Answer to Question #227615 in Optics for Silax

Question

Use the law of reflection to determine the minimum height and position of a plane mirror that just allows a 5'6" woman standing on the floor in front of the mirror to Sense both her head and Feet in the mirror

Answer 1

$\text{Let AB segment denoting the position of a woman.}$

$AB = 5'6''$

$A(0,5'6'') \text{ -point head position}$

$B(0,0)\text{- point leg position}$

$E(0,E_y)\text{-point eye position}$

$CD\text{ segment indicating the position of the mirror}$

$\text {Let's draw the bisector }CT \vartriangle ACE$

$СT \text{ is also the height of the triangle, therefore}$

$C_y = A_y-\frac{AE}{2}$

$\text {Let's draw the bisector }DL \vartriangle BDE$

$DL \text{ is also the height of the triangle, therefore}$

$D_y = \frac{BE}{2}$

$\text{The maximum possible eye point is point } A$

$\text{then}$

$C_y = A_y=5'6''$

$D_y = \frac{AB}{2}= 2''9'$

$CD = 2''9'$

$\text{Answer: mirror length -}2''9'$

$\text{mirror height above floor level - }2''9'$