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# The time in a clock is $8:40:10$ . The time in the image of the clock formed by a plane mirror is (A) $8:40:10$ (B) $8:50:30$ (C) $3:19:50$ (D) none of these

Last updated date: 20th Jun 2024
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Hint: When we view a clock through a plane mirror, the time seen by us is different than the actual time. This happens because of the property of plane mirrors to interchange the left and the right sides of an object so that the image observed seems inverted. This property of plane mirrors is known as lateral inversion.

To find the time in the image of the clock, consider the vertical line passing through the numbers $6$ and $12$ as the axis about which the needles of the clock are to rotate. The hour hand is at $8$ which is two places to the left of the axis. When we take the image, we’ll invert the hour hand to two places to the right of the axis. This means that the hour hand in the image will be at $4$ . Moving ahead, the minute hand in the clock shows $40$ which means it is again at $8$ , the image of the minute hand will hence be at $4$ which means that it’ll mean $20$ .
But the hour hand will move a bit further away from $8$ in the forty minutes that the minute hand takes, hence it will be between the $8th$ and the $9th$ marking on the clock. This means the image’s hour hand should be between $3$ and $4$ , not exactly at $4$.
Similarly, the second-hand shows $10$ which means it is at $2$ , two places to the right of the. When the image is taken, the second hand will be at $10$ which means it’ll show us that it’s $50$ seconds.
Now, putting together our entire analysis, we can say that the time shown in the image of the clock will be $3:19:50$ (since the hour hand in the image is a bit before $3$ and the minute hand is a bit before $4$ )
Note: We can also solve this question using simple subtraction. In the case of a mirror, the sum of the time shown by the object and that shown by the image should be $12$ hours. Breaking it into minutes and seconds as well, we get $11:59:59$ since one hour has sixty minutes and one minute has sixty seconds. If we subtract the actual time in the clock from the above number, we’ll get the same answer.