A man is 6 feet tall and wishes to have a "full length mirror" in his house, meaning a mirror that lets him see himself from top to bottom. He goes to the hardware store to get a piece of flat (plane) mirror that is just barely long enough to work. How long is the mirror that he buys?
half as tall as he is. Look at ray from head to bottom of mirror to feet.
ou can best find this answer with a newspaper and roll of tape on a full length mirror in your home. Cover all the parts of the mirror you DON'T need to see your reflection. You will see that you only need a mirror length of about 1/2 your height.
This is due to the principle of reflection, which states that the angle of incidence equals the angle of reflection. A light ray from your foot strikes the mirror like a ball off a wall. Thus, by striking the mirror half way between your foot and eye, the ray never interacts with that part of the mirror below the half way mark. Since that half way point doesn't change as you move away from the mirror, the useful area of the mirror remains the same, regardless your distance from it.
Another way of looking at this is to imagine your image is another person standing on the other side of a window and the same distance away from it. To see their feet, the bottom of the window need not be to the floor but only along a line connecting your eye with their feet. A full length mirror need not be a doorway, only a window.
To determine the length of the mirror that the man needs to buy, we need to consider that a person's height is typically measured from the base of their feet to the top of their head. In this case, the man is 6 feet tall.
Since the man wants a mirror that allows him to see his full height, the mirror's length should be at least equal to his height of 6 feet. However, this measurement is taken along the vertical axis, while the length of a mirror is typically measured along the horizontal axis.
To visualize this, imagine the man standing upright in front of the mirror. The mirror needs to be tall enough to reflect his entire height, so the vertical dimension should be 6 feet. However, the actual length of the mirror needed (as measured along the horizontal axis) will be slightly greater than 6 feet.
It's common practice for mirrors to have a standard aspect ratio of approximately 2:3, meaning that the vertical height is two-thirds of the horizontal length. Using this ratio, we can calculate the approximate length of the mirror:
Length of mirror = (Height of man) / (2/3) = 6 feet / (2/3) = 9 feet
Therefore, the man needs to buy a mirror that is approximately 9 feet long in order to see his full height.