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Question

An object O is placed between two parallel mirrors M1 and M2 as shown in the figure. Find the distance between the 1st image formed by M1 and 3rd image formed by M2.

[Assume, the first reflection occurs at M1].


A
90 cm
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B
80 cm
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C
100 cm
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D
120 cm
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Solution

The correct option is D 120 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 10 cm behind mirror-1 i.e. 10+30=40 cm from mirror-2 which will act as object for mirror-2.

And first image formed by mirror-2 is 20 cm behind mirror-2 i.e 20+30=50 cm from mirror-1 which will act as object for mirror-1.

So, 2nd image formed by mirror-2 will be 40 cm behind mirror-2 and 2nd image formed by mirror-1 will be 50 cm behind mirror-1.

2nd image formed by mirror-1 will be 50+30=80 cm from mirror-2 and will act as object for mirror-2

Hence, 3rd image formed by mirror-2 will be 80 cm behind mirror-2.

This is represented in the image below.


From the figure, we can deduce that first image formed by mirror-I is at 10 cm from mirror-I.

and, third image formed by mirror-II is at 80 cm from mirror-II.

Total seperation between first image due to mirror-I and third image due to mirror-II is:
x=80+10+30=120 cm

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