The focal length of a convex lens is $f$. An object is placed at a distance $x$ from its first focal point.…
The focal length of a convex lens is $f$. An object is placed at a distance $x$ from its first focal point. The ratio of the size of the real image to that of the object is
$\frac{f}{x^2}$
$\frac{x^2}{f}$
$\frac{f}{x}$
$\frac{x}{f}$
Solution
Given that, focal length of convex lens $=f$
Distance of object from lst focus point $=x$
Now, object distance, $u=-(f+x)$
We know that, ratio of size of real image to that of object
= magnification which is given by
$m=\frac{v}{u}=\frac{f}{f+u}$
$\Rightarrow \quad m=\frac{f}{f-(f+x)}=-\frac{f}{x}$
Taking magnitude only, $|m|=\frac{f}{x}$.