Physics Question from JEE Main 2024 · 30 January, Shift 2

In an experiment to measure the focal length $f$ of a convex lens, the magnitude of object distance $x$ and image distance $y$ are measured with reference to the focal point of the lens. The $y$-$x$ plot is a smooth decreasing curve drawn on axes graduated in $\text{cm}$, both marked at $10$, $20$, $30$ and $40$. The curve carries five circled readings labelled $A$, $B$, $C$, $D$ and $E$ in order of increasing $x$, and a straight line is also drawn across the plot touching the curve at the circled point $C$. Dashed guide lines take $C$ to the axes at $x = 20 \, \text{cm}$ and $y = 20 \, \text{cm}$; two further pairs of dashed guide lines mark the points $(x = 10 \, \text{cm},\, y = 30 \, \text{cm})$ and $(x = 30 \, \text{cm},\, y = 10 \, \text{cm})$ on that straight line. The focal length of the lens is: