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

Question

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 sec.) during which the insect can see the image of the source S in the mirror.

TestHub · Accepted Answer

The image of S is 10 cm behind the mirror.

The insect walks 20 cm in front of the mirror, so the line from the insect to the image crosses the mirror plane at 1/3 of the insect's lateral displacement y.

The image stays visible while this crossing point lies within the 20 cm wide mirror: $∣ y /3∣ \leq 10 \Rightarrow ∣ y ∣ \leq 30 cm$

Total path = 60 cm at 10 cm/s: $t = \frac{60}{10} = 6 s$ .

Answer: 6

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