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  4. 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. A man walks in front of the mirror along a line parallel to the mirror at a distance 2 L from it as shown. The greatest distance over which he can see the image of the light source in the mirror is

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Q. 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. A man walks in front of the mirror along a line parallel to the mirror at a distance $2\,L$ from it as shown. The greatest distance over which he can see the image of the light source in the mirror isPhysics Question Image

Ray Optics and Optical Instruments

Solution:

According to the following ray diagram $H I=A B=d$
image
and $D S=C D=\frac{d}{2}$
$A H=2 A D$
$ \Rightarrow G H=2 C D=\frac{2 d}{2}=d$
Similarly $I J=d$ so $G J=G H+H I+I J$
$=d+d+d=3 d$