Question

The size of image of an object by a convex lens of focal length 20 cm is observed to be reduced to 1/3 of its size. Find the distance of the object from the optical centre of the lens.

Answer 1

Answer:

The distance of the object from the optical center of the lens is 80 cm.

Explanation:

Given that,

Focal length f = 20

The size of the image of an object is reduced to one by third of the size of the object.

Magnification $m = \dfrac{1}{3}$

We know that,

The magnification is

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

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

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

Using lens formula

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

$\dfrac{1}{20}=-\dfrac{3}{u}-\dfrac{1}{u}$

$\dfrac{1}{20}=\dfrac{-4}{u}$

$u =-80\ cm$

Hence, The distance of the object from the optical center of the lens is 80 cm.

Answer 2

To find the distance of the object we need to find the value of v first.

• As we know the magnification formula M= -v/u
• As given the reduces size is M=1/3
• Therefore -v/u=1/3
• 1/v=-3/u
• The lens formula 1/f=1/v-1/u
• Putting the values 1/20=-3/u -1/u
• 1/20= -4/u
• u=-80
• Putting back in magnification formula M=-v/-80=1/3
• M=v=80/3