Question

At what distance should on object be placed from a convex lens of focal length 18 cm to obtain a image of 24 cm from it on the other side what will be magnification produced in this case​

Answer 1

Given :

In convex lens,

Focal length = 18 cm

Image distance = 24 cm

To find :

The position of the object and the Magnification.

Solution :

using lens formula that is,

» The formula which gives the relationship between image distance, object distance and focal length of a lens is known as the lens formula.

The lens formula can be written as :

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

where,

• v denotes image distance
• u denotes object distance
• f denotes focal length

by substituting all the given values in the formula,

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

$\dashrightarrow \sf \dfrac{1}{24} - \dfrac{1}{u}= \dfrac{1}{18}$

$\dashrightarrow \sf - \dfrac{1}{u}= \dfrac{1}{18} - \dfrac{1}{24}$

$\dashrightarrow \sf - \dfrac{1}{u}= \dfrac{4 - 3}{72}$

$\dashrightarrow \sf - \dfrac{1}{u}= \dfrac{1}{72}$

$\dashrightarrow \sf u = - 72 \: cm$

Thus, the object distance is 72 cm.

Magnification of image :

» The Magnification produced by a lens is equal to the ratio of image distance to the object distance .i.e.,

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

$\leadsto\sf m = \dfrac{24}{ - 72}$

$\leadsto\sf m = - 0.3$

Thus, the Magnification of image is 0.3.

Answer 2

Explanation:

By using lens formula 

1/v − 1/u = 1/f

where v=24cm ,f=18cm

1/24−1/u=1/18

from this we get u=−72cm

magnification of lens is m=v/u

m=−24/72=−1/3