Question

at what distance should an object be placed from a convex lens of focal length 18cm to obtain an image at 24cm from it on the other side.

Answer 1

V=+24
F=+18
1/f=1/v-1/u
-1/u=1/f+1/v
-1/u=1/18+1/24
-1/u=4+3/72
-1/u=1/72
-u=72
u=-72
Hope it is helpful for u

Answer 2

Given:

$\sf{f=18cm}$

$\sf{v=24cm}$

$\sf{Lens=Convex \:Lens}$

Solution:

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

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

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

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

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

$\sf{u=-72cm}$

$\bold{Magnification:}$

$\sf{Magnification=}{\dfrac{+24}{-72}}$

$\sf{Magnification=-}{\dfrac{1}{3}}$

Thus, the image formed will be real and inverted, and would be of $\sf{\dfrac{1}{3}}$ times the size of object.

The image formed will be smaller than the height of object.