Physics: Why does a certain lens not project a image onto paper when light passes through it?

Question

In physics lab we were calculating the focal lengths of lenses and mirrors but one lens didn't project an image unless it was put with another lens that did... why didn't the lens project an image by itself? I know it has something to do with light

Answer 1

if the first lens is cut to disperse light, no image can be projected.  however, when the first lens is connected to a second focusing lens, an image can be produced.  consider where the focal point of the first lens alone is located relative to the combined focal point of the two lenses together.

Answer 2

if the lens is a diverging lens, then no image can be formed.

if the lens is a converging one, then the object must be more than one focal length away from the lens.

As long as the object is less than one focal length, the image will be virtual, so nothing can be seen on the screen.

More than one focal length, real and inverted images will be seen as they are projected onto the screen. The only thing that changes is the image size.  

Answer 3

The lens was probably concave, so it formed virtual images rather than real images like a convex lens would do.