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A point source of light $S$ is placed at a distance 10 cm in front of the centre of a mirror of width 20 cm suspended vertically on a wall. An insect walks with a speed 10 cm/s in front of the mirror along a line parallel to the mirror at a distance 20 cm from it as shown in figure. Find the maximum time (in s) during which the insect can see the image of the source $S$ in the mirror.

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answer is 6.

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Detailed Solution

Insect can see the image of source $S$ in the mirror, so far as it remains in field of view of image overlapping with the road.

Shaded portion is the field of view, which overlaps with the road up to length $P Q$ .

By geometry we can see that, $P Q = 3 A B = 60 c m$

$∴ t = \frac{Distance}{Speed} = \frac{60}{10} = 6 s$

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