Simple Optics: Image Formed By Two 15cm Lenses

[beethoven'smahomeboy]

An object is 15 cm from a converging lens of focal length 15 cm. A second positive lens of focal length 15 cm is 20 cm from the first lens. Where is the final image (s)?

Since 1/15+1/s=1/15 by the thin-lens equation, is there an image formed?

 

[andrevdh]

beethoven'smahomeboy,
If light from a far away object (parallel light rays) falls on a convex lens it will form an image of the object in it's focal plane (that is how the focal length of such a lens is defined). If an object is placed at the focus of a lens we get conversely that it forms an image of the object at infinity (very far away) again with parallel light rays leaving the lens. Your equation above get 1/s as zero, which implies that the image is at infinity. For the second lens the light looks like it is coming from an far away object (that is the rays are traveling parallel to each other after leaving the first lens). This means that the second lens will form an image of the original object at it's second focus. The distance between the two lenses are irrelevant. The object is therefore mapped from the focal point of the first lens to that of the second lens. Since both lenses have the same focal length the final image will be the same size as the original.