Final answer:
The myopic dancer will be able to see the last dancer in the mirror clearly when the line is 3.7 meters away from the mirror, taking into account that the dancer's clear vision distance is 6 meters and the line of dancers is 2.3 meters long.
Step-by-step explanation:
The question involves a myopic (nearsighted) dancer approaching a mirror. Myopia is a condition where a person sees near objects clearly but cannot focus properly on distant objects.
In this scenario, the dancer can see clearly only up to 6 meters. As the dancer approaches the mirror, the image of the last dancer in line will also approach him from the opposite side due to the reflection.
Since a flat mirror creates an image at the same distance behind it as the object is in front, the dancer will begin to see the last dancer clearly when the line of dancers is at a distance where the image of the last dancer falls within his clear vision range.
Let's denote the distance from the first dancer to the mirror as x. Once the image of the last dancer is within 6 meters of the first dancer (the myopic dancer's clear vision range), the first dancer will be able to see it clearly.
Given that the line of dancers is 2.3 meters long, the distance from the first dancer to the mirror (x) plus the length of the line (2.3 meters) should be equal to the myopic dancer's maximum clear vision distance (6 meters).
We can express this as the equation x + 2.3 m = 6 m, solving for x gives us x = 6 m - 2.3 m = 3.7 m. Therefore, the first dancer will be able to see the last dancer clearly when they are 3.7 meters away from the mirror.