JEE Physics 2023 Question with Solution

Given: Two vertical parallel mirrors A and B are separated by $10 \, \text{cm}$. The object O is at a distance of $2 \, \text{cm}$ from mirror A.

Find: The distance of the second nearest image behind mirror A from mirror A.

For multiple reflections between two plane mirrors, images are formed alternately behind the two mirrors.

The first image behind mirror A is formed at the same distance as the object is in front of it:

The object is $10 - 2 = 8 \, \text{cm}$ in front of mirror B, so the first image behind mirror B is at

behind B.

This image behind B acts as an object for mirror A. Its distance from mirror A is

So, the second nearest image behind mirror A is at $18 \, \text{cm}$ from mirror A.

Therefore, the required answer is $18$.

Given: Mirror separation is $10 \, \text{cm}$ and the object is $2 \, \text{cm}$ from mirror A.

Find: The second nearest image behind mirror A.

Track the images in order near mirror A:

1. First image behind A is at $2 \, \text{cm}$.
2. First image behind B is formed from the same object. Since the object is $8 \, \text{cm}$ from B, that image is $8 \, \text{cm}$ behind B.
3. Measured from mirror A, that position is

This becomes the next image behind A in the sequence of multiple reflections.

Hence, the nearest image behind A is at $2 \, \text{cm}$ and the second nearest image behind A is at $18 \, \text{cm}$.

Therefore, the answer is $18$.