Answer to Question #76747 in Optics for harsh

Question

What is the min distance between a real object and a real image formed by a convex lens of focal length f?

Answer 1

Let the distance between a real object and a real image formed by a convex lens be d.
Let the distance of the object from the length is x.
The image distance from the lens:
(d-x).
Then,
1/f=1/x+1/((d-x) )
x^2-xd-df=0
x=(d±√(d^2-4fd))/2
For real values of x:
d^2≥4fd
d≥4f.