13.3.21. Two lenses with a focal length of $30$ cm are located at a distance of $15$ cm from each other. Find out at which positions of the object the system gives a valid image.
Solution
In order for the image from the second lens to be a real image, the image from the first lens (which serves as the object for the second lens) has to be farther than $30$ cm (i.e. the focal length) in front of the second lens. This means that the (virtual) image from the first lens has to be farther than $15$ cm in front of the first lens, because the two lenses are $15$ cm apart. From the thin lens equation, the position of the object when the image is $15$ cm in front of the first lens is