A point source of light S , placed at a distance 60 cm infront of the centre of a plane mirror of width 50 cm , hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance 1.2 m from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is ____ cm.
Answer: 150
Solution
The image S′ of the source lies 60 cm behind the mirror, on the perpendicular through its centre, so the man's path is 60+120=180 cm from S′. The man sees the image only when the straight line from S′ to his eye crosses the mirror, so the strip of his path from which the image is visible is the mirror outline projected outwards from S′. The triangles with apex at S′ are similar, and the distances from S′ are in the ratio
60180=3
so the visible strip is three times as wide as the mirror:
3×50=150cm
The two extreme points from which the man can see the image are 150 cm apart.
JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Numerical answer
