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  • Size of image of an object by a mirror having a focal length of 20 cm is observed to be reduced to 1/3rd of its size. At what distance the object has been placed from the mirror? What is the nature of the image and the mirror?

Size of image of an object by a mirror having a focal length of 20 cm is observed to be reduced to 1/3rd of its size. At what distance the object has been placed from the mirror? What is the nature of the image and the mirror?

 

Answers (1)

Using,

 m = - v/u = h?/h?

⇒ - v/u = 1/3 h?/h?

⇒ u = - 3v

Using mirror formula,

1/v + 1/u = 1/f, we get

when f = + 20 cm

⇒ 1/v - 1/3v = 1/20

⇒ 3 - 1/3v = 1/20

⇒ 2/3v = 1/20

⇒ 3v = 2 × 20

⇒ v = 2 × 30/3

⇒ v = 40/3 .. (i)

u = - 3v

By putting v value, we get

⇒ u = - 3 × 40/3

⇒ u = - 40 cm.

Object Distance = - 40 cm

If we take f = - 20 cm, value of u will be + 40 cm which is not possible.

m = - v/v

⇒ m = - 40/3/- 40

⇒ m = + 1/3

⇒ m = 0.33 cm

This implies that the nature of the image is erect and diminished.

Nature of Image = Convex Mirror.

Posted by

infoexpert23

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