Question

The size of image of an object by a convex lens of focal length 20cm is observed to be reduced to one third of its size find the distance of the object from the optical centre of the length.

Answer 1

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Answer 2

The object is placed at a distance of 80 cm from the lens.

Explanation:

Given that,

Focal length of the convex lens, f = +20 cm

It is observed that size of image is to be reduced to one third of its size, $m=-\dfrac{1}{3}$ (negative as image is reduced)

The magnification of the lens is given by :

$m=\dfrac{v}{u}$

$\dfrac{1}{3}=\dfrac{v}{u}$

$u=-3v$.......(1)

Using lens formula as :

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

$\dfrac{1}{v}=\dfrac{1}{20}+\dfrac{1}{(-3v)}$

v = 26.67 cm

So, $u=-3\times 26.67=80\ cm$

So, the object is placed at a distance of 80 cm from the lens. Hence, this is the required solution.

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Lens formula

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