The Place you get your haircut has two nearly parallel mirrors 5.0m apart. As you sit in the chair, yoru head is 2.0 m from the nearer mirror. Looking toward this mirror, you first see your face and then, farther away, the back of your head. ( The mirrors need to be slightly nonparallel for you to be able to see the back of your head, but you can treat them as parallel in this problem.) How far away does the back of your head appear to be? Neglect the thickness of your head.

Answer 1

To find the distance to the back of your head, we have to consider the reflections of reflections between the two mirrors.

The distance from your head to the farther mirror will be 5 - 2 = 3 meters, since the mirrors are 5 meters apart and your head is 2 meters away from the nearer mirror.

Now, let's consider the reflection of your head from the farther mirror to the nearer mirror. It will seem like there's another head 3 meters behind the farther mirror. So this reflection "head" will appear to be at 3 + 3 = 6 meters away.

Next, let's consider the reflection of the reflected head from the nearer mirror to the farther mirror. This is essentially the image of the back of your head since the head is reflecting on both mirrors. To find the total distance to this reflection, we have to add the distance of the reflection head from the nearer mirror to the distance between the mirrors, which is: 6 + 5 = 11 meters.

So the back of your head appears to be 11 meters away when looking into the mirror.