Question

The place you get your hair cut has two nearly parallel mirrors 6.50 m apart. As you sit in the chair, your head is 3.00 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?

Answer 1

`k=13\ m`

Step-by-step explanation:

Given:

• distance between two nearly parallel mirrors,
  `d=6.5\ m`

• distance between the face and the nearer mirror,
  `x=3\ m`

• So, the distance between the back-head and the mirror,
  `y=6.5-3=3.5\ m`

From the given information by the laws of reflection we can deduce the distance of the first reflection of the back of the head of person in the rear mirror.

Distance of the first reflection of the back of the head in the rear mirror from the object head:

`y'=2* y`

`y'=7\ m` is the distance of the image from the object back head.

Now the total distance of this image from the front mirror:

`z=y'+x`

`z=7+3`

`z=10\ m`

• Now the second reflection of this image will be 10 meters inside in the front mirror.

So, the total distance of the image of the back of the head in the front mirror from the person will be:

`k=x+z`

`k=3+10`

`k=13\ m`