Chapter 26, Problem 1CQ

Two plane mirrors meet at right angles at the origin, as indicated in Figure 26-54. Suppose an L-shaped object has the position and orientation labeled A. Draw the location and orientation of all the images of object A formed by the two mirrors.

Figure 26-54

To determine

To draw: The location and orientation of all the images of object $\text{A}$ formed by the two mirrors.

Answer to Problem 1CQ

The all images of object $\text{A}$ in different quadrants on the basis of coordinate points is shown below.

Figure (1)

Explanation of Solution

Introduction: The mirror image of the object shows the opposite position with same size and at same distance. This is described by the reflection and total reflection of light.

Explanation:

Formula to calculate the number of images formed when the two mirrors meet at right angle is,

$n=\frac{360°}{\theta }-1$

Here,

$\theta$ is the angle between two mirrors.

$n$ is the number of images formed.

Substitute $90°$ for $\theta$ in above equation to find $n$.

$\begin{array}{c}n=\frac{360°}{90°}-1\\ =3\end{array}$

Thus, three images will form by reflection and the image formed by the plane mirror is of same size and at same distance as object but behind the mirror.

The coordinates of the image $\text{A}$ are $\left(2\text{m},2\text{m}\right)$, $\left(1\text{m},2\text{m}\right)$ and $\left(1\text{m},3\text{m}\right)$.

The coordinates of the image $\text{A}$ in second quadrant are $\left(-2\text{m},2\text{m}\right)$, $\left(-1\text{m},2\text{m}\right)$ and $\left(-1\text{m},3\text{m}\right)$.

The coordinates of the image $\text{A}$ in third quadrant are $\left(-2\text{m},-2\text{m}\right)$, $\left(-1\text{m},-2\text{m}\right)$ and $\left(-1\text{m},-3\text{m}\right)$.

The coordinates of the image $\text{A}$ in fourth quadrant are $\left(2\text{m},-2\text{m}\right)$, $\left(1\text{m},-2\text{m}\right)$ and $\left(1\text{m},-3\text{m}\right)$.

Thus, the all images of object $\text{A}$ in different quadrants on the basis of above coordinate points is shown below.

Figure (1)