A point source of light B is placed at a distance L in front of the center 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 2L from it, as shown in Fig . Find the greated distance over which he can see the image of the light source form the mirror.

Explanation

Draw the rays BM and BN incident on the mirror edges, and draw the reflected rays (see Fig. ). From the figure, it is clear that the man can observe in the angular region `P^(')B^(')Q^(')`. The observer can see through the distance `P^(')Q^(')`, where reflected ray from B can meet the line.
From geometry,`CD=d=C^(')D^(')`
`BD=DP=d//2,CB=QC=d//2`
`P^(')Q^(')=C^(')D^(')+P^(')D^(')+Q^(')C^(')`
`rArr (ND)/(DP)=(ND^('))/(D^(')P^('))=(L)/(d//2)=(2L)/(D^(')P^('))rarr D^(')P^(')=d`
Similarly, `Q^(')C^(')`=d
Hence, distance through which the man can observe the image
=`Q^(')C^(')+C^(')D^(')+D^(')P^(')=d+d+d=3d`