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

• Correct answer
  A

  $(2 f, 2 f)$
• B

  $\left(\frac{f}{2}, \frac{f}{2}\right)$
• C

  $(f, f)$
• D

  $(4 f, 4 f)$

Solution

It is possible when object kept at centre of curvature. $$ \begin{aligned} & u=v \\ & u=2 f, v=2 f . \end{aligned} $$

Hence, the correct answer is option: 'A'.