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 lens formula relating object distance (u), image distance (v), and focal length (f) for a convex lens is: \(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\). This can be rewritten to express v in terms of u and f:

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

The behavior of v is as follows:

• When u>f (object beyond focal point), v is positive, signifying a real image on the opposite side.
• When u = f, v approaches infinity, meaning parallel rays form an image at infinity.
• When u<f (object within focal point), v is negative, indicating a virtual image on the same side as the object.

A graph of v versus u for a convex lens illustrates these principles. The accurate graph displays this behavior, specifically showing v approaching infinity as u equals f and v becoming negative when u is less than f. Therefore, Graph (III) is the correct representation.