Question

how far should be object be placed from pole of converging mirror of local length 20cm to form a real image of size exactly one - forth the size of the object
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Answer 1

f = -20cm, m = -1/4 (real image)

We know that

m = - (v/u)

-(1/4) = - (v/u)

u = 4v

so

1/v + 1/u = 1/f

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

5/4v = - (1/20)

V = - (100/4) = -25 cm

∴ u = 4v

u = 4 × (-25)

= - 100 cm

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

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.