Question

An object of height $4cm$ is placed at a distance of $24cm$ in front of the convex lens of focal length $8cm.$ The position and size of the image are respectively:

• A. $12cm\&-2cm$
• B. $-12cm\&2cm$
• C. $12cm\&-3cm$
• D. $2cm\&-2cm$

Answer 1

The correct option is A $12cm\&-2cm$

Given:
Object height, $h_o=4cm$
Object distance, $u=-24cm$
Focal length, $f=8cm$
(Using new cartesian sign convention)

Let the image distance be $v$ and size of the image be $h_i$.

Using lens formula,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\frac{1}{8}=\frac{1}{v}-\frac{1}{-24}$
$v=12cm$

Using Magnification formula,
$m=\frac{h_i}{h_o}=\frac{v}{u}$
$\frac{h_i}{h_o}=\frac{v}{u}$
$\frac{h_i}{4}=\frac{12}{-24}$
$h_i=-2cm$