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 plitted using the same scale for the two axes. A straight line passing through the origin and making an angle of `45^circ` with x-axis meets the experimental curve at P. The coordinates of P will be.

Options

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

Answer

B

Explanation

`v=u` and `(1)/(v)+(1)/(u)=(1)/(f)`
`(2)/(v)=(1)/(f)`
`rArr v=2f, u=2f`