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:

1. A
   $(2f,2f)$
2. B
   $\left(\frac{f}{2},\frac{f}{2}\right)$
3. C
   $(f,f)$
4. D
   $(4f,4f)$