Two
thin lenses of focal length
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Solution: Click For PDF Version Let us consider a beam of light parallel to the common axis of the two lenses, which is incident from the left on the lens of focal length .
The first lens of focal length
will form a real image at its focal point, which is at a distance
to the right of it. But to the second lens the rays will appear to
come from a virtual object, as rays bent by the first lens enter it
as though they are converging to a point to the right of the lens.
Therefore, the object distance
for the second lens will be
 .
It will form an image at a distance
from it. We find
using the thin lens formula. We have
The image
distance is positive. Therefore, the final image is real. As an
incident parallel beam is focussed by the two lens combination at a
distance
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are in contact. We have to show that they are equivalent to a single
thin lens with a focal length given by
from
them, the two thin lenses in contact with each other are equivalent
to a thin lens of focal length