In an optics ecperiment, 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 image distance `v` from the lens, is plotted using the same scale for the two axes. A straight line passing through origin and making an angle of `45^(@)` with the x-axis meets the experiment curve at `P`. The coordinate of `P` will be

Options

A. `((f)/(2), (f)/(2))`
B. `(f, f)`
C. `(4 f, 4 f)`
D. `(- 2 f, 2 f)`

Answer

D

Explanation

For a convex lens, plot of `v` versus `u` is as shown in Fig.

Let the co-ordinate of `P` be `(x, x)`
`:. U = - x, v = x`
From `(1)/(v) - (1)/(u) = (1)/(f)`
`(1)/(x) - (1)/(- x) = (1)/(f) or (2)/(x) = (1)/(f), x = 2 f`.
`:.` Co-ordinates of `P` are `(-2 f, 2 f)`