Chapter 14.2, Problem 3E

To determine

To calculate: how high the person can see on a wall 2 m behind point A .

Answer to Problem 3E

Theperson can see 2.7 m high on a wall 2 meter behind him.

Explanation of Solution

Given information:

The eye of the person is at point A , 150 cm above the floor.

The wall is 2 m behind the person.

The mirror extends 30 cm above eye level.

The person faces mirror at a distance of 1 m.

Calculation :

Angle made by the ray connecting mirror and eye with horizontal

$\begin{array}{l}\tan \theta =\frac{\frac{30}{100}}{1}\\ =16.7°\end{array}$

Thus angle made by theray connecting mirror and eye with the normal of the mirror is also $16.7°$ (alternate interior angles between parallel lines are equal).

According to the law reflection the reflected ray will also make same angle with the normal of the mirror.

Therefore, angle of reflection is $16.7°$ .

Consider the height of wall above mirror level which the person can see be x m.

$\begin{array}{l}\tan 16.7°=\frac{x}{3}\\ 0.3=\frac{x}{3}\\ x=.9\left[\text{multiply each side by 3}\right]\end{array}$

The height of wall from floor level which the person can see is

$\frac{150}{100}+\frac{30}{100}+0.9=2.7$

Therefore the person can see 2.7 m high on a wall 2 meter behind him.