A point source of light B is placed at a distance L in front of the centre of a mirror of width d hung vertically on a wall. Aman walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown. The greatest distance over which he can see the image of the light source in the mirror is

3d

As the person moves up at some he receives the light ray which is reflected from the mirror this is the starting point at which he receives and  as when moves on at some point he just receives the light ray that is the endpoint and this area is field of view for the person

From the figure triangle ABG and ADF are similar.

$\Rightarrow \frac{AG}{AF} = \frac{BG}{DF}$

$\Rightarrow \frac{L}{3L} = \frac{d/2}{DF}$

$\Rightarrow DF = \frac{3d}{2}$

Hence a total distance of 3d.