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Question

# An object ′O′ is placed between two parallel mirrors M1 and M2 as shown in the figure. Find distance between the 2nd image formed by M1 and 4th image formed by M2. The first reflection occurs at M1.

A
200 cm
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B
250 cm
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C
170 cm
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D
300 cm
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Solution

## The correct option is D 300 cmWe 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 cm behind mirror-1 i.e. 20+50=70 cm from mirror-2 which will act as object for mirror-2. And first image formed by mirror-2 is 30 cm behind mirror-2 i.e 30+50=80 cm from mirror-1 which will act as object for mirror-1. So, 2nd image formed by mirror-2 will be 70 cm behind mirror-2 and 2nd image formed by mirror-1 will be 80 cm behind mirror-1. Repeating this process, we can say that 3rd image formed by mirror-1 will be 120 cm behind mirror-1 and 3rd image formed by mirror-2 will be 130 cm behind mirror-1. And, 4th image formed by mirror-2 will be 170 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 cm from mirror-I. and, fourth image formed by mirror-II is at 170 cm from mirror-II. Therefore, total seperation between 2nd image due to mirror-I and 4th image due to mirror-II (x)=170+80+50=300 cm

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