Answer
12 cm
Work Step by Step
From the given formula, we have $F=4.8$ and $y=x-4$.
To find how far the object from the lens, solve for $x$:
$\frac{1}{4.8}=\frac{1}{x}+\frac{1}{x-4}$ (Multiply by $48x(x-4)$)
$10x(x-4)=48(x-4)+48x$
$10x^2-40x=48x-192+48x$
$10x^2-40x-48x-48x+192=0$
$10x^2-136x+192=0$ (Factorize)
$(5x-8)(2x-24)=0$
$x=\frac{8}{5}$ or $x=12$
If $x=\frac{8}{5}$, then $y=\frac{8}{5}-4<0$ (impossible).
So, the solution is $x=12$.
Therefore, the distance of the object from the lens is $12$ cm.
