To determine the actual time displayed by a clock observed in a mirror, one must understand the principles of mirror images. A mirror image of a clock hand is horizontally reversed across the vertical axis, effectively positioning it symmetrically on the clock face.
The following method can be used to find the actual time from a mirror image:
- Consider a clock at 12:00. The mirror image of 6:00 places each number diametrically opposite its real position.
- For a mirror image time of 6:45 (quarter to seven), we must find its corresponding actual time.
- Calculate the reflected hour: 12 - 6 = 6. (Note: The hour hand’s reflection is straightforward as it directly opposes once AM/PM is established). This is because 6 serves as a central pivot, and the reflection is across this even number marker.
- Subtract the minutes from 60 to account for the horizontal reflection: 60 - 45 = 15. This corrects for the minute hand's swap across the clock's horizontal midline.
- Based on these calculations, the actual time is 5:15.
Therefore, the actual time shown by the clock is 5:15.