Question

Let \( u \) and \( v \) be the distances of the object and the image from a lens of focal length \( f \). The correct graphical representation of \( u \) and \( v \) for a convex lens when \( |u|>f \), is:

• A.
• B.
• C.
• D.

Hint:

When plotting the image distance \( v \) versus object distance \( u \) for a convex lens, recall that the lens formula \( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \) gives a hyperbolic relationship when \( |u|>f \).

Answer 1

The Correct Option is B

When \( |u|>f \), the image formed by a convex lens is real, inverted, and reduced. The relationship between \( u \) and \( v \) follows from the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] This produces a curve where \( v \) decreases as \( u \) increases. The correct graph shows this relationship as a hyperbolic curve, which is option (2). Thus, the correct answer is option (2).