Question

An object ${}^{\prime }{\text{O}}^{\prime }$ is placed between two parallel mirrors $M_1$ and $M_2$ as shown in the figure. Find the distance between the $1^{st}$ image formed by $M_1$ and $3^{rd}$ image formed by $M_2$.

[Assume, the first reflection occurs at $M_1$].

• A. $90\text{cm}$
• B. $80\text{cm}$
• C. $100\text{cm}$
• D. $120\text{cm}$

Answer 1

The correct option is D $120\text{cm}$

We know, distance between object and plane mirror is the same as the distance between image and plane mirror.

Hence, 1st image formed by mirror-1 is $10\text{cm}$ behind mirror-1 i.e. $10+30=40\text{cm}$ from mirror-2 which will act as object for mirror-2.

And first image formed by mirror-2 is $20\text{cm}$ behind mirror-2 i.e $20+30=50\text{cm}$ from mirror-1 which will act as object for mirror-1.

So, 2nd image formed by mirror-2 will be $40\text{cm}$ behind mirror-2 and 2nd image formed by mirror-1 will be $50\text{cm}$ behind mirror-1.

2nd image formed by mirror-1 will be $50+30=80\text{cm}$ from mirror-2 and will act as object for mirror-2

Hence, 3rd image formed by mirror-2 will be $80\text{cm}$ behind mirror-2.

This is represented in the image below.


From the figure, we can deduce that first image formed by mirror-I is at $10\text{cm}$ from mirror-I.

and, third image formed by mirror-II is at $80\text{cm}$ from mirror-II.

Total seperation between first image due to mirror-I and third image due to mirror-II is:
$x=80+10+30=120\text{cm}$