Question

The graph correctly representing the variation of image distance ’v’ for a convex lens of focal length ’f’ versus object distance ’u’ is ______.
Fill in the blank with the correct answer from the options given below

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is C

The relationship between the object distance (u), image distance (v), and the focal length (f) for a convex lens is given by the lens formula: \(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\). This can be rearranged to get a relationship between v and u:

\(v = \frac{uf}{u - f}\)

Analyzing this equation:

• For u > f (object beyond the focal point), v is positive, indicating a real image on the opposite side of the lens.
• For u = f, v → ∞, suggesting the rays are parallel and do not meet on the image side, forming an image at infinity.
• For u < f (object inside the focal point), v is negative, indicating a virtual image on the same side as the object.

A convex lens graph of v versus u reflects these relationships. The correct option is the one showing the behavior described, characterized by a curve approaching infinity when u equals f and v becoming negative as u decreases below f. Thus, the correct graph is Graph (III).