Question

How far should an object be placed from the pole of converting mirror of focal length of 20cm to from a real image of the size exactly 1/4th the size of the object.

Answer 1

Here is the answer. Hope it helps.

Answer 2

Answer:

   u = -100cm

Explanation:

focal length (f) = -20cm

Magnification (M) = 1 / 4

image distance (v) = v

object distance (u) = u

M = -v / u

Here magnification is negative because it forms a real image

This is because virtual image formed by concave mirror is enlarged whereas according to the question the image is diminished and hence it forms a real image

-(1 / 4) = -v / u

1 / 4 = v / u

u = 4v -------{i}

1 / v + 1 / u = 1 / f

1 / v + 1 / 4v = - 1 / 20

4 / 4v + 1 / 4v = -1 / 20

5 / 4v = -1 / 20

4v = -100

v = -25cm

u = 4v = -100cm

∴ The object should be placed 100 cm to the left of the mirror.