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:

The correct answer is Option (4).

for convex lens,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ [Len's formula]

where,

f = focal length

v = distance of image from lens.

u = distance of object from lens.

$\frac{1}{v}=\frac{1}{f}+\frac{1}{u}$

$v=\frac{fu}{u+f}$

∴ The nature of the graph is hyperbolic.