Question

When two mirrors are parallel to each other why can we see infinity images?

Answer 1

Hint: Use the formula for the number of images formed by the two mirrors placed next to each other at an angle$\theta $. Since the two mirrors are placed parallel to each other, the angle between them is${0^o}$. Any number subtracted from infinity still has the value of infinity.

Formula used:
$N = \dfrac{{{{360}^O}}}{\theta } - 1$

Complete step by step solution:
When we place an object in front of a plane mirror, the virtual image of the object forms behind the mirror at the same distance as the distance of the object from the mirror. The image formed by the plane mirror has the same size as that of the object and it is upright. In case of a single plane mirror, only one image of the object is formed because the rays reflected from the plane mirror never incident on the other mirror which can form another image of that object.
Now, in case of two plane mirrors placed next to each other and the object is placed in between them, the number of images formed is
can be determined by the formula,
$N = \dfrac{{{{360}^O}}}{\theta } - 1$
Here, $\theta $ is the angle between the two mirrors.
Since the two mirrors are facing each other and are placed parallel, the angle between them is
${0^o}$. Therefore, substituting ${0^o}$ in the above equation, we get,
$N = \dfrac{{{{360}^O}}}{\theta } - 1$
\[ \Rightarrow N{\text{ }} = \infty - 1\]
\[\therefore N{\text{ }} = {\text{ }}\infty \]
Thus, we can see an infinite number of images of the object placed between the two parallel mirrors.

Note: An infinite number of images of the object are formed only when the angle between two mirrors in $0$ degrees. If the angle is other than 0 degrees, the number images are finite. We can see from the above equation, the number of images formed decreases when the angle between two mirrors increases.