Question

Suppose you are standing in front of a flat mirror which is mounted to a vertical wall. For this problem you may suppose that your height is 1.70 m and your eyes are 12 cm below the top of your head. What is the smallest mirror that will still allow you to see the full length of your body

Answer 1

The right approach is "0.85 m".

Step-by-step explanation:

According to the question, the diagram will is provided below.

So that as per the diagram,

The values will be:

My height,

AO = 1.70 m

My eyes at,

AB = 12 cm

i.e.,

= 0.12 m

As we can see, the point of incidence lies between the feet as well as the eyes, then

BO = 1.58 m

Now,

⇒
`O'D = (1.58)/(2)`

`=0.79 \ m`

The point of incidence of the ray will be:

⇒
`CO'=1.70-(0.12)/(2)`

`=1.70-0.06`

`=1.64 \ m`

Hence,

The smallest length of the mirror will be:

=
`CO'-O'D`

On substituting the values, we get

=
`1.64-0.79`

=
`0.85 \ m`