d

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 $3d.$