Question

Two mirrors $AB$ and $CD$ are arranged along two parallel lines. The maximum number of images of objects that can be seen by any observer $O$ is:

a. One
b. Two
c. Four
d. Infinite

Answer 1

Hint: We know that when the angle between the mirror decreases the number of images formed by the plane mirror increases. When two mirrors are parallel to each other, the angle is zero, and hence a maximum number of images is formed.

Complete step by step answer:
From the diagram, we know that the mirror $AB$ and $CD$ are parallel to each other.
We know that multiple images can be formed by using more than one plane mirror and keeping them at a certain angle.
As the angle between the two mirrors increases the number of images formed by the mirror increases.
Similarly, to decrease the number of images formed, the angle between the mirrors must be increased.
The number of images formed by the combination of two plane mirrors is given by the formula:
$n = \dfrac{{{{360}^ \circ }}}{\theta } - 1$
$n$ is the number of images formed
$\theta$ is the angle between the mirrors
Now, we know the angle between two parallel lines is zero degrees.
Since the mirrors are parallel to each other, the angle between them is ${0^ \circ }$
Putting the values in the formula above:
$n = \dfrac{{{{360}^ \circ }}}{{{0^ \circ }}} - 1$
$\Rightarrow n = \infty - 1$
This gives us $n = \infty$

Hence, the correct answer is option (D).

Note: The nature of the image formed by the plane mirrors is virtual, which means the light rays meet behind the mirror. The image formed is laterally inverted. The size of the image is always the same as the size of the object and always erect. Another point that is to be noted is the refractive index of the plane mirror is infinite.