We have to show that the distance between a real object and its real image formed by a thin converging lens is always greater than or equal to four times the focal length of the lens.
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Solution: Click For PDF Version As we are considering a real object and its real image formed by a thin converging lens, in the sign conventions that we are using the object distance o, and the image distance
will be real and positive numbers. The focal length f
of a converging lens is also a real positive number. Let us call the
distance between the object and its real image d.
We have
We consider the thin lens equation
The roots of this quadratic equation are
As the image is real, the roots have to be real and positive. This imposes the condition that
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