too but we can ignore that in this case.

So: 4 = v/u and hence v = 4u. So your image distance is four times the object distance. The image distance is 30 cm, so the object distance is 30/4 = 7.5 cm.

Now you can use this in your 1/u + 1/v = 1/f equation to work out the focal length of the lens ...

1/7.5 + 1/30 = 1/f

1/f =1.66666

f = 6 cm

Of course there's an object. It's at an infinite distance, which is why its rays are parallel.
Assume it's a converging lens; otherwise, no image will be formed at all on the right side of the lens.
The parallel rays are turned to go through f and continue on to the wall @ d = 30 cm
I drew a picture of it which showed me that f/(30 - f) = 5/20
or

f = 6.0 cm