Chapter 29, Problem 53A

Stand in front of a mirror and put two pieces of tape on the glass: one piece where you see the top of your head, and the other where you see the bottom of your feet. Compare the distance between the pieces of tape with your height. If a full-length mirror is not handy, use a smaller mirror and find the minimum length of mirror to see your face. Mark where you see the top of your head and the bottom of your chin. Then compare the distance between the marks with the length of your face. What must be the minimum length of a plane mirror in order for you to see a full view of yourself?

To determine

To Find: The length of a mirror that must be used to see a full image of a person. 

Explanation of Solution

Introduction:

Ray diagrams are used to determine the portion of a plane mirror required to see a full image of the object/person.

Explanation: 

The ray diagram shows the lines of sight and the full path of light. To view a person's image, the person must look as low as a low point (feet) and as high as a high point (tip of his head).

To view a full image of a person standing in front of a plane mirror, the person needs a mirror that is equal to one-half of the person’s total height. Example, A $6-foot$ tall man will need a $3-foot$ long mirror in order to view his full image.

Conclusion: 

Simply, the ratio of the mirror and a man should be $1:2$ .