91Ó°ÊÓ

The focal length is the distance between the convex or concave mirror and the focal point of the mirror.

The relation between the distance of object s , the distance of the image $s\text{'}$and the focal length $f$is

$\frac{1}{f}=\frac{1}{s}+\frac{1}{s\text{'}}$

By the relation between the distance of object s , the distance of the image$s\text{'}$ and the focal length $f$

The distance of image written as:

$s\text{'}=\frac{sf}{s-f}$

The distance between the object and image is

$$\begin{gathered} D=s\text{'}+s \\ =\frac{sf}{s-f}+s \\ =\frac{s^2}{s-f} \end{gathered}$$

The minimum distance between the object and image is change in distance with distance of object is zero.

Now, the distance of image is:

$$\begin{gathered} \frac{1}{2f}+\frac{1}{s\text{'}}=\frac{1}{f} \\ s\text{'}=2f \\ ∴D_{min}=4f \end{gathered}$$

Hence, for a lens with focal length $f$the smallest distance possible between the object and its real image is $4f$.

The expression of distance between the object and image is $D=\frac{s^2}{s-f}$.

The graph between the minimum distance and distance of object is:

Hence, the graph of distance between the object and image is drawn above.