Question

Two plane mirrors are parallel to each other and an object \[O\] is placed between them. Then the distance of the first three images from the mirror \[{M_2}\]​ will be (in cm):

A. \[\;5,{\text{ }}10{\text{ }},15\]
B. \[\;\;5,{\text{ }}15,{\text{ }}30\]
C. \[5,{\text{ }}25,{\text{ }}35\]
D. \[5,{\text{ }}15,{\text{ }}25\]

Answer 1

Hint: Two mirrors are placed parallel to each other and an object is kept between them at some distance to both the mirrors. Image development in mirrors takes place by reflection and it abides by the laws of reflection. When two mirrors are placed at some angle to each other, several images are formed by each mirror.

Complete step by step solution:
Given two mirrors are kept parallel to each other and an object is kept between them. The number of images created when two mirrors are placed parallel to each other is given as shown in the ray diagram below

$n = \dfrac{{360}}{\theta }$
Here, $n$is the number of images formed
$\theta $ is the angle between the mirrors

Substituting for the above condition,
$n = \dfrac{{360}}{0} = \infty $
An infinite number of images are formed.
The object is at distance $5cm$ from the mirror \[2\], then its distance from the mirror $1$ will be-
$15 - 5 = 10cm$
As given in the ray diagram above, we identify that the distance of the image formed by a plane mirror is equal to the distance of the object from the mirror.
The first image in the mirror \[2\] will be at distance $\dfrac{L}{3} = \dfrac{{15}}{3} = 5cm$,
the second image will be a reflection of the image in the mirror \[1\],
that is, at $\dfrac{{2 \times L}}{3} = \dfrac{{2 \times 15}}{3} = 10cm$ behind the mirror \[1\]
and, the third image will be at a distance of $\dfrac{{4 \times L}}{3} = \dfrac{{4 \times 15}}{3} = 20cm$ behind the mirror \[1\].
Therefore the distances from the mirror \[{M_2}\] for all the \[3\] images will be $5cm,25cm,35cm$.
Hence, the correct option is C.

Note:
As the angle between the mirrors rises, the number of images created reduces. Light rays that travel along the normal trace their primary path after reflection. The several images created are reflections of objects in addition to reflections. Reflection can only happen on a smooth, shiny surface.