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?
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at middle u should place the object
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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 -
1 / v + 1 / u = 1 / f -------{ii}
from {i} and {ii}
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.
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