Chapter 23, Problem 6P

To determine

(a) To determine:

How far away from you are the first three images of yourself in the mirror front of you?

Answer to Problem 6P

Solution:

Explain in explanation.

Explanation of Solution

From given figure, first image $1/u=-1/v$. So $v=u=-1.6\text{m}$. It means that the image is formed 1.6 m behind the mirror therefore, this is a total of 3.2 m away from you. It will be facing you because the image is formed on the mirror in front of you.

From figure, the second image we using the image distance of our first image as our new object distance, however now we are using the second mirror. Therefore, the object distance will be,

$\text{1}.\text{6}+\text{2}.\text{3}=\text{3}.\text{9 m}$

So, v for the second image is – 3.9 m. There, distance of 1.3 m between you and mirror behind you so the image is $\text{3}.\text{9}+\text{ 1}.\text{3}=\text{5}.\text{2 m}$ away. This image is formed on the mirror behind you so it will be facing away.

From figure, the last image will be on the mirror in front of you and will use the image formed 3.9 m behind the mirror behind you as its object, so object distance is $\text{3}.\text{9}+\text{the distance between both mirrors }\left(\text{2}.\text{3 m}\right)=\text{6}.\text{2m}$ So, the image is $\text{6}.\text{2}+\text{1}.\text{6}=\text{7}.\text{8m}$ away from you and is facing you.

To determine

(b)

Are these first three images facing toward you or away from you.

Answer to Problem 6P

Solution:

Explained in part (a)

Explanation of Solution

In part a, First image will be facing you explained.

Second image will be facing away explained.

Last image will be facing you as explained.