Answer
$22 \ cm$
Work Step by Step
Given:
Distance of the slide from the screen d = 44 cm
Focal length of the lens f = 11 cm
Let the distance between the lens and the slide is p
Then, the image distance (q) = d - p
The formula for the lens equation is:
$\frac{1}{f} = \frac{1}{p}+ \frac{1}{q}$
$\frac{1}{f}=\frac{1}{p}+ \frac{1}{(d-p)}$
$\frac{1}{f} = \frac{d}{pd-p^2}$
$pd - p^2 = fd$
$p^2-dp + df = 0$
$p^2-(44cm) p +(44cm)(11cm) = 0$
$p^2-44p+484 = 0$
$p^2-22p-22p+484 = 0$ (by factorization we get)
$p(p-22) - 22p( p-22) = 0$
$p= 22 \ cm$
Therefore, the lens must be placed at a distance of 22 cm from the slide.
