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 adjustment 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 axes. A straight line passing through origin and making an angle of `45^@` with the x-axis meets the experimental 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, 2f)`

Answer

D

Explanation

For a convex lens, plot of `v` versus `u` is as shown in Fig.
Let the co-ordinates of `P br (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 = 2f`
`:.` Co-ordinates of `P` are `(-2f, 2f)`.
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