Chapter 23, Problem 4P

To determine

The horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror.

Answer to Problem 4P

Solution:

$x=0.6057=61\text{cm}$

Explanation of Solution

Given info:

A person whose eyes are $H=1.72\text{m}$ above the floor stands $L=2.20\text{m}$ in front of a vertical mirror whose bottom edge is $h=0.38\text{cm}$

Formula used:

From figure,

$\begin{array}{l}\tan \theta =(H-h)/L=h/x\\ or,\\ x=hL/(H-h)\end{array}$

Calculation:

Substituting the given values, we get

$\begin{array}{l}x=(0.38)\times (2.20)/(1.72-0.38)\\ x=0.6057=61\text{cm}\end{array}$