Question

how far should an object be placed from the pole of a converging mirror of focal length 20cm to form a real image of the size exactly 1/4th the size of the object?

Answer 1

Answer:begin mathsize 14px style Given : Focal space length comma space straight f equals minus 20 space cm space left parenthesis It space is space concave space mirror right parenthesis Object space distance equals straight u image space distance equals straight v Magnification comma space straight m equals fraction numerator minus straight v over denominator straight u end fraction equals fraction numerator minus 1 over denominator 4 end fraction space left parenthesis space Real space images space are space inverted space right parenthesis therefore comma space straight m equals plus straight v over straight u equals 1 fourth straight v equals straight u over 4 Mirror space formula comma space 1 over straight f equals 1 over straight u plus 1 over straight v fraction numerator 1 over denominator minus 20 end fraction equals 1 over straight u plus 4 over straight u equals 5 over straight u straight u equals minus 100 space cm The space object space should space be space placed space at space straight a space distance space 100 space cm space from space the space pole space of space concave space mirror. end style

Explanation:

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.