Question

A candle C sits between two parallel mirrors at a distance \( 0.2d \) from mirror 1. Here \( d \) denotes the distance between the mirrors. Multiple images of the candle appear in both mirrors. How far behind mirror 1 are the nearest three images of the candle in that mirror?

• A. 0.2d, 1.8d, 2.2d
• B. 0.2d, 2.2d, 4.2d
• C. 0.2d, 1.8d, 3.8d
• D. 0.2d, 0.8d, 1.4d

Hint:

For multiple reflections between parallel mirrors, the distance between successive images will depend on the object’s distance from the mirrors. The images will appear at regular intervals.

Answer 1

The Correct Option is A

In the case of two parallel mirrors, multiple images of an object (in this case, the candle) will appear in both mirrors.
The distance between the images of the candle depends on the distance between the two mirrors, denoted as \( d \).
The candle is placed \( 0.2d \) away from mirror 1, and the images will appear alternately on either side of the mirrors.
The positions of the images can be determined using the following formula for parallel mirrors: \[ \text{Position of Image} = (2n - 1) \times \text{distance between the candle and the mirror}. \] Hence, the positions of the nearest three images of the candle behind mirror 1 are: - \( 0.2d \) (first image) - \( 1.8d \) (second image) - \( 2.2d \) (third image) Thus, the nearest three images are at a distance of 0.2d, 1.8d, and 2.2d behind mirror 1.