Focal Length

You should have known that when an object is placed at distance 2f (where f is the focal length) of a convex lens, the image is formed at a distance of 2f on the other side of the lens, and is of the same size of the object.

When the object moves away from the lens, the image moves towards the lens, and its size reduced. Conversely, when the object moves towards the lens, the image moves away from the lens, and its size increased.

With the above understanding, when the object is placed 17 cm from the lens, it is given that the image is slightly smaller than the object. Therefore, it can be envisaged that the object is at a distance slightly longer than 2f from the lens. Let this distance be (2f + x), where x is a small number.

When the object is at distance 15 cm from the lens, it is given that the image has size slightly larger than the object. Therefore, the object should be at distance slightly shorter than 2f. Let the distance be (2f - x'), where x' is a small number.

For small movement at position 2f, we could assume that x and x' are approximately equal.

Thus, we have the following two equations:
17 = 2f + x
15 = 2f - x

Adding these two equations gives
32 = 4f
this gives f = 8 cm