Answer
$9.24cm$
Work Step by Step
We know that
$\frac{1}{d_{\circ}}+\frac{1}{d_i}=\frac{1}{f}$
$\implies \frac{1}{17.1cm}+\frac{1}{d}=\frac{1}{f}$......eq(1)
In the second case, if the object is moved to distance $12.0cm$ behind the lens, then the image distance is doubled $d_i=2d$
Now $\frac{1}{12.0cm}+\frac{1}{2d}=\frac{1}{f}$......eq(2)
By solving eq(1) and eq(2), we obtain:
$d=20.1176cm$ and $f=9.24cm$
Thus, we conclude that when the object is placed at a distance $9.24cm$ behind a Fresnel lens, then the corresponding image will be formed at infinity.
