To find the focal length of a convex lens, a student performs an experiment by putting an object (pin) at distance 'u' from the lens and measures the distance 'v' of the image (pin) from the lens and plots u-v graph. Choose the correct u-v graph from the following:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4)
The object and image distances of a lens are related by the lens formula, used with the Cartesian sign convention (distances measured from the lens, positive in the direction of the incident light).
\( \displaystyle \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \)
In this experiment the object is real, so \( u \) is negative; the image of a convex lens seen on the other side is real, so \( v \) is positive. The points therefore lie in the quadrant where \( u \lt 0 \) and \( v \gt 0 \).
The shape follows from the formula:
\( \text{as } |u| \to f, \; v \to \infty \)
\( \text{as } |u| \to \infty, \; v \to f \)
So \( v \) falls steadily as the object is moved away, and the graph is a curve (a rectangular hyperbola), not a straight line. This is the graph in Option (4).