Question:
A point source of light S, placed at a distance 60cm in front of the centre of a plane mirror of width 50 cm, hangs vertically on a wall. A man walks in front 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.
A point source of light S, placed at a distance 60cm in front of the centre of a plane mirror of width 50 cm, hangs vertically on a wall. A man walks in front 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.
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The image of S is 60 cm behind the mirror. The man sees it only along lines from the image passing through the mirror; use similar triangles.
Updated On: Nov 4, 2026
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Correct Answer: 150
Solution and Explanation
The image of S is formed 60 cm behind the mirror (on the axis through the centre).
The man can see the image only if the line from the image to his eye passes through the mirror, i.e. within the angle subtended by the mirror edges at the image.
Distance of the image from the mirror = 60 cm; distance of the image from the man's line = \(60 + 120 = 180\ \mathrm{cm}\).
The mirror half-width is 25 cm at 60 cm from the image. By similar triangles, half-width at 180 cm: \(\frac{25}{60}\times 180 = 75\ \mathrm{cm}\).
Total distance between extreme points \(= 2\times 75 = 150\ \mathrm{cm}\).
Answer: 150
The man can see the image only if the line from the image to his eye passes through the mirror, i.e. within the angle subtended by the mirror edges at the image.
Distance of the image from the mirror = 60 cm; distance of the image from the man's line = \(60 + 120 = 180\ \mathrm{cm}\).
The mirror half-width is 25 cm at 60 cm from the image. By similar triangles, half-width at 180 cm: \(\frac{25}{60}\times 180 = 75\ \mathrm{cm}\).
Total distance between extreme points \(= 2\times 75 = 150\ \mathrm{cm}\).
Answer: 150
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