Eduprobe
Question:
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 45o with the x-axis meets the experimental curve at P. The coordinates of P will be?
(f/2, f/2)
(2f, 2f)
(f, f)
(4f, 4f).
Solution:
The mentioned straight line is the line x = y
On this line u = v
Following sign convention, u = -u, v = v = u
Substituting this into the lens equation, we get
1/u - -1/u = 1/f
Solving this, we get u = v = 2f
Therefore the point is (2f, 2f)