JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Geometrical Optics

Using the lens formula (real-is-positive sign convention with $u$ negative for a real object):


This is a rectangular hyperbola with asymptotes $u=-f$ and $v=f$. As the object moves further from the lens ($|u|\to \infty$), $v\to f$; as $|u|$ approaches $f$ from beyond it, $v\to \infty$. So for $|u|>f$, the curve is a branch of this hyperbola: $v$ is large when $|u|$ is just greater than $f$, and $v$ decreases smoothly toward the asymptote $v=f$ as $|u|$ increases — the branch lying between the two asymptotes.