Question

An object ${}^{\prime }{\text{O}}^{\prime }$ is placed between two parallel mirrors $M_1$ and $M_2$ as shown in the figure. Find distance between the $2^{nd}$ image formed by $M_1$ and $4^{th}$ image formed by $M_2$. The first reflection occurs at $M_1$.

• A. $200\text{cm}$
• B. $250\text{cm}$
• C. $170\text{cm}$
• D. $300\text{cm}$

Answer 1

The correct option is D $300\text{cm}$

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 $20\text{cm}$ behind mirror-1 i.e. $20+50=70\text{cm}$ from mirror-2 which will act as object for mirror-2.

And first image formed by mirror-2 is $30\text{cm}$ behind mirror-2 i.e $30+50=80\text{cm}$ from mirror-1 which will act as object for mirror-1.

So, 2nd image formed by mirror-2 will be $70\text{cm}$ behind mirror-2 and 2nd image formed by mirror-1 will be $80\text{cm}$ behind mirror-1.

Repeating this process, we can say that 3rd image formed by mirror-1 will be $120\text{cm}$ behind mirror-1 and 3rd image formed by mirror-2 will be $130\text{cm}$ behind mirror-1.

And, 4th image formed by mirror-2 will be $170\text{cm}$ behind mirror-2.

This is represented in the image below.


From the figure, we can deduce that, second image formed by mirror-I is at $80\text{cm}$ from mirror-I.

and, fourth image formed by mirror-II is at $170\text{cm}$ from mirror-II.

Therefore, total seperation between 2nd image due to mirror-I and 4th image due to mirror-II $\left(x\right)=170+80+50=300\text{cm}$