Question

A point source of light B is placed at a distance L in foirmnt of the centre of mirror of width d hung vertically on a wall . A man walks in fornt of the mirror along a line parellel to 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

• A. $\frac{d}{2}$
• B. $d$
• C. $2d$
• D. $3d$

Answer 1

The correct option is D $3d$

From the figure, it can be seen that the observer can see through distance AC,

where it meets with point B, hence

According to the geometry of the figure

$DE=AD+DB=EC+BE=d$ …… (1)

$AD=EC=DB=BE$ ……. (2)

Hence

$AC=DE+AB+BC$

$AC=d+AD+DB+EC+BE$

From equation (1) and (2)

$AC=d+2\left(AD+EC\right)$

$AC=d+2d$

$\therefore AC=3d$

The greatest distance over which the man can see the image of light source is the mirror is $3d$ .