Two vertical parallel mirrors A and B are separated by 10 cm. A point object O is placed at a distance of 2 cm from mirror A. The distance of the second nearest image behind mirror A from the mirror A is _________ cm.

Solution

Physics sir · 5 steps

The second image behind A comes from light that hits B first and then A.

1. Set up distances. Measure everything from mirror A. The object O is 2 cm in front of A, so it is 10 - 2 = 8 cm in front of B. A plane mirror always forms the image as far behind it as the object is in front.
2. Nearest image. Light from O reflects once in A. The image I₁ is 2 cm behind A. This is the nearest image behind A.
3. Reflect in B. Light from O first reflects in B. Its image I₂ is 8 cm behind B, so it is 10 + 8 = 18 cm from A. This image now acts as an object for mirror A.

   d = 10 + (10 - 2) = 18 cm

4. Reflect in A. I₂ is 18 cm in front of A, so A forms its image 18 cm behind A. The next image behind A follows the path A, then B, then A. It lands at 10 + (10 + 2) = 22 cm, which is farther away.
5. So. The images behind A sit at 2, 18, 22 cm and further out. The second nearest is 18 cm from mirror A.

The common slip: 22. Following the path A, then B, then A gives 22. That image is the third one behind A, not the second.

The idea to keep. With two parallel mirrors, follow each chain of reflections and use the previous image as the new object. Measure its distance from the mirror that does the reflecting, then list the images in order.

Answer from the NTA final answer key. Solution by PrepWiser.