Question #227615
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
1
Expert's answer
2021-08-23T12:38:32-0400

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

AB=56AB = 5'6''

A(0,56) -point head positionA(0,5'6'') \text{ -point head position}

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

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

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

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

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

Cy=AyAE2C_y = A_y-\frac{AE}{2}

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

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

Dy=BE2D_y = \frac{BE}{2}

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

then\text{then}

Cy=Ay=56C_y = A_y=5'6''

Dy=AB2=29D_y = \frac{AB}{2}= 2''9'

CD=29CD = 2''9'


Answer: mirror length -29\text{Answer: mirror length -}2''9'

mirror height above floor level - 29\text{mirror height above floor level - }2''9'


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