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A converging lens forms a three-times magnified image of an object, which can be taken on a screen. If the focal length of the lens is 30 cm, then the distance of the object from the lens is

  1. –55 cm
  2. –50 cm
  3. –45 cm
  4. –40 cm

Refraction Lens

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Answer

–40 cm

Reason — Given, convex lens as converging lens

f = 30 cm

From formula,

m = vu\dfrac{\text{v}}{\text{u}}

-3 = vu\dfrac{\text{v}}{\text{u}} [-ve sign as real and inverted image is formed.]

v = -3u

Using formula,

1f\dfrac{1}{\text{f}} = 1v\dfrac{1}{\text{v}} - 1u\dfrac{1}{\text{u}}

We get,

130\dfrac{1}{\text{30}} = 1-3u\dfrac{1}{\text{-3u}} - 1u\dfrac{1}{\text{u}}

130\dfrac{1}{\text{30}} = −1−33u\dfrac{-1-3}{\text{3u}} = −43u\dfrac{-4}{\text{3u}}

3u = -4 x 30

u = −1203\dfrac{-120}{3} = -40 cm

Hence, distance of the object from the lens = -40 cm.

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