A point source of light S, placed at a
distance L in front of the centre of a mirror of width d,
hangs vertically on a wall. A man walks in front of the
mirror along a line parallel to th mirror at a distane
2L form it as shown.The greatest distance over which
he can see the image of the light source in the mirror is
(a) `d//2` (b) d (c) 2d (d) 3 d.

Options

A. `d//2`
B. d
C. 2d
D. 3d

Answer

D

Explanation

For the ray diagram,
In `Delta`ANM and `Delta`ADC,
`angleADC=angleANM=90^(@)` `[MN_|_AD]`
`angleMAN=angleCAN` (law of reflection)
`=DeltaANM` is similar to `DeltaADC`
`:. (x)/(2L)=(d//2)/(L) or x=d`
So, required distance `=d+d+d=3d`.
Therefore, (d) is the correct option.