A student measures the focal length of convex lens by putting an object pin at a distance 'u' from the lens and measuring the distance ' v ' of the image pin. The graph between ' u ' and ' v ' plotted by the student should look like
(A)(see structure)
(B)(see structure)
(C)(see structure)✓ Correct
(D)(see structure)
Answer: (C)
Solution
For a convex lens the thin-lens relation v1−u1=f1 links object and image distances. With the real-is-positive convention for a real object and its real image it rearranges to v=u−fuf, a rectangular hyperbola: as u approaches f the image distance runs off to infinity, and as u grows large v settles towards f. The curve has asymptotes u=f and v=f and is symmetric about u=v, where object and image are equidistant at 2f. The graph showing this hyperbolic fall from large v towards v=f is the correct one.
JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option