In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and the image distance $v$, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of $45^{\circ}$ with the $x$-axis meets the experimental curve at $P$. The coordinates of $P$ will be

Question

( A ) $(\frac{f}{2}, \frac{f}{2} )$
( B ) $(4f, 4f)$
( C ) $(2f, 2f)$
( D ) $(f, f)$