Hanging a Mirror: Find Optimal Size for Dressing Room

[sarahefried]

Homework Statement

You are preparing to go shopping for a plane mirror that will be hung on the wall of your dressing room. Your overall height is H = 2.4 m, and the vertical distance from the floor to the mid-line of your eyes is H1 = 2.23 m. You want the mirror to be tall enough to allow you to view your entire body from the tip of your head to the soles of your feet, while standing a horizontal distance D = 1.1 m from the mirror. Being frugal, you want to purchase the smallest possible mirror.

Homework Equations

There is only one such ray that obeys the law of reflection: angle of incidence equals angle of reflection: θi = θr

The Attempt at a Solution

I have absolutely no clue where to start!

 

[tiny-tim]

Welcome to PF!

You are preparing to go shopping for a plane mirror that will be hung on the wall of your dressing room. Your overall height is H = 2.4 m, and the vertical distance from the floor to the mid-line of your eyes is H1 = 2.23 m. You want the mirror to be tall enough to allow you to view your entire body from the tip of your head to the soles of your feet, while standing a horizontal distance D = 1.1 m from the mirror. Being frugal, you want to purchase the smallest possible mirror.

Welcome to PF!

Hint: draw the image of yourself on the other side of the mirror.

How large does the mirror have to be so that you can see the whole image without moving your head?