Question

when an object is at distance of u1 and u2 from the pole of a concave mirror, images of the same size are formed. find the focal length of the mirror​

Answer 1

Answer:

Let us say it is a convex lens of focal length f. It can form both real and virtual images.

1/v1 - 1/u = 1/f,      here v & f are positive and u is negative.

1/v1 + 1/u1 = 1/f   --- (1)

=> u1/v1 + 1 = u1/f   -- (2)

The virtual image is formed in front of the lens. So v and u1 are negative.

- 1/v2 + 1/u2 = 1/f    --- (3)

- u2/v2 + 1 = u2/f      --(4)

Magnification = v1/u1 = v2/u2   ---(5)

Add (2) and (4) and use (5) to get:    2 = u1/f + u2/f

  => f = (u1 + u2)/2

Answer 2

Answer:

When an object is placed at a distance of 2F from the pole of the concave mirror, an inverted image of same size is formed at 2F. Therefore, u

u1 =u2.